Quantum Dictionary
Advanced technical reference for quantum computing with in-depth explanations
What Makes This Different
A
Adiabatic Quantum Computation
A paradigm of quantum computing where the system evolves slowly (adiabatically) from an initial simple quantum state to a final state that encodes the solution to a computational problem. Based on the adiabatic theorem of quantum mechanics, which states that a system remains in its instantaneous eigenstate if changes are made sufficiently slowly.
Technical Details
The computation begins with a Hamiltonian H0 whose ground state is easy to prepare, then slowly interpolates to H_problem = (1-s(t))H0 + s(t)Hf where s(t) goes from 0 to 1, and the ground state of Hf encodes the problem solution. The required evolution time scales inversely with the minimum energy gap.
Applications
Related Concepts
Amplitude
The complex number coefficient associated with a quantum state in superposition. For a qubit |psi> = alpha|0> + beta|1>, alpha and beta are the amplitudes. The squared magnitude |alpha|^2 gives the probability of measuring that state.
Technical Details
Amplitudes can be negative or complex, enabling destructive interference when amplitudes cancel. This is fundamental to quantum algorithms like Grover's search, which amplifies the amplitude of the target state while suppressing others.
Applications
Related Concepts
Ancilla Qubit
An auxiliary qubit used temporarily during quantum computation to facilitate certain operations or error correction procedures, then typically reset or discarded. Essential for implementing controlled operations, error syndrome measurement, and magic state distillation.
Technical Details
In quantum error correction, ancilla qubits measure error syndromes through controlled operations with data qubits, collapsing to reveal error information while leaving the data qubits in a superposition. The quality of ancilla operations directly impacts logical error rates.
Applications
Related Concepts
Anyons
Exotic quasiparticles existing in two-dimensional systems with unique braiding statistics that are neither bosonic nor fermionic. When exchanged, the quantum state acquires a phase or unitary transformation depending on the topology of the exchange path.
Technical Details
Non-Abelian anyons form the basis for topological quantum computing. Majorana zero modes (potentially realized in topological superconductors) and Fibonacci anyons are key examples. Microsoft's approach to quantum computing relies on Majorana-based topological qubits.
Applications
Related Concepts
B
Barren Plateau
A phenomenon in variational quantum algorithms where gradients of the cost function become exponentially small in the number of qubits, making optimization extremely difficult. First identified by McClean et al. in 2018.
Technical Details
For random parameterized circuits with global cost functions, the variance of gradients scales as Var[dC/dtheta] ~ O(1/2^n). Mitigation strategies include using local cost functions, structured parameter initialization, and layer-by-layer training approaches.
Applications
Related Concepts
BB84 Protocol
The first quantum key distribution protocol, invented by Charles Bennett and Gilles Brassard in 1984, using polarized photons for unconditionally secure communication.
Technical Details
Alice prepares photons in one of four polarization states in two bases. Bob randomly measures. They compare bases publicly, keeping bits where bases matched. Any eavesdropping introduces detectable errors due to wave function collapse.
Applications
Related Concepts
Bell State
One of four specific maximally entangled quantum states of two qubits, forming an orthonormal basis for the two-qubit Hilbert space. Named after physicist John Stewart Bell.
Technical Details
The four Bell states: |Phi+> = (|00>+|11>)/sqrt(2), |Phi-> = (|00>-|11>)/sqrt(2), |Psi+> = (|01>+|10>)/sqrt(2), |Psi-> = (|01>-|10>)/sqrt(2). These are maximally entangled - measuring one qubit immediately determines the other.
Applications
Related Concepts
Bloch Sphere
A geometrical representation of a qubit's pure quantum state as a point on the surface of a unit sphere. Any qubit state can be written |psi> = cos(theta/2)|0> + e^(i*phi)sin(theta/2)|1>.
Technical Details
North pole represents |0>, south pole |1>. Equator contains equal superpositions. Single-qubit gates correspond to rotations: Pauli-X rotates 180 degrees around X-axis, Hadamard around (X+Z)/sqrt(2) axis.
Applications
Related Concepts
Boson Sampling
A computational problem involving photons through linear optical networks, used to demonstrate quantum computational advantage. Given n photons in m modes, sampling from the output distribution requires computing matrix permanents - classically intractable.
Technical Details
Aaronson and Arkhipov (2011) proved efficient classical boson sampling would collapse the polynomial hierarchy. USTC demonstrated 76-photon Gaussian boson sampling in 2020, claiming quantum advantage.
Applications
Related Concepts
C
CNOT Gate
A two-qubit quantum gate that flips the target qubit if and only if the control qubit is in state |1>. Essential for creating entanglement and fundamental to universal quantum computation.
Technical Details
Truth table: |00>->|00>, |01>->|01>, |10>->|11>, |11>->|10>. Combined with single-qubit gates, forms a universal gate set. The CNOT followed by measurements forms the basis of Bell state preparation.
Applications
Related Concepts
Coherence
The property of a quantum system maintaining definite phase relationships between quantum states, necessary for quantum computation. Loss of coherence (decoherence) causes quantum systems to behave classically.
Technical Details
Coherence enables superposition and interference effects. Characterized by coherence times T1 (relaxation) and T2 (dephasing). Modern superconducting qubits achieve T1, T2 times of hundreds of microseconds.
Applications
Related Concepts
Clifford Gates
A set of quantum gates that map Pauli operators to Pauli operators under conjugation. Includes Hadamard, S, CNOT, and Pauli gates. Efficiently simulable classically via the Gottesman-Knill theorem.
Technical Details
Clifford gates alone are not universal - adding a T gate (or any non-Clifford gate) achieves universality. The Clifford+T gate set is widely used for fault-tolerant quantum computation.
Applications
Related Concepts
D
Decoherence
The loss of quantum coherence due to interaction with the environment, causing quantum systems to behave classically and destroying superposition and entanglement. The primary obstacle to building large-scale quantum computers.
Technical Details
Characterized by T1 (energy relaxation) and T2 (phase decoherence). Caused by thermal noise, electromagnetic interference, material defects, and cosmic rays. Fighting decoherence requires extreme isolation, cryogenic cooling, and quantum error correction.
Applications
Related Concepts
Dilution Refrigerator
A cryogenic device used to cool quantum processors to temperatures below 100 millikelvin, essential for superconducting qubits. Uses the mixing of helium-3 and helium-4 isotopes.
Technical Details
Operating at 10-20 mK, dilution refrigerators provide the thermal isolation needed for superconducting qubit coherence. Major manufacturers include Bluefors, Oxford Instruments, and Leiden Cryogenics. Systems cost $500K-$2M.
Applications
Related Concepts
Diamond NV Center
Nitrogen-vacancy defects in diamond crystals used as qubits, capable of operating at room temperature for sensing applications. The electron spin of the NV center serves as the qubit.
Technical Details
NV centers have long coherence times even at room temperature (milliseconds). Excellent for quantum sensing of magnetic fields, temperature, and strain. Companies like Quantum Diamond Technologies and Element Six develop NV-based sensors.
Applications
Related Concepts
E
Entanglement
A quantum phenomenon where particles become correlated such that the quantum state of each particle cannot be described independently of the others, regardless of the distance separating them.
Technical Details
Einstein called it "spooky action at a distance." Bell test experiments have confirmed entanglement violates local hidden variable theories. Resources for teleportation, dense coding, and quantum networks.
Applications
Related Concepts
Error Correction (Quantum)
Techniques to protect quantum information from decoherence and other quantum noise using redundancy and syndrome measurement. Unlike classical error correction, must handle continuous errors and cannot copy quantum states.
Technical Details
Major codes include surface code, color code, and bosonic codes. Surface code is leading approach with ~1% error threshold. Requires 1000+ physical qubits per logical qubit for practical fault tolerance.
Applications
Related Concepts
G
Grover's Algorithm
A quantum algorithm providing quadratic speedup for searching unsorted databases, reducing search time from O(N) to O(sqrt(N)). Discovered by Lov Grover in 1996.
Technical Details
Uses amplitude amplification through repeated application of Grover's diffusion operator. Optimal number of iterations is approximately pi*sqrt(N)/4. Provides provably optimal speedup for unstructured search.
Applications
Related Concepts
H
Hadamard Gate
A single-qubit quantum gate that creates equal superposition, transforming |0> to (|0>+|1>)/sqrt(2). One of the most fundamental quantum gates.
Technical Details
Matrix representation: (1/sqrt(2))[[1,1],[1,-1]]. Applying Hadamard twice returns to original state. Essential for quantum algorithms like Deutsch-Jozsa and quantum Fourier transform.
Applications
Related Concepts
I
Ion Trap
A quantum computing platform using trapped ions (charged atoms) as qubits, manipulated by precisely controlled laser beams. Leading approach for high-fidelity quantum operations.
Technical Details
Ions are confined using electromagnetic fields (Paul trap). Qubit states are hyperfine levels or optical transitions. IonQ, Quantinuum, and Alpine Quantum Technologies lead ion trap development. Achieved >99.9% gate fidelity.
Applications
Related Concepts
J
Josephson Junction
A superconducting device consisting of two superconductors separated by a thin insulating layer, used to create superconducting qubits. The nonlinear inductance enables qubit-like behavior.
Technical Details
Current-phase relation I = Ic*sin(phi) provides the anharmonicity needed for qubit operation. Junction critical current and capacitance determine qubit frequency and anharmonicity. Fabricated using shadow evaporation of aluminum.
Applications
Related Concepts
L
Logical Qubit
An error-corrected qubit encoded across multiple physical qubits to protect against errors through quantum error correction. The fundamental unit of fault-tolerant quantum computation.
Technical Details
Encoding ratios vary: surface code ~1000:1, color code ~50:1, bosonic codes can achieve 1:1. December 2024 leaders: Quantinuum (48 LQ), QuEra (48 LQ), Atom Computing/Microsoft (24 LQ). First logical qubits achieved in 2023.
Applications
Related Concepts
N
Neutral Atom QC
A quantum computing platform using arrays of neutral atoms trapped by optical tweezers as qubits, typically manipulated through Rydberg interactions. Highly scalable approach.
Technical Details
Companies: QuEra (256 atoms), Pasqal (100+ atoms), Atom Computing (1180 atoms). Uses focused laser beams to trap individual atoms. Rydberg states enable strong atom-atom interactions for entangling gates.
Applications
Related Concepts
NISQ
Noisy Intermediate-Scale Quantum - current-era quantum computers with 50-1000 qubits that lack full error correction. Term coined by John Preskill in 2018.
Technical Details
NISQ devices can demonstrate quantum advantage for specific problems but are limited by noise. Variational algorithms (VQE, QAOA) are designed for NISQ hardware. Transition to fault-tolerant era expected mid-2020s.
Applications
Related Concepts
Q
Qubit
The basic unit of quantum information, analogous to the classical bit but able to exist in superposition of |0> and |1> states. The general state is |psi> = alpha|0> + beta|1>.
Technical Details
Physical implementations include superconducting circuits, trapped ions, photons, neutral atoms, NV centers, and semiconductor quantum dots. Key metrics: coherence time, gate fidelity, connectivity.
Applications
Related Concepts
QAOA
Quantum Approximate Optimization Algorithm - a hybrid primary-classical algorithm for solving combinatorial optimization problems. Proposed by Farhi, Goldstone, and Gutmann in 2014.
Technical Details
Alternates between cost Hamiltonian and mixer Hamiltonian operations. Depth parameter p controls approximation quality. Subject to barren plateau issues for deep circuits. Promising for MaxCut and satisfiability problems.
Applications
Related Concepts
S
Shor's Algorithm
A quantum algorithm for efficiently factoring large integers, threatening current public-key cryptography systems like RSA. Discovered by Peter Shor in 1994.
Technical Details
Reduces factoring to period-finding using quantum Fourier transform. Runs in polynomial time O((log N)^3) versus exponential for classical algorithms. Requires fault-tolerant quantum computer with millions of qubits for cryptographically relevant numbers.
Applications
Related Concepts
Superposition
A fundamental quantum principle where a quantum system can exist in multiple states simultaneously until measured. For a qubit: |psi> = alpha|0> + beta|1>.
Technical Details
Enables quantum parallelism - processing all possible inputs simultaneously. Collapses to definite state upon measurement with probabilities |alpha|^2, |beta|^2. The Schrodinger cat thought experiment illustrates macroscopic superposition.
Applications
Related Concepts
Surface Code
A leading quantum error correction code using qubits arranged in a 2D lattice with nearest-neighbor interactions. Dominant approach for superconducting and neutral atom platforms.
Technical Details
Requires ~1000 physical qubits per logical qubit at current error rates. Threshold error rate ~1%. Uses X and Z stabilizer measurements. Google's 2023 experiment first demonstrated below-threshold operation.
Applications
Related Concepts
T
Transmon
A type of superconducting qubit design that reduces charge noise sensitivity through a large shunting capacitor. The dominant superconducting qubit architecture.
Technical Details
Developed at Yale (Koch et al., 2007). EJ/EC ratio ~50-80 provides charge noise insensitivity. Used by IBM, Google, Rigetti, IQM. Typical frequencies 4-6 GHz, anharmonicity ~200-300 MHz.
Applications
Related Concepts
V
VQE
Variational Quantum Eigensolver - a hybrid primary-classical algorithm for finding ground state energies of molecules. Uses parameterized quantum circuits optimized by classical computers.
Technical Details
Proposed by Peruzzo et al. (2014). Ansatz circuit prepares trial state, quantum computer measures energy expectation value, classical optimizer updates parameters. Limited by barren plateaus and hardware noise.