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 Lab. (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. doi:10.22331/q20190513140.
Khatri, Sumeet, LaRose, Ryan, Poremba, Alexander, Cincio, Lukasz, Sornborger, Andrew Tyler, and Coles, Patrick Joseph. Mon .
"Quantumassisted quantum compiling". United States. doi: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}
}
Works referenced in this record:
A simple formula for the average gate fidelity of a quantum dynamical operation
journal, October 2002
 Nielsen, Michael A.
 Physics Letters A, Vol. 303, Issue 4
Compiling quantum circuits to realistic hardware architectures using temporal planners
journal, February 2018
 Venturelli, Davide; Do, Minh; Rieffel, Eleanor
 Quantum Science and Technology, Vol. 3, Issue 2
Glassy Phase of Optimal Quantum Control
journal, January 2019
 Day, Alexandre G. R.; Bukov, Marin; Weinberg, Phillip
 Physical Review Letters, Vol. 122, Issue 2
Power of One Bit of Quantum Information
journal, December 1998
 Knill, E.; Laflamme, R.
 Physical Review Letters, Vol. 81, Issue 25
Quantum circuit learning
journal, September 2018
 Mitarai, K.; Negoro, M.; Kitagawa, M.
 Physical Review A, Vol. 98, Issue 3
Barren plateaus in quantum neural network training landscapes
journal, November 2018
 McClean, Jarrod R.; Boixo, Sergio; Smelyanskiy, Vadim N.
 Nature Communications, Vol. 9, Issue 1
Optimal quantum circuits for general twoqubit gates
journal, March 2004
 Vatan, Farrokh; Williams, Colin
 Physical Review A, Vol. 69, Issue 3
Asymptotically Optimal Topological Quantum Compiling
journal, April 2014
 Kliuchnikov, Vadym; Bocharov, Alex; Svore, Krysta M.
 Physical Review Letters, Vol. 112, Issue 14
In situ upgrade of quantum simulators to universal computers
journal, August 2018
 Dive, Benjamin; Pitchford, Alexander; Mintert, Florian
 Quantum, Vol. 2
Simulating physics with computers
journal, June 1982
 Feynman, Richard P.
 International Journal of Theoretical Physics, Vol. 21, Issue 67
A software methodology for compiling quantum programs
journal, February 2018
 Häner, Thomas; Steiger, Damian S.; Svore, Krysta
 Quantum Science and Technology, Vol. 3, Issue 2
A variational eigenvalue solver on a photonic quantum processor
journal, July 2014
 Peruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter
 Nature Communications, Vol. 5, Issue 1
An efficient quantum compiler that reduces T count
journal, September 2018
 Heyfron, Luke E.; Campbell, Earl T.
 Quantum Science and Technology, Vol. 4, Issue 1
Quantum computations: algorithms and error correction
journal, December 1997
 Kitaev, A. Yu
 Russian Mathematical Surveys, Vol. 52, Issue 6
Adding control to arbitrary unknown quantum operations
journal, August 2011
 Zhou, XiaoQi; Ralph, Timothy C.; Kalasuwan, Pruet
 Nature Communications, Vol. 2, Issue 1
Fractal decomposition of exponential operators with applications to manybody theories and Monte Carlo simulations
journal, June 1990
 Suzuki, Masuo
 Physics Letters A, Vol. 146, Issue 6
Quantum compiling with diffusive sets of gates
journal, July 2018
 Zhiyenbayev, Y.; Akulin, V. M.; Mandilara, A.
 Physical Review A, Vol. 98, Issue 1
Learning the quantum algorithm for state overlap
journal, November 2018
 Cincio, Lukasz; Subaşı, Yiğit; Sornborger, Andrew T.
 New Journal of Physics, Vol. 20, Issue 11
Automated optimization of large quantum circuits with continuous parameters
journal, May 2018
 Nam, Yunseong; Ross, Neil J.; Su, Yuan
 npj Quantum Information, Vol. 4, Issue 1
General teleportation channel, singlet fraction, and quasidistillation
journal, September 1999
 Horodecki, Michał; Horodecki, Paweł; Horodecki, Ryszard
 Physical Review A, Vol. 60, Issue 3
A review of procedures to evolve quantum algorithms
journal, February 2009
 Gepp, Adrian; Stocks, Phil
 Genetic Programming and Evolvable Machines, Vol. 10, Issue 2
PolynomialTime Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
journal, October 1997
 Shor, Peter W.
 SIAM Journal on Computing, Vol. 26, Issue 5
Asymptotically Optimal Approximation of Single Qubit Unitaries by Clifford and $T$ Circuits Using a Constant Number of Ancillary Qubits
journal, May 2013
 Kliuchnikov, Vadym; Maslov, Dmitri; Mosca, Michele
 Physical Review Letters, Vol. 110, Issue 19
On the Hardness of Distinguishing MixedState Quantum Computations
conference, January 2005
 Rosgen, B.; Watrous, J.
 20th Annual IEEE Conference on Computational Complexity (CCC'05)
Quantum Circuit Simplification and Level Compaction
journal, March 2008
 Maslov, D.; Dueck, G. W.; Miller, D. M.
 IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems, Vol. 27, Issue 3
Optimization of the SolovayKitaev algorithm
journal, May 2013
 Pham, Tien Trung; Van Meter, Rodney; Horsman, Clare
 Physical Review A, Vol. 87, Issue 5
swap test and HongOuMandel effect are equivalent
journal, May 2013
 GarciaEscartin, Juan Carlos; ChamorroPosada, Pedro
 Physical Review A, Vol. 87, Issue 5
A blueprint for demonstrating quantum supremacy with superconducting qubits
journal, April 2018
 Neill, C.; Roushan, P.; Kechedzhi, K.
 Science, Vol. 360, Issue 6385
Quantum autoencoders for efficient compression of quantum data
journal, August 2017
 Romero, Jonathan; Olson, Jonathan P.; AspuruGuzik, Alan
 Quantum Science and Technology, Vol. 2, Issue 4
Programming languages and compiler design for realistic quantum hardware
journal, September 2017
 Chong, Frederic T.; Franklin, Diana; Martonosi, Margaret
 Nature, Vol. 549, Issue 7671
Error mitigation extends the computational reach of a noisy quantum processor
journal, March 2019
 Kandala, Abhinav; Temme, Kristan; Córcoles, Antonio D.
 Nature, Vol. 567, Issue 7749
Impossibility of Classically Simulating OneCleanQubit Model with Multiplicative Error
journal, May 2018
 Fujii, Keisuke; Kobayashi, Hirotada; Morimae, Tomoyuki
 Physical Review Letters, Vol. 120, Issue 20
A generative modeling approach for benchmarking and training shallow quantum circuits
journal, May 2019
 Benedetti, Marcello; GarciaPintos, Delfina; Perdomo, Oscar
 npj Quantum Information, Vol. 5, Issue 1
Variational quantum state diagonalization
journal, June 2019
 LaRose, Ryan; Tikku, Arkin; O’NeelJudy, Étude
 npj Quantum Information, Vol. 5, Issue 1
Works referencing / citing this record:
Variational consistent histories as a hybrid algorithm for quantum foundations
journal, July 2019
 Arrasmith, Andrew; Cincio, Lukasz; Sornborger, Andrew T.
 Nature Communications, Vol. 10, Issue 1
Variational quantum state diagonalization
journal, June 2019
 LaRose, Ryan; Tikku, Arkin; O’NeelJudy, Étude
 npj Quantum Information, Vol. 5, Issue 1
Variational quantum unsampling on a quantum photonic processor
journal, January 2020
 Carolan, Jacques; Mohseni, Masoud; Olson, Jonathan P.
 Nature Physics, Vol. 16, Issue 3
Parameterized quantum circuits as machine learning models
journal, October 2019
 Benedetti, Marcello; Lloyd, Erika; Sack, Stefan
 Quantum Science and Technology, Vol. 4, Issue 4
Strong bound between trace distance and HilbertSchmidt distance for lowrank states
journal, August 2019
 Coles, Patrick J.; Cerezo, M.; Cincio, Lukasz
 Physical Review A, Vol. 100, Issue 2
Shortdepth circuits for efficient expectationvalue estimation
journal, February 2020
 Roggero, A.; Baroni, A.
 Physical Review A, Vol. 101, Issue 2