Quantumassisted quantum compiling
Abstract
Compiling quantum algorithms for nearterm 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 quantumclassical algorithm called quantumassisted 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 $\mathrm{T}\mathrm{r}\left({V}^{\u2020}U\right)$ but also the local overlaps with respect to individual qubits. We introduce novel shortdepth 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 gradientfree and gradientbased approaches to minimizing this cost. As a demonstration of QAQC, we compile various onequbit 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, blackbox compiling, noise mitigation, and benchmarking.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Louisiana State Univ., Baton Rouge, LA (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Michigan State Univ., East Lansing, MI (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE; Laboratory Directed Research & Development (LDRD)
 OSTI Identifier:
 1530785
 Report Number(s):
 LAUR1825861
Journal ID: ISSN 2521327X
 Grant/Contract Number:
 89233218CNA000001
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Quantum
 Additional Journal Information:
 Journal Volume: 3; Journal ID: ISSN 2521327X
 Publisher:
 Quantum Science Open Community
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
Citation Formats
Khatri, Sumeet, LaRose, Ryan, Poremba, Alexander, Cincio, Lukasz, Sornborger, Andrew Tyler, and Coles, Patrick Joseph. Quantumassisted quantum compiling. United States: N. p., 2019.
Web. doi:10.22331/q20190513140.
Khatri, Sumeet, LaRose, Ryan, Poremba, Alexander, Cincio, Lukasz, Sornborger, Andrew Tyler, & Coles, Patrick Joseph. Quantumassisted quantum compiling. United States. https://doi.org/10.22331/q20190513140
Khatri, Sumeet, LaRose, Ryan, Poremba, Alexander, Cincio, Lukasz, Sornborger, Andrew Tyler, and Coles, Patrick Joseph. Mon .
"Quantumassisted quantum compiling". United States. https://doi.org/10.22331/q20190513140. https://www.osti.gov/servlets/purl/1530785.
@article{osti_1530785,
title = {Quantumassisted quantum compiling},
author = {Khatri, Sumeet and LaRose, Ryan and Poremba, Alexander and Cincio, Lukasz and Sornborger, Andrew Tyler and Coles, Patrick Joseph},
abstractNote = {Compiling quantum algorithms for nearterm 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 quantumclassical algorithm called quantumassisted quantum compiling (QAQC). In QAQC, we use the overlap between a target unitaryUand a trainable unitary Vas 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 Tr(V†U) but also the local overlaps with respect to individual qubits. We introduce novel shortdepth 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 gradientfree and gradientbased approaches to minimizing this cost. As a demonstration of QAQC, we compile various onequbit 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, blackbox compiling, noise mitigation, and benchmarking.},
doi = {10.22331/q20190513140},
journal = {Quantum},
number = ,
volume = 3,
place = {United States},
year = {2019},
month = {5}
}
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