Example: Gate synthesis

This example demonstrates how the built-in compiler can be used to perform gate synthesis.

Synthesizing Single-Qubit Gates

We begin by generating a random gate in \(SU(2)\); we will synthesize this gate later.

[2]:

import trueq as tq

# create a Haar random SU(2) gate and print its matrix representation
U = tq.Gate.random(2)
U

[2]:

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We can perform single qubit gate decomposition into a number of possible “modes”. Here we decompose the gate U into a ZXZXZ decomposition, which is short hand for \(Z(\theta)X(90)Z(\phi)X(90)Z(\gamma)\). See QubitMode for a complete list of all available single qubit decompositions.

[3]:

synthesized_gate = tq.math.QubitMode.ZXZXZ.decompose(U)

# print the synthesized gate as a list of single-qubit rotations about Z and X
synthesized_gate

[3]:

[('Z', -257.7385690112652),
 ('X', 90),
 ('Z', 122.042638725902),
 ('X', 90),
 ('Z', -106.283141468562)]

Synthesizing Two-Qubit Gates

In the event that we want to express a two-qubit gate in terms of a different two-qubit gate, we can use the compiler to synthesize the desired gate. Here we decompose a random \(SU(4)\) operation so that it can be implemented using iSWAP gates.

[4]:

# define the gate to be synthesized
gate_to_be_synthesized = tq.Gate.random(4)

# re-express the gate using an iswap gate as the two-qubit gate
two_qubit_synthesized_gate = tq.math.decompose_unitary(
    target_gate=gate_to_be_synthesized, given_gate=tq.Gate.iswap
)

# print the synthesized gate
two_qubit_synthesized_gate

[4]:

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Circuit Key: No key present in circuit.
Marker 0 Compilation tools may only recompile cycles with equal markers.	(0): Gate(Y, X, ...) Name: Gate(Y, X, ...) Generators: 'Y': -30.76 'X': 167.589 'Z': 74.986 Matrix:	(1): Gate(Y, X, ...) Name: Gate(Y, X, ...) Generators: 'Y': -81.07 'X': 50.75 'Z': -33.329 Matrix:
Marker 0 Compilation tools may only recompile cycles with equal markers.	(0, 1): Gate.iswap Name: Gate.iswap Aliases: Gate.iswap Likeness: iSWAP Generators: 'YY': -90.0 'XX': -90.0 Matrix:
Marker 0 Compilation tools may only recompile cycles with equal markers.	(0): Gate(Y, X, ...) Name: Gate(Y, X, ...) Generators: 'Y': 67.651 'X': 34.193 'Z': 33.037 Matrix:	(1): Gate(Y, X, ...) Name: Gate(Y, X, ...) Generators: 'Y': 0.889 'X': 43.484 'Z': -83.916 Matrix:
Marker 0 Compilation tools may only recompile cycles with equal markers.	(0, 1): Gate.iswap Name: Gate.iswap Aliases: Gate.iswap Likeness: iSWAP Generators: 'YY': -90.0 'XX': -90.0 Matrix:
Marker 0 Compilation tools may only recompile cycles with equal markers.	(0): Gate(Y, X, ...) Name: Gate(Y, X, ...) Generators: 'Y': 18.218 'X': 96.185 'Z': -139.688 Matrix:	(1): Gate(Y, X, ...) Name: Gate(Y, X, ...) Generators: 'Y': -139.535 'X': -64.795 'Z': 30.824 Matrix:
Marker 0 Compilation tools may only recompile cycles with equal markers.	(0, 1): Gate.iswap Name: Gate.iswap Aliases: Gate.iswap Likeness: iSWAP Generators: 'YY': -90.0 'XX': -90.0 Matrix:
Marker 0 Compilation tools may only recompile cycles with equal markers.	(0): Gate(Y, X, ...) Name: Gate(Y, X, ...) Generators: 'Y': -135.41 'X': 56.091 'Z': -64.089 Matrix:	(1): Gate(Y, X, ...) Name: Gate(Y, X, ...) Generators: 'Y': -39.749 'X': -23.555 'Z': 0.606 Matrix:

This circuit can be verified to reproduce the original random unitary using an ideal simulator:

[5]:

matrix = tq.Simulator().operator(two_qubit_synthesized_gate).mat()

# This will result in an identity gate up to a global complex phase.
tq.plot_mat(matrix @ gate_to_be_synthesized.adj.mat)

../../_images/guides_compilation_synthesis_8_0.png

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Download this file as Jupyter notebook: synthesis.ipynb.