Glossary¶
A reference for the terminology used across the QuantumEd curriculum. It answers one question, "What does this term mean?", and points you to the learning modules when you want to know how a concept works and why it matters.
Each entry has:
- a definition: a concise, technically accurate statement of the term;
- a beginner interpretation: the same idea in plainer language, meant to build intuition, not replace the definition;
- related terms: neighboring concepts worth reading next; and
- appears in: the lessons where the term is taught or used (this list grows as modules are added).
Abbreviations and alternate names are listed on the entry they belong to, so searching for "QEC" finds Quantum Error Correction. A few entries describe active research areas; those are worded to avoid implying that any one approach is standard.
155 terms
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Quantum Foundations¶
Fundamental concepts describing quantum information and quantum mechanics as used in quantum computing.
Basis State¶
Definition One of a set of mutually orthogonal states that can be used to express any other state of the system as a superposition.
Beginner interpretation Basis states are the reference states that every other state is described in terms of, much as east and north are the reference directions for describing any position on a map.
Appears in Quantum Computing Fundamentals → Quantum States · Quantum Computing Fundamentals → Qubit Representation
Bell State¶
Also known as Bell Pair
Definition One of four maximally entangled states of two qubits, such as (|00⟩ + |11⟩)/√2. Each qubit alone is equally likely to give 0 or 1, but the two outcomes are perfectly correlated: they always agree, or always differ.
Beginner interpretation A Bell state is the standard example of two entangled qubits. Each qubit alone looks like a coin flip, but the pair's results always match (or always differ), and no pair of independent qubits can do that.
Appears in Quantum Computing Fundamentals → Multi-Qubit Systems · Quantum Computing Fundamentals → Measurement
Bloch Sphere¶
Definition A geometric representation of the state of a single qubit as a point on a sphere (inside it, for mixed states), with |0⟩ and |1⟩ at opposite poles and relative phase appearing as the angle around the vertical axis.
Beginner interpretation The Bloch sphere is a globe-like picture of one qubit: the poles are 0 and 1, and every other spot is a different blend. It only works for a single qubit.
Appears in Foundations → What Is Quantum Computing? · Quantum Error Correction → Errors and Noise · Quantum Computing Fundamentals → Bloch Sphere
Bra-Ket Notation¶
Also known as Dirac notation
Definition Notation in which a state vector is written as a ket |ψ⟩ and its conjugate transpose as a bra ⟨ψ|; the inner product of two states is written ⟨φ|ψ⟩.
Beginner interpretation Bra-ket notation is shorthand for writing quantum states: |ψ⟩ names a state, and expressions like ⟨φ|ψ⟩ describe how much two states overlap.
Appears in Quantum Computing Fundamentals → Qubit Representation
Computational Basis¶
Also known as Z basis
Definition The standard basis for a register of qubits, made of the states |0⟩ and |1⟩ for each qubit and their products for several qubits. Measurements are described in this basis unless stated otherwise.
Beginner interpretation The computational basis is the set of 'plain' states, all 0s and 1s, that qubits are normally read out in.
Appears in Quantum Error Correction → Errors and Noise · Quantum Error Correction → Repetition Codes · Quantum Computing Fundamentals → Measurement
Density Matrix¶
Also known as Density operator
Definition A matrix that describes a quantum state, covering both pure and mixed states; its diagonal entries give the probabilities of the basis states.
Beginner interpretation A density matrix is a table of numbers that describes a quantum state, including states that are partly random or noisy.
Entanglement¶
Definition A property of a multi-qubit quantum state that cannot be written as a product of separate states for the individual qubits, so the qubits must be described together.
Beginner interpretation Entangled qubits are linked: you can't fully describe one without the other, and measuring them gives correlated results.
Appears in Foundations → What Is Quantum Computing? · Quantum Computing Fundamentals → Multi-Qubit Systems · Quantum Computing Fundamentals → Measurement
Global Phase¶
Also known as Overall Phase
Definition A phase factor that multiplies every amplitude of a state by the same complex number of magnitude 1. It has no effect on any measurement probability, so two states that differ only by a global phase describe the same physical state.
Beginner interpretation A global phase is a shared twist applied to the whole state at once. It changes nothing you can ever observe, unlike a relative phase, which does.
Appears in Quantum Computing Fundamentals → Qubit Representation · Quantum Computing Fundamentals → Bloch Sphere
Hilbert Space¶
Definition The complex vector space, equipped with an inner product, in which the pure states of a quantum system are described. A register of n qubits has a Hilbert space of dimension 2^n.
Beginner interpretation The Hilbert space is the mathematical arena containing every state a quantum system could be in. Each added qubit doubles its size.
Inner Product¶
Definition A way of combining two states into a single number: multiply the complex conjugate of each amplitude of the first state by the matching amplitude of the second, and add the results. The inner product of a normalized state with itself is 1, and the inner product of two orthogonal states is 0.
Beginner interpretation The inner product is a single number that compares two states. A normalized state compared with itself gives 1, and two states that are completely different in this sense give 0.
Appears in Quantum Computing Fundamentals → Qubit Representation
Measurement¶
Definition The process of extracting classical information from a quantum system. A measurement returns one of its possible outcomes with probabilities set by the state and, in general, changes the state of the system.
Beginner interpretation Measurement is how you read out a qubit. You get a definite 0 or 1, and the act of reading it generally disturbs the quantum state.
Appears in Foundations → What Is Quantum Computing? · Quantum Error Correction → Errors and Noise · Quantum Error Correction → Encoding & Syndrome Measurement · Quantum Computing Fundamentals → Quantum States · Quantum Computing Fundamentals → Measurement
Mixed State¶
Definition A statistical mixture of pure states, representing uncertainty about which pure state the system is in; it is described by a density matrix rather than a single state vector.
Beginner interpretation A mixed state is what you have when you are unsure which quantum state a system is in, for example after noise has acted on it.
No-Cloning Theorem¶
Definition The result that no physical operation can make an identical, independent copy of an arbitrary unknown quantum state.
Beginner interpretation You can't photocopy an unknown qubit. This is one reason quantum error correction can't simply store backup copies.
Appears in Quantum Error Correction → Why QEC? · Quantum Error Correction → Physical vs Logical Qubits · Quantum Error Correction → Repetition Codes
Normalization¶
Definition The requirement that the squared magnitudes of a state's amplitudes add up to 1, so that the probabilities of all measurement outcomes add up to 100%. A state whose amplitudes do not satisfy it is rescaled, or normalized, before it is used.
Beginner interpretation Normalization is the rule that the probabilities of all the possible results must add up to 100%. A valid qubit state always follows it.
Appears in Quantum Computing Fundamentals → Qubit Representation
Orthogonal States¶
Definition Two states whose inner product is zero. A suitable measurement can in principle tell orthogonal states apart with certainty. On the Bloch sphere, orthogonal states are opposite points.
Beginner interpretation Orthogonal states are as different as two states can be: a suitable measurement can always tell them apart. |0⟩ and |1⟩ are an example.
Appears in Quantum Computing Fundamentals → Qubit Representation · Quantum Computing Fundamentals → Bloch Sphere
Phase¶
Definition The angle of the complex number that multiplies a basis state's probability amplitude. A phase shared by the whole state cannot be observed, but phase differences between components affect how they interfere.
Beginner interpretation Phase is like a hidden dial on each part of a quantum state. A single 0-or-1 readout can't show it, but it controls how the parts combine in later steps.
Appears in Foundations → What Is Quantum Computing? · Quantum Error Correction → Errors and Noise · Quantum Computing Fundamentals → Qubit Representation · Quantum Computing Fundamentals → Bloch Sphere
Probability Amplitude¶
Also known as Amplitude
Definition A complex number associated with each basis state in a quantum state; the squared magnitude of an amplitude gives the probability of measuring that basis state.
Beginner interpretation Amplitudes are the numbers that, once squared in size, give the chances of each measurement result. Unlike probabilities they can be negative or complex, which lets different contributions cancel or reinforce each other.
Appears in Quantum Computing Fundamentals → Qubit Representation
Pure State¶
Definition A quantum state described by a single state vector, representing complete knowledge of the system's quantum state, as opposed to a statistical mixture of states.
Beginner interpretation A pure state is a fully specified quantum state, with no leftover uncertainty about which state the system is in.
Quantum State¶
Definition A complete mathematical description of a quantum system, from which the probabilities of every possible measurement outcome can be calculated. It is written as a state vector (a ket) or, more generally, as a density matrix.
Beginner interpretation The quantum state is everything you would need to know about a quantum system to predict the odds of each result if you measured it.
Appears in Quantum Computing Fundamentals → Quantum States · Quantum Computing Fundamentals → Qubit Representation
Qubit¶
Also known as Quantum bit
Definition The basic unit of quantum information: a two-level quantum system whose state can be a superposition of its two basis states, usually written |0⟩ and |1⟩.
Beginner interpretation A qubit is the quantum counterpart of a bit. Instead of holding just a 0 or a 1, it can be prepared in a blend of both, and measuring it gives a single 0 or 1.
Appears in Foundations → What Is Quantum Computing? · Quantum Error Correction → Physical vs Logical Qubits
Relative Phase¶
Definition The phase difference between the amplitudes of two basis states in a superposition. Unlike a shared global phase, relative phase is physically meaningful: it distinguishes states such as |+⟩ and |−⟩ and determines how the state interferes in later operations.
Beginner interpretation Relative phase is how out of step two parts of a superposition are. A plain 0-or-1 readout can't see it, but it changes what later operations do.
Appears in Quantum Error Correction → Errors and Noise · Quantum Computing Fundamentals → Qubit Representation
State Preparation¶
Definition The process of putting a quantum system into a chosen starting state, for example by resetting qubits to |0⟩ and then applying operations. Preparing a system the same way again aims to produce the same state, although a single measurement of that state can still give different outcomes.
Beginner interpretation State preparation is the recipe that sets up the state you start with. The same recipe gives the same state, even though one measurement of it may give a different result each time.
Superposition¶
Definition A quantum state expressed as a combination of two or more basis states, each with an associated probability amplitude.
Beginner interpretation Superposition means a qubit can be in a blend of 0 and 1, and the makeup of the blend sets the odds of each result when it is measured. It is not the same as secretly being 0 or 1 and simply not knowing which.
Appears in Foundations → What Is Quantum Computing? · Quantum Computing Fundamentals → Quantum States
Gates & Circuits¶
Operations, gates, circuit concepts, and computational primitives.
Ancilla Qubit¶
Also known as Ancilla, Helper qubit
Definition An auxiliary qubit used to assist a computation or measurement, for example to extract information from other qubits, and usually not part of the computation's input or output.
Beginner interpretation An ancilla is a helper qubit. It is brought in to carry out a task, such as collecting clues about errors, and isn't where the main information is kept.
Appears in Quantum Error Correction → Encoding & Syndrome Measurement · Quantum Error Correction → Stabilizer Codes · Quantum Error Correction → Surface Codes
Circuit Depth¶
Definition The number of sequential layers of gates in a circuit, where gates acting on different qubits at the same time share a layer; it is a measure of how long the computation takes to run.
Beginner interpretation Circuit depth is how many steps deep a circuit is. Deeper circuits give errors more time and more opportunities to accumulate.
CNOT Gate¶
Also known as CNOT, CX, Controlled-NOT
Definition A two-qubit controlled gate that flips the target qubit (applies X to it) when the control qubit is |1⟩.
Beginner interpretation CNOT flips one qubit only if another is 1. It is the standard way to link qubits and to build entanglement.
Appears in Quantum Error Correction → Encoding & Syndrome Measurement · Quantum Error Correction → Stabilizer Codes · Quantum Error Correction → Lattice Surgery · Quantum Computing Fundamentals → Multi-Qubit Systems · Quantum Computing Fundamentals → Quantum Circuits
Controlled Gate¶
Definition A gate that applies an operation to a target qubit depending on the state of a control qubit: the operation is applied when the control is |1⟩. For a control in superposition, the gate acts on each component accordingly.
Beginner interpretation A controlled gate says 'do this to one qubit only if another qubit is 1'. When the control is in a superposition, this can link the qubits together.
Appears in Quantum Computing Fundamentals → Multi-Qubit Systems
Hadamard Gate¶
Also known as H gate
Definition A single-qubit gate that maps |0⟩ and |1⟩ to the equal superpositions |+⟩ and |−⟩ and back again; it converts between the computational basis and the X basis.
Beginner interpretation The Hadamard gate turns a definite 0 or 1 into an even blend of both, which is the usual way to start building a superposition.
Appears in Quantum Computing Fundamentals → Quantum Gates · Quantum Computing Fundamentals → Quantum Circuits
Identity Gate¶
Also known as I gate
Definition The gate, written I, that leaves a qubit's state unchanged. In hardware it can represent a deliberate idle period during which the qubit is still exposed to noise.
Beginner interpretation The identity gate does nothing. It stands for 'wait one step', which still matters because real qubits can pick up errors while waiting.
Mid-Circuit Measurement¶
Definition A measurement performed on some qubits partway through a circuit, rather than only at the end, with the computation continuing afterward and sometimes depending on the result.
Beginner interpretation A mid-circuit measurement is a readout taken while the program is still running. It is needed, for example, to check for errors as a computation proceeds.
Multi-Qubit Gate¶
Definition A gate acting on two or more qubits at once; the most common case is the two-qubit gate. Multi-qubit gates can create entanglement and are typically harder to implement accurately than single-qubit gates.
Beginner interpretation A multi-qubit gate acts on several qubits together. These are what let qubits interact, and on real hardware they are usually the noisiest operations.
Pauli-X Gate¶
Also known as X gate, NOT gate, Bit-flip gate
Definition A single-qubit gate that swaps |0⟩ and |1⟩, the quantum analogue of a classical NOT; it corresponds to a rotation by π about the x-axis of the Bloch sphere.
Beginner interpretation The X gate turns a 0 into a 1 and a 1 into a 0, like flipping a bit.
Appears in Quantum Error Correction → Errors and Noise · Quantum Computing Fundamentals → Quantum Gates · Quantum Computing Fundamentals → Quantum Circuits
Pauli-Y Gate¶
Also known as Y gate
Definition A single-qubit gate that performs a bit flip and a phase flip together, up to an overall phase; it corresponds to a rotation by π about the y-axis of the Bloch sphere.
Beginner interpretation The Y gate flips a qubit the way X does and also flips its phase.
Appears in Quantum Error Correction → Errors and Noise · Quantum Computing Fundamentals → Quantum Gates
Pauli-Z Gate¶
Also known as Z gate, Phase-flip gate
Definition A single-qubit gate that leaves |0⟩ unchanged and multiplies |1⟩ by −1; it flips the relative phase of a superposition and corresponds to a rotation by π about the z-axis of the Bloch sphere.
Beginner interpretation The Z gate doesn't change whether a qubit reads 0 or 1, but it flips the phase of the 1 part, something that only shows up through later interference.
Appears in Quantum Error Correction → Errors and Noise · Quantum Computing Fundamentals → Quantum Gates · Quantum Computing Fundamentals → Quantum Circuits
Phase Gate¶
Definition A single-qubit gate that applies a phase to the |1⟩ state while leaving |0⟩ unchanged. Common examples are the S gate (a quarter turn) and the T gate (an eighth turn).
Beginner interpretation Phase gates adjust the phase of the 1 part of a qubit by a chosen angle without changing the odds of reading 0 or 1.
Quantum Circuit¶
Definition A sequence of quantum gates, and usually measurements, applied to qubits in a specified order to carry out a computation.
Beginner interpretation A quantum circuit is a program drawn as a diagram: qubits run along lines, and gates and measurements are placed along them in time order.
Appears in Quantum Algorithms & Methods → Variational Quantum Eigensolver (VQE) · Quantum Error Correction → Encoding & Syndrome Measurement · Quantum Computing Fundamentals → Quantum Circuits
Quantum Gate¶
Definition A basic operation that changes the state of one or more qubits. In the standard circuit model, gates are unitary operations.
Beginner interpretation A quantum gate is a step that transforms qubits. It is the quantum counterpart of a logic gate, but always reversible.
Appears in Quantum Algorithms & Methods → Variational Quantum Eigensolver (VQE) · Quantum Error Correction → Encoding & Syndrome Measurement · Quantum Computing Fundamentals → Quantum Gates
Reset¶
Also known as Qubit reset
Definition An operation that returns a qubit to a known initial state, usually |0⟩. It is used to initialize qubits and to reuse them during a computation.
Beginner interpretation Reset puts a qubit back to a known starting state, usually 0, so it can be used again.
Rotation Gate¶
Definition A single-qubit gate that rotates the qubit's state about the x-, y-, or z-axis of the Bloch sphere by an adjustable angle, written RX(θ), RY(θ), or RZ(θ).
Beginner interpretation A rotation gate turns a qubit by an angle you choose, like adjusting a dial. It is useful when an algorithm needs adjustable settings.
Appears in Quantum Algorithms & Methods → Variational Quantum Eigensolver (VQE) · Quantum Computing Fundamentals → Quantum Gates
SWAP Gate¶
Definition A two-qubit gate that exchanges the states of two qubits.
Beginner interpretation A SWAP gate trades the contents of two qubits. It is often used to move data between qubits that aren't directly connected.
Unitary Operation¶
Also known as Unitary
Definition A reversible, norm-preserving linear transformation of a quantum state; the mathematical form of an ideal quantum gate acting on a closed system.
Beginner interpretation A unitary operation is a reversible change to a quantum state that neither loses nor creates probability, so it could always be run backward.
Hardware & Physical Systems¶
Physical implementations of quantum computers and concepts describing qubit hardware.
Calibration¶
Definition The process of measuring a quantum device's characteristics and adjusting its control parameters so that gates and measurements behave as intended.
Beginner interpretation Calibration is tuning a quantum computer: testing how its qubits respond and adjusting the settings so operations work as intended.
Appears in Quantum Error Correction → Hardware-Aware QEC · Quantum Software Stack → Understanding the Quantum Software Stack
Coherence¶
Also known as Quantum coherence
Definition The property of a quantum system keeping well-defined phase relationships between the components of a superposition, which interference and other quantum behavior depend on.
Beginner interpretation Coherence means a qubit is still behaving in a quantum way, with its blend of 0 and 1 and its phase intact. Noise gradually destroys it.
Coherence Time¶
Definition A characteristic duration over which a qubit retains its quantum coherence, commonly quantified by the times T1 and T2.
Beginner interpretation Coherence time is roughly how long a qubit stays quantum before noise scrambles it. Longer is better, but it is only one of several measures of qubit quality.
Connectivity¶
Also known as Qubit connectivity
Definition Which pairs of qubits in a device can interact directly through a native two-qubit operation, often described as a connectivity graph.
Beginner interpretation Connectivity is the map of which qubits can work together directly. Qubits that aren't directly linked need extra steps to interact.
Coupling¶
Definition A physical interaction between two qubits, used to implement entangling operations and to define which qubit pairs are connected. Unintended residual coupling is one source of crosstalk.
Beginner interpretation Coupling is the physical link that lets two qubits influence each other.
Crosstalk¶
Definition Unintended interaction in which an operation or measurement on one qubit affects other qubits.
Beginner interpretation Crosstalk is when something done to one qubit accidentally disturbs its neighbors.
Decoherence¶
Definition The loss of coherence of a quantum system through its interaction with its environment, which causes quantum superpositions to degrade toward classical mixtures.
Beginner interpretation Decoherence is what happens when a qubit's surroundings interact with it and its delicate quantum behavior fades away.
Appears in Quantum Error Correction → Why QEC?
Gate Fidelity¶
Definition A measure of how closely an implemented gate matches its ideal operation, where a value of 1 (100%) means a perfect match. Its estimated value depends on the characterization method used.
Beginner interpretation Gate fidelity is a score for how accurately a gate does what it is supposed to. Closer to 100% is better, and the number depends on how it was measured.
Logical Qubit¶
Definition A qubit of quantum information encoded across multiple physical qubits by a quantum error-correcting code, so that errors on the individual physical qubits can be detected and corrected.
Beginner interpretation A logical qubit is protected quantum information spread over many physical qubits, so a single hardware hiccup doesn't destroy it. It is a pattern across qubits rather than a single physical object.
Appears in Quantum Error Correction → Why QEC? · Quantum Error Correction → Physical vs Logical Qubits · Quantum Error Correction → Repetition Codes · Quantum Error Correction → Lattice Surgery
Neutral-Atom Qubit¶
Definition A physical qubit encoded in internal states of an uncharged atom, commonly held in arrays by tightly focused laser beams known as optical tweezers.
Beginner interpretation Neutral-atom qubits are individual atoms held in place by laser light and arranged in patterns, with information stored in their energy levels.
Photonic Qubit¶
Definition A qubit encoded in a degree of freedom of a photon, such as its polarization or the path it takes.
Beginner interpretation Photonic qubits store information in particles of light, for example in the direction their light wave is polarized.
Physical Qubit¶
Definition An individual physical quantum system used by hardware as a qubit, such as a superconducting circuit, a trapped ion, or a neutral atom.
Beginner interpretation A physical qubit is a real hardware object that behaves as a qubit. It is imperfect, which is why error correction combines many of them.
Appears in Quantum Error Correction → Why QEC? · Quantum Error Correction → Physical vs Logical Qubits · Quantum Error Correction → Hardware-Aware QEC
Quantum Processing Unit¶
Also known as QPU, Quantum processor
Definition The quantum hardware that executes quantum circuits, consisting of physical qubits together with the means to control and read them out.
Beginner interpretation The QPU is the quantum computer's processor: the chip, or the arrangement of atoms or ions, where qubits live and quantum operations actually happen.
Readout Fidelity¶
Also known as Measurement fidelity
Definition A measure of how reliably a qubit measurement reports the state the qubit was actually in; the complement of readout error.
Beginner interpretation Readout fidelity says how often reading a qubit gives the right answer. Low fidelity means the measurement itself often gets it wrong.
Spin Qubit¶
Definition A physical qubit encoded in the spin of an electron or nucleus, for example in a semiconductor quantum dot or an atomic defect in a crystal.
Beginner interpretation Spin qubits store information in spin, an intrinsic quantum property of electrons and nuclei that can point 'up' or 'down'.
Superconducting Qubit¶
Definition A physical qubit implemented as a superconducting electrical circuit operated at very low temperatures, with the two qubit states encoded in the circuit's quantized energy levels.
Beginner interpretation Superconducting qubits are tiny electrical circuits, cooled to extremely low temperatures, that behave like artificial atoms.
T1 Relaxation Time¶
Also known as T1, Energy relaxation time
Definition The characteristic time over which a qubit in its excited state relaxes toward its lower-energy ground state by exchanging energy with its environment.
Beginner interpretation T1 is a time scale for how long it takes an excited qubit to lose energy and drop back to its resting state.
T2 Dephasing Time¶
Also known as T2, Phase coherence time
Definition The characteristic time over which a qubit's phase coherence is lost under the relevant measurement protocol; it reflects both energy relaxation and pure dephasing.
Beginner interpretation T2 is a time scale for how long a qubit keeps its phase, the delicate timing information in a superposition, before it is lost.
Transmon¶
Definition A widely used type of superconducting qubit, built from a Josephson junction shunted by a large capacitor, designed to be less sensitive to charge noise.
Beginner interpretation The transmon is a popular kind of superconducting qubit, designed to be steadier against certain electrical disturbances.
Trapped-Ion Qubit¶
Definition A physical qubit encoded in internal energy levels of an individual ion held in place by electromagnetic fields and manipulated with lasers or microwaves.
Beginner interpretation Trapped-ion qubits are individual charged atoms held in place by electric fields, with information stored in their energy levels.
Noise & Errors¶
Physical and computational error mechanisms affecting quantum information.
Amplitude Damping¶
Definition A noise process in which a qubit loses energy to its environment, causing decay from the excited state toward the ground state; it is the process behind T1 relaxation.
Beginner interpretation Amplitude damping is a qubit gradually losing energy and sliding from its higher-energy state down to its resting state.
Bit-Flip Error¶
Also known as X error
Definition An error that swaps the computational-basis states |0⟩ and |1⟩, described by the Pauli X operator.
Beginner interpretation A bit flip changes a 0 into a 1 or a 1 into a 0, like flipping a classical bit.
Appears in Quantum Error Correction → Errors and Noise · Quantum Error Correction → Repetition Codes · Quantum Error Correction → Physical vs Logical Qubits · Quantum Error Correction → Encoding & Syndrome Measurement · Quantum Error Correction → Decoding
Correlated Error¶
Definition Errors that affect multiple qubits or multiple time steps in a statistically dependent way, rather than occurring independently.
Beginner interpretation Correlated errors tend to happen together instead of separately, which can be harder on error-correction methods that assume errors are independent.
Dephasing¶
Definition A noise process that randomizes the relative phase between a qubit's basis states without changing the probabilities of measuring them, which degrades superpositions.
Beginner interpretation Dephasing blurs a qubit's phase: it still reads 0 or 1 with the same odds, but the superposition's delicate timing is scrambled.
Depolarizing Noise¶
Also known as Depolarizing channel
Definition A noise model in which, with some probability, a qubit suffers a random Pauli error (X, Y, or Z with equal likelihood). It is commonly used as a simple, symmetric model of noise.
Beginner interpretation Depolarizing noise is a simple model where errors strike at random and each of the three basic error types is equally likely.
Erasure¶
Also known as Erasure error
Definition An error whose location is known, such as a qubit flagged as lost or corrupted, as opposed to an error whose location must be inferred from a syndrome.
Beginner interpretation An erasure is an error you know about: you are told which qubit was lost or damaged, which makes it easier to handle than an error at an unknown location.
Error Channel¶
Also known as Noise channel, Quantum channel
Definition A mathematical description of how noise transforms a quantum state, usually written as a set of operations that occur with given probabilities.
Beginner interpretation An error channel is a precise description of what a particular kind of noise does to a qubit and how often.
Error Rate¶
Definition The probability, or an estimate of the probability, that a particular operation, qubit, or measurement results in an error. Its value depends on how an error is defined and measured.
Beginner interpretation Error rate is how often something goes wrong, for example the chance that a gate gives the wrong result.
Appears in Quantum Error Correction → Decoding
Leakage¶
Definition An error in which a qubit leaves its two computational states and enters another energy level of the physical system.
Beginner interpretation Leakage is when a qubit escapes the 0 and 1 it is supposed to live in and ends up in some other state the hardware happens to have.
Noise Model¶
Also known as Error model
Definition A set of assumptions describing which errors occur, on which qubits, operations, and measurements, and with what probabilities. It is used for simulation, analysis, and decoding.
Beginner interpretation A noise model is a written-down guess about how a device goes wrong: which errors happen, where, and how often.
Appears in Quantum Error Correction → Decoding · Quantum Error Correction → Minimum-Weight Perfect Matching · Quantum Error Correction → Hardware-Aware QEC
Pauli Error¶
Definition An error described by one of the Pauli operators X, Y, or Z (or the identity, meaning no error) applied to one or more qubits. Any single-qubit error can be written as a combination of Pauli operators.
Beginner interpretation Pauli errors are the three basic kinds of single-qubit error: bit flip (X), phase flip (Z), and both at once (Y). More complicated errors can be understood as combinations of them.
Appears in Quantum Error Correction → Errors and Noise · Quantum Error Correction → Stabilizer Codes
Phase-Flip Error¶
Also known as Z error
Definition An error that changes the relative phase between |0⟩ and |1⟩ by mapping |1⟩ to −|1⟩, described by the Pauli Z operator.
Beginner interpretation A phase flip doesn't change whether a qubit reads 0 or 1, but it flips the sign of the 1 part of a superposition, which changes how the qubit behaves later.
Appears in Quantum Error Correction → Errors and Noise · Quantum Error Correction → Repetition Codes
Quantum Error¶
Definition A deviation of a quantum state or operation from its intended behavior, typically caused by noise, that changes the encoded information.
Beginner interpretation A quantum error is the actual damage noise does to the information in a qubit.
Appears in Quantum Error Correction → Errors and Noise
Quantum Noise¶
Also known as Noise
Definition Unwanted physical processes, such as interaction with the environment and imperfect control, that cause a qubit's actual behavior to deviate from the ideal.
Beginner interpretation Noise is anything physical that disturbs a qubit from doing exactly what it should.
Appears in Quantum Error Correction → Why QEC? · Quantum Error Correction → Errors and Noise
Readout Error¶
Also known as Measurement error
Definition An error in the measurement process in which the reported outcome differs from the qubit's actual state at the time of measurement.
Beginner interpretation A readout error is when reading a qubit gives the wrong answer even though the qubit itself was fine.
Quantum Error Correction & Fault Tolerance¶
Concepts associated with detecting, correcting, decoding, and tolerating quantum errors.
Ancilla-Assisted Measurement¶
Definition A measurement technique in which information about a property of the data qubits is transferred to an ancilla qubit, and the ancilla is measured instead of measuring the data qubits directly.
Beginner interpretation Instead of looking at the important qubits, you let a helper qubit pick up the answer and then measure the helper.
Appears in Quantum Error Correction → Encoding & Syndrome Measurement · Quantum Error Correction → Stabilizer Codes
Code Deformation¶
Definition A technique in which a code's stabilizers or geometry are changed over time, for example by growing, shrinking, merging, or moving encoded regions, while the information stays encoded.
Beginner interpretation Code deformation reshapes a code's checks step by step so that a protected qubit can be moved, enlarged, or combined with another without leaving the code.
Code Distance¶
Definition The minimum number of physical-qubit errors that can change the encoded logical information without being detected, equal to the weight of the smallest nontrivial logical operator. It determines how many errors a code can correct.
Beginner interpretation Code distance measures how hard it is to fool the code: the larger it is, the more errors it takes to corrupt the information without anyone noticing.
Appears in Quantum Error Correction → Repetition Codes · Quantum Error Correction → Surface Codes
Decoder¶
Definition A classical algorithm or system that takes syndrome information, and often a noise model, and infers a recovery operation intended to preserve the logical information.
Beginner interpretation A decoder is the detective of error correction: it reads the clues from the syndrome and decides what correction to apply.
Appears in Quantum Error Correction → Decoding · Quantum Error Correction → Minimum-Weight Perfect Matching · Quantum Error Correction → Surface Codes · Quantum Error Correction → Hardware-Aware QEC
Decoding¶
Definition The process of inferring, from a syndrome, which recovery operation to apply to the encoded qubits.
Beginner interpretation Decoding is the step of turning error clues into a decision about how to fix the qubits.
Appears in Quantum Error Correction → Decoding · Quantum Error Correction → Minimum-Weight Perfect Matching · Quantum Error Correction → Surface Codes
Error-Correction Threshold¶
Also known as Threshold
Definition The physical error rate below which, for a given code family, noise model, and decoder, increasing the size of the code reduces the logical error rate. Above it, adding qubits stops helping.
Beginner interpretation The threshold is a tipping point: if the hardware's errors are rarer than it, bigger codes get better, and if they are more common, bigger codes stop helping.
Fault Tolerance¶
Definition A property of a computation or protocol designed so that failures of individual components, including those in the error-correction procedure itself, do not cause uncontrolled errors in the result.
Beginner interpretation Fault tolerance means designing the whole computation so that small failures, even in the error correction itself, don't snowball into a wrong answer.
Fault-Tolerant Quantum Computing¶
Also known as FTQC
Definition Quantum computation carried out with quantum error correction and fault-tolerant operations so that long computations can be run reliably, provided the physical error rates are low enough.
Beginner interpretation FTQC is the goal of running long quantum programs reliably by protecting the information at every step.
Lattice Surgery¶
Definition A technique for performing operations between logical qubits encoded in surface-code patches by temporarily merging and splitting the patches, which measures joint logical information through changes to the stabilizer checks along their shared boundary.
Beginner interpretation Lattice surgery lets protected qubits interact by temporarily changing which checks are measured where two patches meet, instead of taking the information out of the code.
Appears in Quantum Error Correction → Lattice Surgery
Logical Error¶
Also known as Logical failure
Definition A failure in which the encoded logical information is changed, for example when physical errors combine with the decoder's recovery to apply a logical operator.
Beginner interpretation A logical error is when the protected information itself gets corrupted. It can still happen while error correction is running, if too many errors pile up or the decoder guesses wrong.
Appears in Quantum Error Correction → Why QEC? · Quantum Error Correction → Decoding · Quantum Error Correction → Surface Codes · Quantum Error Correction → Minimum-Weight Perfect Matching
Logical Error Rate¶
Definition The probability that the encoded logical information is corrupted over a given operation or time interval; it is the quantity quantum error correction aims to push below the underlying physical error rates.
Beginner interpretation The logical error rate is how often the protected information fails. Error correction aims to make this smaller than how often the raw qubits fail, as long as the hardware is good enough.
Logical Operator¶
Definition An operator acting on the encoded qubits that changes the logical information (for example a logical X or logical Z) while keeping the state within the code space. Undetected errors that happen to implement a logical operator cause logical errors.
Beginner interpretation A logical operator is an action on the protected information itself, such as flipping the logical qubit. Errors that look exactly like one slip past the checks.
Appears in Quantum Error Correction → Stabilizer Codes · Quantum Error Correction → Decoding
Magic State¶
Definition A specially prepared quantum state used as a resource to implement gates outside a code's easily protected set, such as the T gate, within fault-tolerant schemes.
Beginner interpretation Magic states are specially prepared ingredient states that let an error-corrected computer perform a kind of gate it can't do directly.
Magic-State Distillation¶
Definition A procedure that uses many imperfectly prepared magic states, together with error-corrected operations, to produce fewer magic states of higher fidelity.
Beginner interpretation Distillation is a kind of refining: it takes many rough magic states and turns them into fewer, better ones.
Minimum-Weight Perfect Matching¶
Also known as MWPM
Definition A decoding technique that pairs up the detection events in a syndrome so that the total weight, or cost, of the pairing is as small as possible. It is widely used as a decoder for surface codes.
Beginner interpretation MWPM links the failed checks in pairs, using the cheapest overall pairing as its best guess for where the errors were.
Appears in Quantum Error Correction → Minimum-Weight Perfect Matching · Quantum Error Correction → Decoding · Quantum Error Correction → Hardware-Aware QEC
Quantum Error Correction¶
Also known as QEC
Definition A family of techniques that protect quantum information by encoding it across many physical qubits and using measurements that reveal information about errors without directly measuring the encoded logical information, so that errors can be detected and corrected.
Beginner interpretation QEC protects fragile quantum information by spreading it over many qubits and checking for signs of errors, without peeking at the information itself.
Appears in Quantum Error Correction → Why QEC? · Quantum Error Correction → Physical vs Logical Qubits · Quantum Error Correction → Repetition Codes · Quantum Error Correction → Lattice Surgery · Quantum Error Correction → Hardware-Aware QEC
Quantum Error-Correcting Code¶
Also known as QEC code, Quantum code
Definition A scheme for encoding logical quantum information into a larger number of physical qubits so that a specified set of errors can be detected and corrected.
Beginner interpretation A quantum error-correcting code is a specific recipe for spreading information over qubits so that certain errors can be spotted and fixed. Different codes trade off protection against cost.
Appears in Quantum Error Correction → Repetition Codes · Quantum Error Correction → Stabilizer Codes · Quantum Error Correction → Surface Codes
Repetition Code¶
Definition The simplest quantum error-correcting code: it encodes one logical qubit into several physical qubits by repeating the computational-basis value (for example |0⟩ → |000⟩ and |1⟩ → |111⟩). It can correct bit-flip errors but not phase flips.
Beginner interpretation The repetition code spreads a qubit's 0-or-1 value across several qubits and uses pairwise checks to find and fix a flipped one. On its own it protects only against bit flips.
Appears in Quantum Error Correction → Repetition Codes · Quantum Error Correction → Encoding & Syndrome Measurement · Quantum Error Correction → Stabilizer Codes · Quantum Error Correction → Errors and Noise
Shor Code¶
Also known as Nine-qubit code
Definition A nine-qubit quantum error-correcting code that encodes one logical qubit and can correct an arbitrary error on any single physical qubit. It was the first code shown to protect against both bit-flip and phase-flip errors.
Beginner interpretation The Shor code was the first demonstration that quantum information can be protected against any single-qubit error. It uses nine qubits to protect one.
Stabilizer¶
Definition An operator, built from Pauli operators acting on several qubits, whose measurement outcome is +1 for every valid encoded state of a stabilizer code. Measuring stabilizers reveals whether errors have changed the state.
Beginner interpretation A stabilizer is a check that every correctly encoded state passes. If an error breaks the check, the failed result is a clue that something went wrong.
Appears in Quantum Error Correction → Stabilizer Codes · Quantum Error Correction → Surface Codes · Quantum Error Correction → Encoding & Syndrome Measurement · Quantum Error Correction → Lattice Surgery
Stabilizer Code¶
Definition A quantum error-correcting code defined by a set of commuting Pauli operators, the stabilizers; its code space is the set of states that every stabilizer leaves unchanged.
Beginner interpretation A stabilizer code is a code described by a list of checks. States that pass every check are the valid encoded states.
Appears in Quantum Error Correction → Stabilizer Codes
Stabilizer Measurement¶
Definition A measurement of a stabilizer operator. It yields +1 or −1 and reveals information about errors without revealing the logical information.
Beginner interpretation Measuring a stabilizer is running one of the code's checks. A +1 means it passed, and a −1 means an error disturbed it.
Appears in Quantum Error Correction → Encoding & Syndrome Measurement · Quantum Error Correction → Stabilizer Codes
Steane Code¶
Also known as Seven-qubit code
Definition A seven-qubit stabilizer code, written [[7,1,3]], that encodes one logical qubit and can correct an arbitrary error on any single physical qubit.
Beginner interpretation The Steane code is a seven-qubit code that protects one logical qubit against any single-qubit error. It is a standard textbook example of a stabilizer code.
Surface Code¶
Definition A stabilizer code in which physical qubits are arranged on a two-dimensional lattice, with local X-type and Z-type checks measured on neighboring qubits. It is one of the most widely studied codes for scalable quantum error correction.
Beginner interpretation A surface code arranges qubits in a grid and checks small groups of neighbors. The pattern of failed checks reveals where errors happened.
Appears in Quantum Error Correction → Surface Codes · Quantum Error Correction → Minimum-Weight Perfect Matching · Quantum Error Correction → Lattice Surgery
Syndrome¶
Also known as Error syndrome
Definition Information obtained from measurements associated with a quantum error-correcting code that indicates the presence or characteristics of errors without directly measuring the encoded logical quantum information.
Beginner interpretation A syndrome is a set of clues that tells an error-correction system what may have gone wrong with the qubits without revealing the quantum information being protected.
Appears in Quantum Error Correction → Encoding & Syndrome Measurement · Quantum Error Correction → Stabilizer Codes · Quantum Error Correction → Decoding · Quantum Error Correction → Surface Codes · Quantum Error Correction → Repetition Codes · Quantum Error Correction → Minimum-Weight Perfect Matching
Syndrome Extraction¶
Also known as Syndrome measurement
Definition The procedure of measuring a code's stabilizers, typically using ancilla qubits, to obtain the syndrome.
Beginner interpretation Syndrome extraction is the step where the system runs its checks to gather the clues about errors.
Appears in Quantum Error Correction → Encoding & Syndrome Measurement · Quantum Error Correction → Stabilizer Codes
Threshold Theorem¶
Also known as Fault-tolerant threshold theorem
Definition The result that arbitrarily long quantum computations can be performed reliably, with a resource overhead that grows only polylogarithmically in the size of the computation, provided the error rate per operation is below a constant threshold and the noise satisfies suitable assumptions.
Beginner interpretation The threshold theorem says that if hardware errors are rare enough, under certain assumptions, error correction can in principle make a quantum computation as reliable as you like.
Transversal Gate¶
Definition A logical gate implemented by applying gates independently to corresponding physical qubits of the encoded blocks, so that a single physical fault cannot spread to several qubits within the same block.
Beginner interpretation A transversal gate does a logical operation by acting separately on each physical qubit, which keeps errors from spreading. Not every code allows every gate to be done this way.
Algorithms & Computational Methods¶
Quantum algorithms and major algorithmic techniques.
Amplitude Amplification¶
Definition A quantum technique that increases the probability of measuring desired outcomes by repeatedly applying operations that boost their amplitudes; it generalizes the idea behind Grover's algorithm.
Beginner interpretation Amplitude amplification repeatedly nudges a quantum state so that the answers you want become more likely to show up when you measure.
Expectation Value¶
Definition The average result of measuring an observable on a quantum state, taken over many repetitions of the same experiment.
Beginner interpretation The expectation value is what you would get on average if you repeated a measurement many times.
Appears in Quantum Algorithms & Methods → Variational Quantum Eigensolver (VQE) · Quantum Computing Fundamentals → Measurement
Grover's Algorithm¶
Also known as Grover search
Definition A quantum algorithm for searching an unstructured collection of N items using about √N oracle queries, a quadratic improvement over the roughly N queries needed classically.
Beginner interpretation Grover's algorithm finds a marked item in an unsorted collection with far fewer lookups than checking items one by one. The speedup is quadratic, not exponential.
Appears in Quantum Algorithms & Methods → Overview
Hamiltonian¶
Definition An operator representing the total energy of a quantum system. Its eigenvalues are the energies the system can have, and it governs how the system evolves in time.
Beginner interpretation The Hamiltonian is the rulebook for a quantum system's energy. Algorithms such as VQE ask what the lowest energy it allows is.
Appears in Quantum Algorithms & Methods → Variational Quantum Eigensolver (VQE)
Oracle¶
Also known as Black-box function
Definition A black-box operation, implemented as a quantum circuit, that encodes a problem's input function. Oracles are used in many quantum algorithms and in arguments about what quantum computers can do.
Beginner interpretation An oracle stands in for the problem itself: a sealed box the algorithm can query without seeing what is inside.
Appears in Quantum Algorithms & Methods → Overview
Parameterized Quantum Circuit¶
Also known as PQC
Definition A quantum circuit containing gates that depend on adjustable numerical parameters, such as rotation angles, so that one circuit design defines a whole family of states. When used to prepare a trial state in a variational algorithm it is often called an ansatz.
Beginner interpretation A parameterized circuit is a circuit with adjustable dials. Turning the dials produces different quantum states from the same basic design.
Appears in Quantum Algorithms & Methods → Variational Quantum Eigensolver (VQE)
Quantum Algorithm¶
Definition A procedure, expressed as a quantum circuit or a sequence of quantum operations, that solves a computational problem by exploiting quantum effects such as superposition, interference, and entanglement.
Beginner interpretation A quantum algorithm is a step-by-step recipe for a quantum computer, designed so that quantum effects help it reach an answer.
Appears in Quantum Algorithms & Methods → Overview
Quantum Approximate Optimization Algorithm¶
Also known as QAOA
Definition A variational quantum algorithm for finding approximate solutions to combinatorial optimization problems, using a parameterized circuit that alternates between operations encoding the problem's cost and a mixing operation.
Beginner interpretation QAOA is a variational method for optimization puzzles. It tunes a short, repeating circuit to find good solutions, which are not guaranteed to be the best.
Appears in Quantum Algorithms & Methods → Overview
Quantum Fourier Transform¶
Also known as QFT
Definition The quantum analogue of the discrete Fourier transform, applied to a state's amplitudes using a number of gates that grows only polynomially with the number of qubits. It is a building block of several algorithms, including Shor's algorithm.
Beginner interpretation The QFT helps reveal repeating patterns hidden in a quantum state, and it is a key ingredient of algorithms such as Shor's.
Quantum Interference¶
Also known as Interference
Definition The combining of probability amplitudes so that contributions to an outcome can reinforce (constructive interference) or cancel (destructive interference) one another, depending on their relative phases.
Beginner interpretation Interference is how quantum algorithms steer results: contributions toward wrong answers cancel out while contributions toward the right answer add up.
Appears in Quantum Error Correction → Errors and Noise · Quantum Computing Fundamentals → Measurement
Quantum Parallelism¶
Definition The ability of a quantum circuit to act on a superposition of many inputs at once, producing a superposition of the corresponding outputs. It does not by itself allow all of those results to be read out.
Beginner interpretation Quantum parallelism means a circuit can work on a blend of many inputs together. A measurement still returns only one result, so algorithms have to be clever about extracting an answer.
Quantum Phase Estimation¶
Also known as QPE
Definition A quantum algorithm that estimates the eigenvalue phase of a unitary operator for a given eigenstate, using controlled operations followed by an inverse quantum Fourier transform.
Beginner interpretation QPE measures a hidden 'phase' associated with an operation, with precision that improves as more qubits are used. It is a core subroutine in many quantum algorithms.
Shor's Algorithm¶
Also known as Shor factoring
Definition A quantum algorithm for integer factorization and discrete logarithms whose running time grows polynomially with the number of digits, in contrast to the best known classical algorithms.
Beginner interpretation Shor's algorithm factors large numbers dramatically faster than any known classical method, which is why it matters for cryptography. Running it at useful sizes is expected to need error-corrected quantum computers far larger than today's.
Appears in Quantum Algorithms & Methods → Overview
Variational Quantum Algorithm¶
Also known as VQA
Definition A hybrid algorithm in which a parameterized quantum circuit prepares a trial state, a classical optimizer adjusts the circuit's parameters, and the loop repeats to minimize a cost function.
Beginner interpretation A variational algorithm is a team effort between a quantum computer and a classical one: the quantum side tries a setting, the classical side improves it, and they repeat.
Appears in Quantum Algorithms & Methods → Variational Quantum Eigensolver (VQE) · Quantum Algorithms & Methods → Overview
Variational Quantum Eigensolver¶
Also known as VQE
Definition A hybrid quantum-classical algorithm that estimates the lowest energy, the ground-state energy, of a Hamiltonian by preparing a parameterized trial state, measuring its energy, and using a classical optimizer to adjust the parameters.
Beginner interpretation VQE searches for the lowest energy a quantum system can have: a quantum computer measures the energy of a trial state, and a classical computer tweaks the trial to push that energy lower.
Appears in Quantum Algorithms & Methods → Variational Quantum Eigensolver (VQE) · Quantum Algorithms & Methods → Overview
Architecture & Execution¶
Concepts describing how quantum programs are compiled, executed, and mapped to hardware.
Backend¶
Definition The system on which a quantum circuit is executed, either quantum hardware or a simulator, reached through a software interface.
Beginner interpretation A backend is whatever actually runs your circuit: a real quantum device or a simulation of one.
Appears in Quantum Software Stack → Understanding the Quantum Software Stack
Circuit Mapping¶
Definition The process of adapting a circuit to a device's physical layout, including assigning circuit qubits to physical qubits (qubit mapping) and inserting operations so that two-qubit gates act only on connected qubits (routing).
Beginner interpretation Circuit mapping fits your circuit onto the actual chip: deciding which physical qubits to use and adding any extra steps needed to connect them.
Circuit Optimization¶
Definition Transformations that reduce a circuit's resource cost, such as its gate count, depth, or expected error, while preserving the computation it performs.
Beginner interpretation Circuit optimization trims a circuit, using fewer gates or a shorter run, so less can go wrong while the answer stays the same.
Compilation¶
Definition The process of translating a quantum program into lower-level operations suited to a specific target, including decomposition into native gates, mapping to hardware, and optimization.
Beginner interpretation Compilation is the translation step between the circuit you have in mind and what the hardware can really do.
Appears in Quantum Software Stack → Understanding the Quantum Software Stack
Execution Target¶
Definition The system selected to carry out a quantum computation, whether a classical simulator or a physical quantum device.
Beginner interpretation The execution target is where your circuit actually gets run, either on a simulation or on real quantum hardware.
Appears in Quantum Software Stack → Understanding the Quantum Software Stack
Hardware Backend¶
Definition A backend that executes circuits on physical quantum hardware, a quantum processing unit, rather than on a simulator.
Beginner interpretation A hardware backend is a real quantum device that you send your circuit to.
Native Gate¶
Definition A gate that a quantum device can implement directly through its physical control operations, without first decomposing it into other gates.
Beginner interpretation A native gate is a move the hardware can do directly. Every other operation has to be built out of these.
Native Gate Set¶
Also known as Basis gates
Definition The collection of gates a given device implements directly. Any other gate or circuit must be expressed in terms of these.
Beginner interpretation The native gate set is the hardware's built-in vocabulary of operations.
NISQ¶
Also known as Noisy Intermediate-Scale Quantum
Definition Noisy Intermediate-Scale Quantum: a term for quantum devices that have enough qubits to be hard to simulate classically but are too noisy, and too small, to run fully error-corrected computations.
Beginner interpretation NISQ describes the kind of noisy, pre-error-correction devices available in the early era of quantum hardware: big enough to be interesting, but without full error correction.
Appears in Quantum Algorithms & Methods → Overview · Quantum Algorithms & Methods → Variational Quantum Eigensolver (VQE)
Quantum Advantage¶
Also known as Quantum computational advantage
Definition A demonstrated case in which a quantum computer performs a specific task better, whether faster, more accurately, or with fewer resources, than the best known classical methods.
Beginner interpretation Quantum advantage is when a quantum computer genuinely beats ordinary computers at a particular task.
Quantum Compiler¶
Definition Software that translates a quantum program into a form a target backend can execute, which may include decomposing gates, optimizing circuits, and mapping qubits to hardware.
Beginner interpretation A quantum compiler turns the circuit you wrote into the specific instructions a particular device can run.
Quantum Runtime¶
Also known as Orchestration
Definition Software that coordinates the execution of a quantum computation, which can include submitting jobs, tracking them, exchanging data with classical processing, and handling results.
Beginner interpretation The runtime is the coordinator: it hands work to the target, keeps track of the run, and helps bring the results back.
Appears in Quantum Software Stack → Understanding the Quantum Software Stack
Quantum Simulator¶
Definition A controllable quantum system used to model the behavior of another quantum system of interest. In some usage the term is also applied to classical software that simulates quantum systems or circuits.
Beginner interpretation A quantum simulator uses one quantum system to study another that is too hard to calculate directly. People also sometimes use the phrase for software simulators.
Quantum Software Stack¶
Also known as Software Stack
Definition A way of organizing the software responsibilities that cooperate to run a quantum computation, such as describing a program, adapting it to a target, executing it, coordinating the run, and returning results. It is a teaching model rather than one fixed architecture, and real platforms may combine, distribute, or reorder these responsibilities.
Beginner interpretation The software stack is the set of cooperating jobs that sit between the code you write and the results you get back. It is a way of thinking about the pieces, not a design every platform follows exactly.
Appears in Quantum Software Stack → Understanding the Quantum Software Stack
Quantum Supremacy¶
Definition An earlier term for a quantum computer performing a well-defined computational task that is infeasible for any classical computer in practical time, regardless of whether the task is useful. Many researchers now prefer 'quantum computational advantage'.
Beginner interpretation Quantum supremacy named the milestone of a quantum computer beating classical computers at some task, even a useless one. Many researchers now say 'quantum advantage' instead.
Quantum-Classical Hybrid Computing¶
Also known as Hybrid quantum-classical computing
Definition A computational approach in which a quantum processor and a classical computer work together, typically with the classical side preparing parameters, processing measurement results, and deciding what the quantum side runs next.
Beginner interpretation Hybrid computing pairs a quantum computer with an ordinary one, with each handling the part of the job it is suited to.
Appears in Quantum Algorithms & Methods → Variational Quantum Eigensolver (VQE) · Quantum Algorithms & Methods → Overview
Qubit Mapping¶
Also known as Qubit allocation, Layout
Definition The assignment of a circuit's abstract, or virtual, qubits to the physical qubits of a device.
Beginner interpretation Qubit mapping decides which physical qubit plays the role of each qubit in your program.
Routing¶
Also known as Qubit routing
Definition The insertion of operations, typically SWAP gates, so that two-qubit gates can be applied between qubits that are not directly connected on the device.
Beginner interpretation Routing shuffles qubits around on the chip so that two qubits that need to interact end up next to each other.
Sampling¶
Definition Drawing outcomes from a quantum circuit's measurement distribution by running it repeatedly; the collected samples are used to estimate probabilities and expectation values.
Beginner interpretation Sampling means running a circuit over and over and looking at which results come up and how often.
Shot¶
Definition A single execution of a circuit followed by measurement, producing one set of classical outcomes. Results are gathered by repeating many shots.
Beginner interpretation A shot is one run of the circuit and one readout. Because results are probabilistic, you take many shots to see the pattern.
Appears in Quantum Computing Fundamentals → Quantum States · Quantum Computing Fundamentals → Measurement
Simulator¶
Also known as Circuit simulator
Definition A program that emulates the behavior of quantum circuits on a classical computer, allowing circuits to be run and tested without quantum hardware. Its cost generally grows rapidly with the number of qubits.
Beginner interpretation A simulator is a quantum computer imitated on an ordinary computer. It is great for testing small circuits but becomes very expensive as the number of qubits grows.
Appears in Quantum Software Stack → Understanding the Quantum Software Stack
Transpilation¶
Definition A circuit-to-circuit transformation that rewrites a quantum circuit in terms of a target backend's native gates and connectivity while preserving its function. The term is widely used in some quantum software frameworks for part of the compilation process.
Beginner interpretation Transpiling rewrites a circuit into an equivalent one that the chosen device can run directly.
Advanced & Emerging Concepts¶
Concepts that are more specialized, research-oriented, or dependent on advanced prerequisite knowledge.
Bias-Preserving Gate¶
Definition A gate designed so that it does not turn the dominant type of error into other error types, so that a noise bias is maintained during computation.
Beginner interpretation A bias-preserving gate is built not to spread the hardware's most common kind of error into other kinds, keeping the noise lopsided in a way error correction can use.
Biased Noise¶
Also known as Noise bias
Definition A noise regime in which some error types, such as phase flips, occur much more often than others, such as bit flips.
Beginner interpretation Biased noise means one kind of error is far more common than the others, which some error-correcting approaches try to take advantage of.
Calibration Data¶
Definition Measured or estimated parameters describing a device's characteristics and control settings at a particular time, such as coherence times, gate and readout error estimates, and qubit frequencies, produced by calibration and characterization procedures.
Beginner interpretation Calibration data is the set of numbers describing how each part of a device was behaving the last time it was measured. They are estimates, not perfect truth.
Calibration Telemetry¶
Definition Information, reported by a device's calibration and characterization processes, that describes measured or estimated characteristics of the device and when they were obtained.
Beginner interpretation Telemetry is the reported readings about a device. They are measurements and estimates that software can use to understand how the hardware is doing, not exact truth.
Appears in Quantum Error Correction → Hardware-Aware QEC · Quantum Software Stack → Understanding the Quantum Software Stack
Dynamic Decoding¶
Definition A class of decoding approaches, under active research, in which the decoder's assumptions, such as the weights it assigns to error explanations, are updated over time rather than fixed in advance.
Beginner interpretation Dynamic decoding is research on decoders that update their expectations as conditions change instead of relying on one fixed model.
Erasure Conversion¶
Definition An approach in which hardware or protocols are designed so that the dominant physical errors are converted into erasures, whose locations can be detected, rather than errors at unknown locations.
Beginner interpretation Erasure conversion is a research strategy of making hardware flag when most errors happen, so that error correction knows where to look.
Erasure Qubit¶
Definition A qubit encoding designed so that its most common errors can be detected and located as erasures, for example by taking the qubit out of its computational states in a way that can be flagged.
Beginner interpretation An erasure qubit is built so that its most common failures can be noticed and located, which makes them easier to correct.
Feedforward¶
Also known as Classical feedforward, Feed-forward
Definition The use of mid-circuit measurement results, processed classically, to determine operations applied later in the same computation.
Beginner interpretation Feedforward means the program reacts to what it measured: a result taken now decides what happens next.
Hardware-Aware Quantum Computing¶
Definition An umbrella description for approaches that use information about the physical behavior and constraints of quantum devices to inform how quantum programs are compiled, mapped, or executed.
Beginner interpretation Hardware-aware quantum computing means designing and running programs with a real device's quirks in mind instead of assuming every qubit and gate is identical. It is a broad direction, not one fixed method.
Hardware-Aware Quantum Error Correction¶
Also known as Hardware-aware QEC
Definition An umbrella description for approaches that incorporate information about physical-device behavior into the design or operation of quantum error correction, for example in decoder weighting or code and layout choices. It does not refer to a single standardized architecture.
Beginner interpretation Hardware-aware QEC is an area of research asking how knowing a device's real strengths and weaknesses could improve error correction. It is not one fixed method, and not the only direction QEC research takes.
Logical Architecture¶
Definition An approach to organizing a quantum computer in terms of logical qubits and logical operations, treating the layer of error-corrected qubits as the unit of computation while the physical implementation is managed beneath it.
Beginner interpretation A logical architecture is a design in which programs run on error-corrected qubits and operations, with the physical details handled underneath.
Noise-Aware Decoding¶
Definition Methods that incorporate a model of a device's noise, such as which qubits or operations are more error-prone, into a decoder's decisions, for example through the weights assigned to error explanations.
Beginner interpretation Noise-aware decoding means the decoder doesn't treat every error as equally likely. It uses what is known about where the hardware is noisier.
Appears in Quantum Error Correction → Minimum-Weight Perfect Matching · Quantum Error Correction → Hardware-Aware QEC
Real-Time Decoding¶
Definition Decoding performed fast enough to keep up with the rate at which syndrome information is produced, so that corrections can be determined while the computation is still running.
Beginner interpretation Real-time decoding means the decoder's answers arrive in time to be used, instead of piling up behind the quantum computer.
Time-Dependent Noise¶
Also known as Drift, Noise drift
Definition Noise whose strength or character changes over time, so that a measurement of device behavior taken at one time may not describe it later.
Beginner interpretation Time-dependent noise means a device's error behavior isn't fixed: what was true at the last calibration may be out of date later.