Using XIR

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Examples

The examples below demonstrate how the XIR can be used to model quantum circuits.

Qubit Circuits

For the sake of brevity, the following preamble is omitted from the qubit circuit examples:

// Gate Declarations
gate H [a];
gate X [a];
gate Z [a];
gate SWAP [a, b];
gate Phase(theta) [a];

// Output Declarations
out amplitude(state) [a, b];

// Gate Definitions
gate CNOT [c, t]:
    ctrl [c] X | [t];
end;

Bell State Amplitudes

To return the amplitudes of a Bell state:

H | [0];
CNOT | [0, 1];

amplitude(state: [0, 0]) | [0, 1];
amplitude(state: [0, 1]) | [0, 1];
amplitude(state: [1, 0]) | [0, 1];
amplitude(state: [1, 1]) | [0, 1];

GHZ State Preperation

To prepare a Greenberger–Horne–Zeilinger state over four qubits:

H | [0];
ctrl [0] X | [1];
ctrl [1] X | [2];
ctrl [2] X | [3];

Qubit State Teleportation

To (locally) teleport a qubit state from wire 0 to wire 2:

H | [1];
CNOT | [1, 2];

CNOT | [0, 1];
H | [0];

ctrl [1] X | [2];
ctrl [0] Z | [2];

Grover Diffusion Operator

To apply the Grover Diffusion Operator to three qubits:

gate H2:
    H | [0];
    H | [1];
end;

gate X2:
    X | [0];
    X | [1];
end;

H2 | [0, 1];
X2 | [0, 1];

Z | [2];
ctrl [0, 1] X | [2];
Z | [2];

X2 | [0, 1];
H2 | [0, 1];

Quantum Fourier Transform

To apply the Quantum Fourier Transform to four qubits:

gate P2 [w]: Phase(theta: pi / 2) | [w]; end;
gate P3 [w]: Phase(theta: pi / 4) | [w]; end;
gate P4 [w]: Phase(theta: pi / 8) | [w]; end;

H | [0];
ctrl [1] P2 | [0];
ctrl [2] P3 | [0];
ctrl [3] P4 | [0];

H | [1];
ctrl [2] P2 | [1];
ctrl [3] P3 | [1];

H | [2];
ctrl [3] P2 | [2];

H | [3];

SWAP | [0, 3];
SWAP | [1, 2];

Continuous Variable Circuits

Similar to the qubit examples, the preamble below is assumed for all continuous variable circuits:

// Function Declarations
func sqrt;

// Gate Declarations
gate S(z) [a];
gate X(p) [a];
gate Z(p) [a];
gate BS(theta, phi) [a, b];

// Output Declarations
out MeasureX [a];
out MeasureP [a];
out MeasureFock [a, b, c];

Gaussian State Teleportation

To teleport a Gaussian state from wire 0 to wire 2:

S(-1.23) | [1];
S(1.23) | [2];
BS(theta: pi / 4, phi: pi) | [1, 2];

BS(theta: pi / 4, phi: pi) | [0, 1];
MeasureX | [0];
MeasureP | [1];

X(sqrt(2) * outs[0]) | [2];
Z(sqrt(2) * outs[1]) | [2];

GKP State Approximation

To approximate a Gottesman-Kitaev-Preskill state with a Fock cutoff dimension of 4:

options:
    cutoff: 4;
end;

S(-1.38155106) | [0];
S(-1.21699567) | [1];
S(0.779881700) | [2];

BS(1.04182349, 1.483536390) | [0, 1];
BS(0.87702211, 1.696290600) | [1, 2];
BS(0.90243916, -0.24251599) | [0, 1];

S(0.1958) | [2];

MeasureFock | [0, 1, 2];
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