Optimal Synthesis into RXX(theta)

[ecpeterson]

Summary

This PR installs moves a few TwoQubitBasisDecomposer constructors into a helper, then constructs an XXDecomposer if the target gateset includes rzx. This implements some internal, nearly-published theory work.

Details and comments

Here's a brief usage demonstration:

from qiskit import transpile, QuantumRegister, QuantumCircuit
from qiskit.quantum_info import random_unitary
import numpy as np

# generate a random unitary
u = random_unitary(4)

q = QuantumRegister(2)
circuit = QuantumCircuit(q)
circuit.append(u, q)
output_circuit, = transpile([circuit], optimization_level=1, basis_gates=['rzx', 'rz', 'sx'], translation_method='synthesis')

print(output_circuit)

[ajavadia]

The rzx angles are not mentioned anywhere in the sample code. I know this is a limitation of basis_gates but how do you supply that?

[ecpeterson]

@ajavadia : At present, this is hard-coded in the internal package, exactly because I didn't want to make a decision about how basis_gates should be modified to cope with parameters. I'd love to hear opinions, of course.

[ajavadia]

I'm checking the code functionality. When I run this:

from qiskit import transpile, QuantumRegister, QuantumCircuit
from qiskit.quantum_info import random_unitary
import numpy as np

# generate a random unitary
u = random_unitary(4, seed=9)

q = QuantumRegister(2)
circuit = QuantumCircuit(q)
circuit.append(u, q)
output_circuit = transpile(circuit, basis_gates=['rzx', 'rz', 'sx'], translation_method='synthesis')

output_circuit.draw('mpl')

I get two uses of RZX(pi/4) and one use of CX:

However when I change translation_method='translator' I get something that can be simplified to just two uses of RZX(pi/4) (not sure why it emits RZX(-pi/4) at all, but it does). this

And finally when I use translation_method='unroller' it errors (I guess that's separate from this PR but it would be good to get to the bottom of it).

[ajavadia]

This is looking mostly good, and thanks for the recent updates. I left some comments which shouldn't be too much work, mostly around documenting user interfaces.

I think the main thing that I will work on after this is for a way to automatically convert transpiler basis_gates to embodiments in this decomposer. I like that the option exists to request certain XX embodiments, but using it is a bit involved at the moment. e.g. if I want XX everywhere and CX instead of XX(pi/2), I need to do:

xx_circuit = QuantumCircuit(2)
theta = Parameter('theta')
xx_circuit.rxx(theta, 0, 1)

cx_circuit = QuantumCircuit(2)
cx_circuit.h(0)
cx_circuit.cx(0, 1)
cx_circuit.h(1)
cx_circuit.s(0)
cx_circuit.s(1)
cx_circuit.h(0)
cx_circuit.h(1)
cx_circuit.global_phase += np.pi / 4
embodiments = {t: xx_circuit.bind_parameters({theta: t}) for t in [np.pi/4, np.pi/6]}
embodiments.update({np.pi/2: cx_circuit})

decomposer = XXDecomposer(euler_basis='U3', embodiments=embodiments)
output_circuit = decomposer(u, basis_fidelity=.99)

[ecpeterson]

I agree that the "embodiments" stuff is not super slick, mainly since it hasn't been flexed much. I'm sure you'll be able to find ergonomic improvements as you poke around.

[coveralls]

Pull Request Test Coverage Report for Build 1418807430

• 399 of 441 (90.48%) changed or added relevant lines in 11 files are covered.
• 3 unchanged lines in 1 file lost coverage.
• Overall coverage increased (+0.05%) to 82.37%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/transpiler/passes/synthesis/unitary_synthesis.py	11	13	84.62%
qiskit/quantum_info/synthesis/xx_decompose/paths.py	37	40	92.5%
qiskit/quantum_info/synthesis/xx_decompose/circuits.py	88	96	91.67%
qiskit/quantum_info/synthesis/xx_decompose/polytopes.py	95	103	92.23%
qiskit/quantum_info/synthesis/xx_decompose/decomposer.py	103	113	91.15%
qiskit/transpiler/passes/utils/gate_direction.py	3	14	21.43%

Files with Coverage Reduction	New Missed Lines	%
qiskit/pulse/library/waveform.py	3	90.38%

Totals
Change from base Build 1418224622:	0.05%
Covered Lines:	49655
Relevant Lines:	60283

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💛 - Coveralls