Quantum-assisted quantum compiling
Compiling quantum algorithms for near-term quantum computers (accounting for
connectivity and native gate alphabets) is a major challenge that has received
significant attention both by industry and academia. Avoiding the exponential
overhead of classical simulation of quantum dynamics will allow compilation of
larger algorithms, and a strategy for this is to evaluate an algorithm's cost
on a quantum computer. To this end, we propose a variational hybrid
quantum-classical algorithm called quantum-assisted quantum compiling (QAQC).
In QAQC, we use the overlap between a target unitary $U$ and a trainable
unitary $V$ as the cost function to be evaluated on the quantum computer. More
precisely, to ensure that QAQC scales well with problem size, our cost involves
not only the global overlap ${\rm Tr} (V^\dagger U)$ but also the local
overlaps with respect to individual qubits. We introduce novel short-depth
quantum circuits to quantify the terms in our cost function, and we prove that
our cost cannot be efficiently approximated with a classical algorithm under
reasonable complexity assumptions. We present both gradient-free and
gradient-based approaches to minimizing this cost. As a demonstration of QAQC,
we compile various one-qubit gates on IBM's and Rigetti's quantum computers
into their respective native gate alphabets. Furthermore, we successfully
simulate QAQC up to a problem size of 9 qubits, and these simulations highlight
both the scalability of our cost function as well as the noise resilience of
QAQC. Future applications of QAQC include algorithm depth compression,
black-box compiling, noise mitigation, and benchmarking.
Sumeet Khatri Ryan LaRose Alexander Poremba Lukasz Cincio Andrew T. Sornborger Patrick J. Coles