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Type of superconducting quantum bit
operate as a quantum bit, or qubit. The phase qubit is closely related, yet distinct from, the flux qubit and the charge qubit, which are also quantum bits
Phase_qubit
Basic unit of quantum information
computing, a qubit (/ˈkjuːbɪt/) or quantum bit is a basic unit of quantum information, the quantum version of the classic binary bit. A qubit can be physically
Qubit
Quantum computing implementation
superconducting qubits were invented, including the phase qubit, flux qubit, quatronium, the transmon qubit, and the fluxonium. Successive advances in qubit design
Superconducting quantum computing
Superconducting_quantum_computing
Superconducting qubit implementation
superconducting quantum computing, a transmon is a type of superconducting charge qubit designed to have reduced sensitivity to charge noise. The transmon was developed
Transmon
Superconducting qubit implementation
In quantum computing, a charge qubit (also known as Cooper-pair box) is a qubit whose basis states are charge states (i.e. states which represent the presence
Charge_qubit
Process in quantum computing
noise processes in most qubit implementations. As noted earlier, most QECCs assume that the dominant errors are bit flips, phase flips, or combinations
Quantum_error_correction
Types of quantum information
In quantum computing, a qubit is a unit of information analogous to a bit (binary digit) in classical computing, but it is affected by quantum mechanical
Physical_and_logical_qubits
Proposed semiconductor implementation of quantum computers
The spin qubit quantum computer is a quantum computer based on controlling the spin of charge carriers (electrons and electron holes) in semiconductor
Spin_qubit_quantum_computer
Code used in quantum error correction
single logical qubit into a system of nine physical qubits, allowing simultaneous correction of both bit-flip, phase-flip or a joint phase and bit flip
Shor_code
Quantum algorithm for eigenvalue estimation
{\displaystyle m} -qubit register. The eigenvalues of a unitary operator have unit modulus, and are therefore characterized by their phase. Thus if | ψ ⟩
Quantum phase estimation algorithm
Quantum_phase_estimation_algorithm
Proposed quantum computer implementation
applied to induce coupling between the qubit states (for single qubit operations) or coupling between the internal qubit states and the external motional states
Trapped-ion_quantum_computer
Computer hardware technology that uses quantum mechanics
states (a binary), a qubit can exist in a linear combination of states known as a quantum superposition. The result of measuring a qubit is one of the two
Quantum_computing
Superconducting qubit implementation
specifically in superconducting quantum computing, flux qubits (also known as persistent current qubits) are micrometer sized loops of superconducting metal
Flux_qubit
Basic circuit in quantum computing
quantum gate) is a basic quantum circuit operating on a small number of qubits. Quantum logic gates are the building blocks of quantum circuits, like classical
Quantum_logic_gate
Type of quantum computer
described a new device that can represent a logical qubit with hardware stability, measuring a phase of matter consistent with the observation of topological
Topological_quantum_computer
Type of error correction in quantum computing
protect a logical qubit from any arbitrary single qubit error. In this code, 5 physical qubits are used to encode the logical qubit. With X {\displaystyle
Five-qubit error correcting code
Five-qubit_error_correcting_code
Quantum algorithm for integer factorization
Martinis, John M. (2012). "Computing prime factors with a Josephson phase qubit quantum processor". Nature Physics. 8 (10): 719. arXiv:1202.5707. Bibcode:2012NatPh
Shor's_algorithm
Quantum key distribution protocol
the states of the qubits. Also, after Bob has received the qubits, we know that Eve cannot be in possession of a copy of the qubits sent to Bob, by the
BB84
Criteria for a usable quantum computer
quantum devices. Some of these proposals involve using superconducting qubits, trapped ions, liquid and solid state nuclear magnetic resonance, or optical
DiVincenzo's_criteria
Type of quantum computer built out of Rydberg atoms
demonstrate a 48 logical qubit processor. To perform computation, the atoms are first trapped in a magneto-optical trap. Qubits are then encoded in the
Neutral_atom_quantum_computer
Definition of quantum circuits
Clifford group, a set of mathematical transformations which normalize the n-qubit Pauli group, i.e., map tensor products of Pauli matrices to tensor products
Clifford_gate
Topological quantum error correcting code
same qubit, and vice versa. This ensures the correct commutation relations between logical operators. Consider the noise model for which bit and phase errors
Surface_code
Description of a quantum-mechanical system
{\displaystyle S(\mathbf {x} ,t)} is a real function that represents the complex phase of the wavefunction, then the probability flux is calculated as: j = ρ ∇
Schrödinger_equation
Quantum error correcting code
(GKP) code is a quantum error correcting code that encodes logical qubits into the continuous degrees of freedom of a quantum system. It is named
Gottesman–Kitaev–Preskill code
Gottesman–Kitaev–Preskill_code
physical qubit numbers do not reflect the performance levels of the processor. This is instead achieved through the number of logical qubits or benchmarking
List_of_quantum_processors
Theorem of quantum circuits
circuits—circuits that only consist of gates from the normalizer of the qubit Pauli group, also called Clifford group—can be perfectly simulated in polynomial
Gottesman–Knill_theorem
Cloud quantum computing platform
service was launched in May 2016 as the IBM Quantum Experience with a five-qubit quantum processor and matching simulator connected in a star shaped pattern
IBM_Quantum_Platform
Theorem in quantum information science
use the controlled NOT gate and the Walsh–Hadamard gate to entangle two qubits without violating the no-cloning theorem as no well-defined state may be
No-cloning_theorem
Foundational object in quantum communication theory
information. An example of quantum information is the general dynamics of a qubit. An example of classical information is a text document transmitted over
Quantum_channel
Change of basis applied in quantum computing
O(n^{2})} Hadamard gates and controlled phase shift gates, where n {\displaystyle n} is the number of qubits. This can be compared with the classical
Quantum_Fourier_transform
Algorithm to be run on quantum computers
input qubits and terminates with a measurement. A quantum circuit consists of simple quantum gates, each of which acts on some finite number of qubits. Quantum
Quantum_algorithm
Code for quantum correction
correct for both qubit flip errors (X errors) and phase flip errors (Z errors). The Steane code encodes one logical qubit in 7 physical qubits and is able
Steane_code
Technique for comparing quantum states
\rangle )} The measurement gate on the first qubit ensures that it's 0 with a probability of P ( First qubit = 0 ) = 1 2 ( ⟨ ϕ | ⟨ ψ | + ⟨ ψ | ⟨ ϕ | ) 1
Swap_test
Computational benchmark
superconducting qubits. In early January 2018, Intel announced a similar hardware program. In October 2017, IBM demonstrated the simulation of 56 qubits on a classical
Quantum_supremacy
Means of studying the interaction of light and matter
demonstrated deterministic gate teleportation and other operations on multiple qubits. The resonant devices in the circuit QED architecture can be implemented
Circuit quantum electrodynamics
Circuit_quantum_electrodynamics
Theorem in quantum mechanics
construct a counterexample for 2-dimensional Hilbert space, known as a qubit, let the hidden variable be a unit vector λ → {\displaystyle {\vec {\lambda
Gleason's_theorem
Planned quantum technology campus in Chicago
the IQMP, PsiQuantum intends to build and deploy America’s first million-qubit scale, fault-tolerant quantum computer. Other tenants include the DARPA-Illinois
Illinois Quantum and Microelectronics Park
Illinois_Quantum_and_Microelectronics_Park
Quantum computing algorithm
to simulate classically. A variety of qubit magic state distillation routines and distillation routines for qubits with various advantages have been proposed
Magic_state_distillation
Mechanism in quantum computing
(target) qubit is conditioned on the state of the first (control) qubit. Because the phase of the second qubit is being "kicked back" to the first qubit, this
Phase_kickback
Quantum error correction code
protect against single-qubit phase-flip errors Zi, its code distance as a quantum code is d = 1. The stabilizer group of the 3-qubit repetition code has
Stabilizer_code
Open-source software development kit
circuits and execute them on real quantum processors (such as superconducting qubit systems) or on various other compatible quantum devices. Over time, Qiskit’s
Qiskit
Computational complexity class of problems
such that For all n ∈ N {\displaystyle n\in \mathbb {N} } , Qn takes n qubits as input and outputs 1 bit For all x in L, P r ( Q | x | ( x ) = 1 ) ≥ 2
BQP
Model of computation
In quantum information, the one clean qubit model of computation is performed an n {\displaystyle n} qubit system with one pure state and n − 1 {\displaystyle
One_clean_qubit
Forecasting rules for quantum computing
unexpected challenges and breakthroughs. Rose's law observes that the number of qubits on chips doubles roughly every 18 months. The law is often described as
Quantum computing scaling laws
Quantum_computing_scaling_laws
Property of computational resources needed
configuration that a classical computer could track efficiently. In single-qubit systems, magic can be visualized as a departure from certain discrete points
Magic_(quantum_information)
Two-bit quantum communication protocol
classical bits of information by only transmitting a smaller number of qubits, under the assumption of sender and receiver pre-sharing an entangled resource
Superdense_coding
Elementary particle with negative charge
below a point called the critical temperature, materials can undergo a phase transition in which they lose all resistivity to electric current, in a
Electron
Intermediate representation for quantum instructions
} qubit[1] cin; qubit[4] a; qubit[4] b; qubit[1] cout; bit[5] ans; uint[4] a_in = 1; // a = 0001 uint[4] b_in = 15; // b = 1111 // initialize qubits reset
OpenQASM
Unit of quantum information
states. The qutrit is analogous to the classical radix-3 trit, just as the qubit, a quantum system described by a superposition of two orthogonal states
Qutrit
Programming language for quantum algorithms
Qubits as topological qubits. The quantum simulator that is shipped with the Quantum Development Kit today is capable of processing up to 32 qubits on
Q_Sharp
Quantum algorithm
.} Another Hadamard transform is applied to each qubit which makes it so that for qubits where s i = 1 {\displaystyle s_{i}=1} , its state is converted
Bernstein–Vazirani_algorithm
Simulators of quantum mechanical systems
Bose-Hubbard system and studies of phase transitions in lattices of superconducting resonators coupled to qubits. Hamiltonian simulation Quantum Turing
Quantum_simulator
Interdisciplinary theory behind quantum computing
bits that can only be 0 or 1, quantum information uses quantum bits or qubits that can exist simultaneously in multiple states because of superposition
Quantum_information_science
Quantum search algorithm
standard oracle, denoted here as U f {\displaystyle U_{f}} , uses an ancillary qubit system. The operation then represents an inversion (NOT gate) on the main
Grover's_algorithm
Information held in the state of a quantum system
which are based on the quantum bit "qubit". Qubit is somewhat analogous to the bit in classical computation. Qubits can be in a 1 or 0 quantum state, or
Quantum_information
Theorem in physics
\sigma _{y}} measurement upon Charlie's qubit. Indeed, this same logic applies to both measurements and all three qubits. Per the EPR criterion of reality,
Bell's_theorem
Model of quantum computing
structure of the qubits permits many quantum gates that are not induced by classical ones. For example, a relative phase shift is a 1 qubit gate given by
Quantum_circuit
Cryptography secured against quantum computers
doi:10.1145/3708471. ISSN 0004-5411. Gershon, Eric (2013-01-14). "New qubit control bodes well for future of quantum computing". phys.org. Heger, Monica
Post-quantum_cryptography
Deterministic quantum algorithm
\right)(|0\rangle -|1\rangle ).\end{aligned}}} We ignore the second qubit and the global phase and therefore have the state 1 2 ( | 0 ⟩ + ( − 1 ) f ( 0 ) ⊕ f
Deutsch–Jozsa_algorithm
Quantum algorithm
sequence of 1 qubit rotational gates and 2 qubit entangling gates.[citation needed] The number of repetitions of 1-qubit rotational gates and 2-qubit entangling
Variational quantum eigensolver
Variational_quantum_eigensolver
Quantum mechanics idea
"Entanglement swapping for Bell states and Greenberger–Horne–Zeilinger states in qubit systems". Physica A: Statistical Mechanics and Its Applications. 585 (585)
Entanglement_swapping
Experimental technology level
computing is characterized by quantum processors containing up to 1,000 qubits which are not advanced enough yet for fault-tolerance or large enough to
Noisy intermediate-scale quantum computing
Noisy_intermediate-scale_quantum_computing
Physical phenomenon
0.66. Three qubits are required for this process: the source qubit from the sender, the ancillary qubit, and the receiver's target qubit, which is maximally
Quantum_teleportation
Quantum mechanical macroscopic object
property enabled the resonator to be coupled with a superconducting phase qubit, a device used in quantum computing whose quantum state can be accurately
Quantum_machine
Networks connecting quantum processors
the transmission of information in the form of quantum bits, also called qubits, between physically separated quantum processors. A quantum processor is
Quantum_network
entanglement rate with the number of qubits. 12 March – Physicists at EPFL directly observed dissipative phase transitions (DPTs) in a superconducting
Timeline of quantum computing and communication
Timeline_of_quantum_computing_and_communication
Quantum-mechanical version of computer memory
retrieval. These states hold useful computational information known as qubits. Unlike the classical memory of everyday computers, the states stored in
Quantum_memory
Computer programming for quantum computers
# Put qubit `a` in a superposition cnot(a, b) # Entangle the two qubits in the Bell state m_a = measure(a) # Measure qubit `a`, collapsing qubit `b` as
Quantum_programming
Quantum error correction schemes can suppress the logical error rate arbitrarily low
surface code would require approximately 1,000–10,000 physical qubits per logical data qubit, though more pathological error types could drastically change
Threshold_theorem
Sub-field of quantum physics and optics
entanglement (e.g., BB84 protocol) Photonic Quantum Computing – Using photons as qubits to store and process quantum information. Trapped Ion Quantum Computing
Quantum_optics
Quantum state
to symmetric Dicke states. For the 4-qubit case, 7 local measurement settings is sufficient, while for the 6-qubit case 21 local measuement settings is
Dicke_state
Paradigm of quantum computer
encoded qubits efficiently with respect to the accuracy achieved, and can make LOQC fault-tolerant for photon loss, detector inefficiency and phase decoherence
Linear optical quantum computing
Linear_optical_quantum_computing
Upper bound on the knowable information of a quantum state
which completes the proof. In essence, the Holevo bound proves that given n qubits, although they can "carry" a larger amount of (classical) information (thanks
Holevo's_theorem
Theorem in quantum information theory
and computation, the Solovay–Kitaev theorem says that if a set of single-qubit quantum gates generates a dense subgroup of SU(2), then that set can be
Solovay–Kitaev_theorem
Quantum Mechanics in Neural Networks
structure intakes input from one layer of qubits, and passes that input onto another layer of qubits. This layer of qubits evaluates this information and passes
Quantum_neural_network
Problem in computer science
Trapped-ion QC Spin-based Kane QC Spin qubit QC NV center NMR QC Superconducting Charge qubit Flux qubit Phase qubit Transmon Quantum programming OpenQASM–Qiskit–IBM
Simon's_problem
Type of quantum information processing
classical) occur when multiple qubits are close to a tipping point. It is exactly at this point when the ground state (one set of qubit orientations) gets very
Adiabatic_quantum_computation
Theorem of quantum information theory
experimentally tested using nuclear magnetic resonance devices where a single qubit undergoes complete randomization; i.e., a pure state transforms to a random
No-hiding_theorem
Applications of machine learning to quantum physics
unitary transformations and measurements; Engineering of quantum gates from qubit networks with pairwise interactions, using time dependent or independent
Machine_learning_in_physics
Interdisciplinary research area
sometimes called quantum-enhanced machine learning. QML algorithms use qubits and quantum operations to try to improve the space and time complexity of
Quantum_machine_learning
Quantum logic gate
qubit controls whether a phase flip (which corresponds to applying the Pauli σ z {\displaystyle \sigma _{z}} matrix) is applied to the second qubit.
Cirac–Zoller controlled-NOT gate
Cirac–Zoller_controlled-NOT_gate
Theorem in quantum computing
between two logical qubits each of which is encoded in N physical qubits by pairing up the physical qubits of each encoded qubit ("code block"), and performing
Eastin–Knill_theorem
Linear optical quantum computing implementation
encoded qubits efficiently with respect to the accuracy achieved, and can make LOQC fault-tolerant for photon loss, detector inefficiency and phase decoherence
KLM_protocol
Search problem in quantum mechanics
a constant-depth quantum circuit restricted to a 2-dimensional grid of qubits using bounded fan-in gates but can't be solved by any sub-exponential size
Hidden linear function problem
Hidden_linear_function_problem
Continuous (non-quantized) quantities in quantum information science
continuous-variable quantum computation is "analog", while quantum computation using qubits is "digital." In more technical terms, the former makes use of Hilbert spaces
Continuous-variable quantum information
Continuous-variable_quantum_information
Point defect in diamonds
imaging and cellular process modeling. NV centers can also be initialized as qubits and enable the implementation of quantum algorithms and networks. It has
Nitrogen-vacancy_center
Very general problem in computer science
Trapped-ion QC Spin-based Kane QC Spin qubit QC NV center NMR QC Superconducting Charge qubit Flux qubit Phase qubit Transmon Quantum programming OpenQASM–Qiskit–IBM
Hidden_subgroup_problem
Structure that repeats in time; a novel type or phase of non-equilibrium matter
on Google's Sycamore processor, a quantum computing device. A chip of 20 qubits was used to obtain a many-body localization configuration of up and down
Time_crystal
Atoms kept at temperatures close to absolute zero
S2CID 17023076. Nemirovsky, Jonathan; Sagi, Yoav (2021), "Fast universal two-qubit gate for neutral fermionic atoms in optical tweezers", Physical Review Research
Ultracold_atom
Computational complexity of quantum algorithms
S ( n ) {\displaystyle S(n)} qubits must be accounted for. Each of the states of the S ( n ) {\displaystyle S(n)} qubits can be described by a two-dimensional
Quantum_complexity_theory
Entangled state of qubits
a type of highly entangled state of multiple qubits. Cluster states are generated in lattices of qubits with Ising type interactions. A cluster C is a
Cluster_state
Procedure in quantum information science
science used for error detection in quantum qubits. A parity measurement checks the equality of two qubits to return a true or false answer, which can
Parity_measurement
Remote quantum processors for computation
to a variety of quantum hardware modalities, including superconducting qubits, trapped ions, neutral atoms, and photonic systems. Major platforms such
Cloud-based_quantum_computing
Quantum computing applied to natural language processing
Trapped-ion QC Spin-based Kane QC Spin qubit QC NV center NMR QC Superconducting Charge qubit Flux qubit Phase qubit Transmon Quantum programming OpenQASM–Qiskit–IBM
Quantum natural language processing
Quantum_natural_language_processing
Cryptography based on quantum mechanical phenomena
string of qubits that perfectly correlates with what Bob measured in the opposite table. Her chance of generating a matching string of qubits will decrease
Quantum_cryptography
Metric for a quantum computer's capabilities
more qubits are added. To run an algorithm that only requires n < N qubits on an N-qubit machine, it could be beneficial to select a subset of qubits with
Quantum_volume
Quantum information paradigm
Trapped-ion QC Spin-based Kane QC Spin qubit QC NV center NMR QC Superconducting Charge qubit Flux qubit Phase qubit Transmon Quantum programming OpenQASM–Qiskit–IBM
Quantum_illumination
Model of quantum computation
Trapped-ion QC Spin-based Kane QC Spin qubit QC NV center NMR QC Superconducting Charge qubit Flux qubit Phase qubit Transmon Quantum programming OpenQASM–Qiskit–IBM
Quantum_Turing_machine
Method of inferring the results of a computation without running a quantum computer
Trapped-ion QC Spin-based Kane QC Spin qubit QC NV center NMR QC Superconducting Charge qubit Flux qubit Phase qubit Transmon Quantum programming OpenQASM–Qiskit–IBM
Counterfactual quantum computation
Counterfactual_quantum_computation
Class of quantum error correcting codes
Shor code and the Steane code are examples of this condition. The five-qubit error correcting code is not a CSS code because it mixes X and Z in its
CSS_code
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