simulate

Simulate quantum circuit

Since R2023a

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Installation Required: This functionality requires MATLAB Support Package for Quantum Computing.

Syntax

s = simulate(c)
s = simulate(c,inputState)

Description

s = simulate(c) simulates the quantum circuit c and returns the final state s after running the circuit. By default, each qubit in the circuit is initially in the |0〉 state.

example

s = simulate(c,inputState) additionally specifies the initial quantum state of the circuit.

The default value of inputState is "0...0" with as many "0" characters as there are qubits in c, where each qubit is in the |0〉 state. You can specify inputState as a string containing "0", "1", "+", or "-" with as many characters as there are qubits in c, a numeric vector, or a QuantumState object.

example

Examples

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Create a quantum circuit that consists of a Hadamard gate and a controlled X gate to entangle two qubits.

gates = [hGate(1); cxGate(1,2)];
c = quantumCircuit(gates);

Simulate the circuit using the default initial state where each qubit is in the |0〉 state.

s = simulate(c)
s = 

  QuantumState with properties:

    BasisStates: [4×1 string]
     Amplitudes: [4×1 double]
      NumQubits: 2

Show the final state of the circuit.

formula(s)
ans = 

    "0.70711 * |00> +
     0.70711 * |11>"

Plot the histogram of probabilities to measure possible states from the final state of the circuit.

histogram(s)

Histogram of probabilities to measure possible states

Create a quantum circuit that consists of a controlled X gate.

c = quantumCircuit(cxGate(1,2));

Simulate the circuit using initial states of "00", "01", "10", and "11". Show the final state of the circuit for each initial state after running the circuit.

for ket=["00", "01", "10", "11"]
    s = simulate(c,ket);
    disp("|" + ket + "> -> " + formula(s));
end
|00> -> 1 * |00>
|01> -> 1 * |01>
|10> -> 1 * |11>
|11> -> 1 * |10>

Input Arguments

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Quantum circuit, specified as a quantumCircuit object.

Initial state of the quantum circuit, specified as one of these values:

  • String scalar containing "0", "1", "+", or "-" with as many characters as there are qubits in c. For example, to specify four qubits that are in the initial state |0+1−〉, use "0+1-".

  • Numeric vector containing amplitudes of the initial states. The simulate function normalizes the amplitudes as inputState/norm(inputState). For example, you can construct the initial state |11〉 using [0 0 0 1]. (since R2023b)

  • QuantumState object, which accepts string scalar and numeric vector input to create a quantum state. For example, you can construct the initial state |11〉 using inputState = quantum.gate.QuantumState("11") or inputState = quantum.gate.QuantumState([0 0 0 1]). You can also specify a QuantumState object that is returned by running simulate on another quantum circuit (with the same number of qubits).

By default, the inputState is "0...0" with as many characters "0" as there are qubits in c.

Output Arguments

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Final state after running the circuit, returned as a QuantumState object. This object contains the normalized amplitudes of all possible 2n basis states of n qubits that form the quantum state. The quantum state can include a global phase or relative phases among the amplitudes of the basis states that do not affect the probabilities of measuring these states.

Limitations

  • Because the number of possible basis states of a quantum state scales as 2n as the number of qubits n grows, using simulate is practical for finding the final state s of a circuit only when n is less than about 15.

Version History

Introduced in R2023a

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See Also

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