Quantum-assisted quantum compiling

Journal Article · 13 May 2019 · Quantum

DOI: https://doi.org/10.22331/q-2019-05-13-140 · OSTI ID:1530785

Khatri, Sumeet ^[1]; LaRose, Ryan ^[2]; Poremba, Alexander ^[3]; Cincio, Lukasz  ^[4]; Sornborger, Andrew Tyler  ^[4]; Coles, Patrick Joseph  ^[4]

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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)

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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE; Laboratory Directed Research & Development (LDRD)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1530785
• Report Number(s): LA-UR--18-25861
• Journal Information: Quantum, Journal Name: Quantum Vol. 3; ISSN 2521-327X
• Publisher: Quantum Science Open CommunityCopyright Statement
• Country of Publication: United States
• Language: English