Abstract
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 unitaryUand a trainable unitaryVas 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 overlapTr(V†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.
Highlights
Factoring [1], approximate optimization [2], and simulation of quantum systems [3] are some of the applications for which quantum computers have been predicted to provide speedups over classical computers
We propose an alternative cost function involving a weighted average between the function in (5) and a “local” cost function: Cq(U, V ) := qCHST(U, V ) + (1 − q)CLHST(U, V ), (7)
In Appendix B, we show that CLHST is a faithful cost function: Proposition 1
Summary
Factoring [1], approximate optimization [2], and simulation of quantum systems [3] are some of the applications for which quantum computers have been predicted to provide speedups over classical computers. As a proof-of-principle, we implement QAQC on both IBM’s and Rigetti’s quantum computers, and we compile various one-qubit gates to the native gate alphabets used by these hardwares. To our knowledge, this is the first compilation of a target unitary with cost evaluation on actual NISQ hardware. We successfully implement QAQC on both a noiseless and noisy simulator for problems as large as 9-qubit unitaries These larger scale implementations illustrate the scalability of our cost function, and in the case of the noisy simulator, show a somewhat surprising resilience to noise.
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