Title: Quantum-assisted quantum compiling

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 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 $\mathrm{T}\mathrm{r}\left(V^{†}U\right)$ 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.

Authors:

Khatri, Sumeet ^[1]; LaRose, Ryan ^[2]; Poremba, Alexander ^[3]; Cincio, Lukasz  ^[4];

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Sornborger, Andrew Tyler  ^[4];

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Coles, Patrick Joseph  ^[4]

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+ Show Author Affiliations

1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Louisiana State Univ., Baton Rouge, LA (United States)
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Michigan State Univ., East Lansing, MI (United States)
3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States)
4. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:

2019-05-13

Research Org.:

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:

USDOE; Laboratory Directed Research & Development (LDRD)

OSTI Identifier:

1530785

Report Number(s):

LA-UR-18-25861
Journal ID: ISSN 2521-327X

Grant/Contract Number:  

89233218CNA000001

Resource Type:

Accepted Manuscript

Journal Name:

Quantum

Additional Journal Information:

Journal Volume: 3; Journal ID: ISSN 2521-327X

Publisher:

Quantum Science Open Community

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING