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initGate

Initialization gate with specified qubit states

Since R2023b

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

    Syntax

    cg = initGate(targetQubits,state)
    cg = initGate(targetQubits,state,RotationThreshold=thresh)

    Description

    example

    cg = initGate(targetQubits,state) returns a quantum.gate.CompositeGate object that initializes the target qubits to the specified state up to a global phase, that is, scaled by a constant factor. The target qubits must be in the |0〉 state.

    cg = initGate(targetQubits,state,RotationThreshold=thresh) also removes single-qubit rotation gates that have an angle magnitude less than the rotation threshold.

    Examples

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    This example uses:

    Open Live Script

    Create an initialization gate that initializes three target qubits to amplitudes between pi/4 and 2*pi.

    cg = initGate(1:3,pi/4*(1:8))
    cg = 
  CompositeGate with properties:

             Name: "init"
    ControlQubits: [1×0 double]
     TargetQubits: [1 2 3]
            Gates: [3×1 quantum.gate.CompositeGate]

    Plot the initialization gate. The plotted gate consists of three inverse UCRY gates. The first inverse UCRY gate acts on qubit 1, the second inverse UCRY gate acts on qubits 1 and 2, and the third inverse UCRY gate acts on qubits 1, 2, and 3.

    plot(cg)

    Simulate a quantum circuit with the initialization gate. Here, the global phase is 0.28/pi.

    s = simulate(quantumCircuit(cg));
formula(s)
    ans = 
    "0.070014 * |000> +
     0.14003  * |001> +
     0.21004  * |010> +
     0.28006  * |011> +
     0.35007  * |100> +
     0.42008  * |101> +
     0.4901   * |110> +
     0.56011  * |111>"

    This example uses:

    Open Live Script

    Create an initialization gate for six target qubits. Use a basis string to initialize three qubits to the + state and three qubits to the - state.

    cg = initGate(1:6,"+++---")
    cg = 
  CompositeGate with properties:

             Name: "init"
    ControlQubits: [1×0 double]
     TargetQubits: [1 2 3 4 5 6]
            Gates: [9×1 quantum.gate.SimpleGate]

    Plot the initialization gate.

    plot(cg)

    Simulate a quantum circuit with the initialization gate and verify that the qubits are initialized to the input state, up to a global phase.

    s = simulate(quantumCircuit(cg));
formula(s)
    ans = 
"1 * |+++--->"

    Input Arguments

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    Target qubits of the gate, specified as a positive integer scalar index or vector of qubit indices.

    Example: 1

    Example: 3:5

    Target state to initialize, specified as one of these values:

    • String scalar containing "0", "1", "+", or "-" with as many characters as the number of target qubits. For example, to specify four qubits with a target state of |0+1−〉, use "0+1-".

    • Numeric vector containing amplitudes of the target states. The vector must have length 2n, where n is the number of target qubits. The initGate function normalizes the amplitudes as state/norm(state).

    • QuantumState object that has the same number of qubits as the number of target qubits.

    Rotation threshold, specified as one of these values:

    • positive real number

    • "auto" — Set the threshold to the default value of 2*pi*eps.

    • "none" — Do not remove gates.

    The initGate function removes single-qubit rotation gates that have an angle magnitude less than this rotation threshold.

    References

    [1] Shende, Vivek V., Stephen S. Bullock, and Igor L. Markov. "Synthesis of Quantum Logic Circuits." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 25, no. 6 (June 2006): 1000–1010. https://doi.org/10.1109/TCAD.2005.855930.

    Version History

    Introduced in R2023b

    See Also

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