Glossary

Glossary#

Definitions of key terms used throughout this book.

Amplitude#: A complex number \(\alpha\) in a quantum state \(|\psi\rangle = \alpha|0\rangle + \beta|1\rangle\). The probability of measuring a basis state is \(|\alpha|^2\).
Ancilla qubit#: An auxiliary qubit used as workspace during a quantum computation, typically initialized to \(|0\rangle\) and measured or discarded at the end.
Annealing#: A quantum computation model where the system evolves from an easy-to-prepare ground state to the ground state of a problem Hamiltonian. Used by D-Wave systems.
Barren plateau#: A region in the parameter space of a variational quantum circuit where the gradient of the cost function is exponentially small, making optimization impractical.
Bell state#: One of four maximally entangled two-qubit states: \(|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)\), \(|\Phi^-\rangle\), \(|\Psi^+\rangle\), \(|\Psi^-\rangle\).
Bloch sphere#: A geometric representation of a single-qubit state as a point on the surface of a unit sphere. Pure states lie on the surface; mixed states lie inside.
Born rule#: The probability of measuring outcome \(m\) is \(P(m) = |\langle m | \psi \rangle|^2\).
CNOT gate#: Controlled-NOT: flips the target qubit if the control qubit is \(|1\rangle\). The standard two-qubit entangling gate.
Coherence time#: The duration over which a qubit maintains its quantum properties (superposition, phase). Denoted \(T_1\) (energy relaxation) and \(T_2\) (dephasing).
CRQC#: Cryptographically Relevant Quantum Computer. A quantum computer large enough to break RSA-2048 or equivalent classical cryptography using Shor’s algorithm.
CSPRNG#: Cryptographically Secure Pseudorandom Number Generator. A deterministic algorithm that produces output indistinguishable from random bits by any efficient adversary.
Decoherence#: The process by which a quantum system loses coherence due to interaction with its environment, transitioning from a pure state to a mixed state.
Density matrix#: A matrix \(\rho\) that describes quantum states (pure or mixed). For a pure state, \(\rho = |\psi\rangle\langle\psi|\). Satisfies \(\text{Tr}(\rho) = 1\) and \(\rho \geq 0\).
DiVincenzo criteria#: Five requirements for building a quantum computer: scalable qubits, initialization, long coherence, universal gates, and qubit-specific measurement.
DORA#: Digital Operational Resilience Act. EU regulation (effective July 2025) requiring financial institutions to maintain resilient ICT systems, including cryptographic policies.
Entanglement#: A quantum correlation between two or more qubits that cannot be described by the states of individual qubits. The entangled system is in a superposition that spans multiple qubits.
Error correction (quantum)#: Encoding logical qubits into multiple physical qubits to detect and correct errors without measuring (and thus destroying) the quantum information.
FIPS 203#: Federal Information Processing Standard defining ML-KEM (Module-Lattice-Based Key Encapsulation Mechanism). Published by NIST in 2024.
FIPS 140-3#: The standard for validating cryptographic modules. Requires testing by a CMVP-accredited laboratory. Distinct from algorithm specifications like FIPS 203.
Gate fidelity#: The accuracy of a quantum gate operation, measured as the overlap between the ideal and actual output states. Current state of the art: 99.5-99.9% for two-qubit gates.
GHZ state#: Greenberger-Horne-Zeilinger state. An \(n\)-qubit entangled state: \(\frac{1}{\sqrt{2}}(|00\ldots0\rangle + |11\ldots1\rangle)\).
Grover’s algorithm#: A quantum search algorithm that finds a marked item among \(N\) unsorted items in \(O(\sqrt{N})\) queries, compared to \(O(N)\) classically.
Hadamard gate#: A single-qubit gate that creates superposition: \(H|0\rangle = \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)\).
HNDL#: Harvest Now, Decrypt Later. The strategy of collecting encrypted data today to decrypt it when a CRQC becomes available.
HHL algorithm#: The Harrow-Hassidim-Lloyd algorithm for solving linear systems \(Ax = b\) in \(O(\log N)\) time (under specific conditions).
KEM#: Key Encapsulation Mechanism. A cryptographic primitive for establishing shared secrets: KeyGen, Encaps, Decaps.
Lattice (cryptographic)#: A discrete subgroup of \(\mathbb{R}^n\). The hardness of lattice problems (SVP, LWE) underpins post-quantum cryptographic algorithms.
Logical qubit#: A fault-tolerant qubit encoded across multiple physical qubits using an error-correcting code.
LWE#: Learning With Errors. A computational problem: given \(\mathbf{b} = \mathbf{A}\mathbf{s} + \mathbf{e}\), recover \(\mathbf{s}\). The foundation of ML-KEM and ML-DSA.
Majorana fermion#: A particle that is its own antiparticle. Majorana bound states in condensed matter are candidates for topological qubits.
ML-KEM#: Module-Lattice-Based Key Encapsulation Mechanism. Standardized as FIPS 203. Formerly known as CRYSTALS-Kyber.
ML-DSA#: Module-Lattice-Based Digital Signature Algorithm. Standardized as FIPS 204. Formerly known as CRYSTALS-Dilithium.
NISQ#: Noisy Intermediate-Scale Quantum. The current era of quantum computing with 50-1000+ qubits but without full error correction.
No-cloning theorem#: It is impossible to create an exact copy of an arbitrary unknown quantum state. A consequence of the linearity of quantum mechanics.
NTT#: Number Theoretic Transform. The finite-field analog of the FFT, used for efficient polynomial multiplication in lattice-based cryptography.
PQC#: Post-Quantum Cryptography. Cryptographic algorithms designed to be secure against both classical and quantum computers.
QAOA#: Quantum Approximate Optimization Algorithm. A variational algorithm for solving combinatorial optimization problems.
QPE#: Quantum Phase Estimation. An algorithm for estimating eigenvalues of unitary operators, used in Shor’s algorithm and quantum chemistry.
QRAM#: Quantum Random Access Memory. A hypothetical device that can load classical data into quantum states efficiently. Required for many quantum speedup claims.
QRNG#: Quantum Random Number Generator. Produces random numbers from quantum mechanical processes (e.g., photon detection, qubit measurement).
Qubit#: The fundamental unit of quantum information. A two-level quantum system described by \(|\psi\rangle = \alpha|0\rangle + \beta|1\rangle\).
Shor’s algorithm#: A quantum algorithm for factoring integers in polynomial time, breaking RSA and related cryptosystems.
SLH-DSA#: Stateless Hash-Based Digital Signature Algorithm. Standardized as FIPS 205. Based on SPHINCS+.
Surface code#: A topological quantum error-correcting code using a 2D grid of qubits. The leading candidate for practical fault-tolerant quantum computing.
Superposition#: A quantum state that is a linear combination of basis states: \(|\psi\rangle = \alpha|0\rangle + \beta|1\rangle\) with \(|\alpha|^2 + |\beta|^2 = 1\).
T gate#: The \(\pi/8\) phase gate. Combined with Clifford gates, it forms a universal gate set. T gates are the most expensive gates in fault-tolerant quantum computing.
Topological qubit#: A qubit encoded in the topological properties of a physical system (e.g., Majorana bound states), providing inherent protection against local noise.
Transmon#: A type of superconducting qubit used by IBM and Google. A charge qubit made insensitive to charge noise by increasing the ratio of Josephson energy to charging energy.
VQE#: Variational Quantum Eigensolver. A hybrid quantum-classical algorithm for finding the ground state energy of a Hamiltonian.