Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`QuantumFramework`
QuantumCircuitOperator  |
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| wraps a single quantum object (operator, channel, state or measurement operator) as a one-element circuit. | |
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| "Bell" "Toffoli" "Grover"[f] | |
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| "IXYZ" | |
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QuantumCircuitOperator[…]["prop"] will give the property prop of the circuit.
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The following properties prop are supported:
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"Arity" | the arity of the circuit: the number of input qudits it acts on | |
"Width" | the number of wires (qudits) the circuit spans | |
"Depth" | the depth of the circuit: the number of gate layers | |
"OperatorCount" "GateCount" | the total number of operators (gates) in the circuit | |
"InputDimensions" "OutputDimensions" | the list of input / output qudit dimensions of the circuit | |
"Operators" | the list of operators (gates) in the circuit | |
"CircuitOperator" | the circuit operator: the single quantum operator representing the overall transformation done by the circuit | |
"Association" | the underlying data of the circuit, as an Association | |
"Orders" | the list of orders (input/output qudits) of the operators in the circuit | |
"Label" | the label of the circuit | |
"Picture" | the picture of the circuit (e.g. Schrodinger, Heisenberg or PhaseSpace) | |
"Parameters" | the list of parameters of a parametrized circuit | |
"ParameterArity" | the number of parameters of the circuit | |
"Properties" | the list of supported properties | |
"Diagram" | the diagram of the quantum circuit | |
"Topology" | the circuit topology graph, with qudits/wires as vertices and gates as edges | |
"TensorNetwork" | the corresponding tensor network representing the circuit | |
"TensorNetworkGraph" | the graph of the circuit's tensor network | |
"QASM" | the circuit in OpenQASM 3.0 | |
"QiskitCircuit" "Qiskit" | the corresponding circuit in Qiskit (note you need Python as external evaluator for this property) | |
"Shift" | shift the order of the circuit (the qudits it acts on) by n |
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There are many named-circuits, , for example, Bell, Toffoli, Grover (and its many oracles), quantum phase estimation, quantum fourier transform, Bernstein-Vazirani algorithm (and its many oracles), Graph and etc.
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"Bell" | Bell-state preparation circuit ({H, CNOT}); prepares a Bell pair from the all-zeros state | |
"GHZ"[n] | preparation circuit for the n-qubit GHZ state (H, then a CNOT chain) | |
"Graph"[g] | graph-state preparation circuit for a graph g (Hadamard on each vertex, then an entangling gate along each edge) | |
"QuantumState"[qs] "StatePreparation"[qs] | a circuit that prepares the quantum state qs (qubit states via the multiplexer / RZY decomposition, general qudits via a block-diagonal construction) | |
"Number"[n,qubits] | encodes the integer n as a computational basis state (X gates on the 1-bits of n) | |
"PhaseNumber"[n,qubits,h] | encodes the number n in qubits qubits as relative phases; with a leading Hadamard layer (one H per qubit) when h is True | |
"Toffoli" | Toffoli (CCNOT) gate as a Clifford+T decomposition (15 gates) | |
"Fredkin" | Fredkin (controlled-SWAP) gate as a decomposition (18 gates) | |
"Magic" | the magic-basis circuit mapping the computational basis to the Bell basis ({S, S, H, CNOT}) | |
"Fourier"[n] | n-qubit quantum Fourier transform (QFT) | |
"InverseFourier"[n] | n-qubit inverse quantum Fourier transform | |
"BooleanOracle"[f] | Boolean oracle for a Boolean function f (ESOP-decomposed into multi-controlled NOT gates) | |
"BooleanOracleR"[f] | Boolean oracle for a Boolean function f built from rotation gates (controlled rotations and CNOTs; default rotation "RZ"[Pi] | |
"PhaseOracle"[f] | phase oracle for a Boolean function f (encodes f in the phase via kickback) | |
"GrayOracle"[angles,prec] | Gray-code-optimized rotation oracle encoding a list or function of angles to precision prec (default "RY" | |
"Grover"[f] | Grover operator (oracle and diffusion) for a Boolean function f | |
"Grover0"[f] | Grover operator for f, with the diffusion reflecting about the all-zeros state (controlled-on-0 gate) | |
"GroverPhase"[f] | Grover operator for f using a phase oracle | |
"GroverPhase0"[f] | Grover operator for f using a phase oracle, with controlled-on-0 diffusion | |
"GroverDiffusion"[n] | the Grover diffusion (amplitude-amplification) operator on n qubits | |
"GroverDiffusion0"[n] | Grover diffusion on n qubits, with a controlled-on-0 gate | |
"GroverPhaseDiffusion"[n] | Grover diffusion on n qubits, for a phase oracle | |
"GroverPhaseDiffusion0"[n] | Grover diffusion on n qubits, for a phase oracle and with a controlled-on-0 gate | |
"Deutsch"[f] | Deutsch circuit for a Boolean function f (single-qubit Deutsch-Jozsa) | |
"DeutschPhase"[f] | Deutsch circuit for f using a phase oracle | |
"DeutschJozsa"[k,n] "DeutschJozsa"[BooleanFunction[k-1,n]] | Deutsch-Jozsa circuit for the (k-1)th Boolean function in n variables | |
"DeutschJozsaPhase"[k,n] "DeutschJozsaPhase"[BooleanFunction[k-1,n]] | Deutsch-Jozsa circuit using the phase oracle of the (k-1)th Boolean function in n variables | |
"DeutschJozsaBooleanOracle"[k,n] "DeutschJozsaBooleanOracle"[BooleanFunction[k-1,n]] | Deutsch-Jozsa Boolean oracle of the (k-1)th Boolean function in n variables | |
"DeutschJozsaPhaseOracle"[k,n] "DeutschJozsaPhaseOracle"[BooleanFunction[k-1,n]] | Deutsch-Jozsa phase oracle of the (k-1)th Boolean function in n variables | |
"BernsteinVazirani"[s] | Bernstein-Vazirani circuit for a secret bit-string s | |
"BernsteinVaziraniOracle"[s] | Bernstein-Vazirani oracle for a secret binary vector or bit-string s | |
"Simon"[s] | Simon circuit for a secret binary vector or bit-string s | |
"SimonOracle"[s] | Simon oracle for a secret binary vector or bit-string s | |
"PhaseEstimation"[u,n] | quantum phase-estimation circuit for a unitary operator u using n counting qubits (qubit operators only) | |
"Trotterization"[ops,order,reps,t] | Trotter-Suzuki decomposition of a list of operators ops, for a given order (1, 2, 4, 6, …), number of repetitions reps, and time t (based on Suzuki's recursion relation) | |
"Controlled"[qc,c1,c0] "C"[qc,c1,c0] | the controlled version of a circuit qc, controlled on the c1 qubits (value 1) and the c0 qubits (value 0) | |
"Multiplexer"[op1,op2,...] | a multiplexer (uniformly-controlled gate): applies the operator selected by the binary value of the control qubits | |
"ControlledMultiplexer"[m,v] | the multiplexer-based linear-solver circuit produced by QuantumLinearSolve for a matrix m and vector v | |
"Switch"[a,b] | quantum-switch circuit of two operators a and b (their order of application coherently controlled) | |
"CHSH" | CHSH Bell-test circuit with measurement angle θ π/4 | |
"LeggettGarg" | Leggett-Garg circuit for the Leggett-Garg inequality, with measurement angle θ π/4 | |
"WignerCHSH" | CHSH circuit in the Wigner (WignerMIC) basis, with measurement angle θ π/4 |
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Tutorials
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Related Workflows
Examples
(39)
Basic Examples
(4)
Create a quantum circuit composed of only single qubit gates:
In[1]:=
qc=
["X"],
["Y",{2}]
 | QuantumCircuitOperator |
 | QuantumOperator |
| QuantumOperator |
Out[1]=
QuantumCircuitOperator
 |
|
Draw the associated circuit diagram:
In[2]:=
qc["Diagram"]
Out[2]=
Shorthand representation of the circuit:
Recover a shorthand specification of the circuit:
The shorthand, fed back to the constructor, rebuilds the same circuit:
Create a circuit with multi-qubit gates:
Draw the associated circuit diagram:
The above circuit has a shorthand representation, too:
The dashed line between the two Hadamards indicates that they are defined as a tensor product, although they are separable. Compare it with this case, where each gate is placed separately:
A quantum state is transformed by applying the circuit to it:
If no input is given, the initial state is taken to be the corresponding register state:
A quantum circuit can include many kinds of quantum objects: here a state, gates, a noise channel, a phase, and measurements:
Draw its circuit diagram:
The outcome probabilities after running the circuit on the register state: