Learning the quantum algorithm for state overlap
Abstract
Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning approach for discovering such algorithms. We apply our method to a ubiquitous primitive: computing the overlap $$\mathrm{Tr}(\rho \sigma )$$ between two quantum states ρ and σ. The standard algorithm for this task, known as the Swap Test, is used in many applications such as quantum support vector machines, and, when specialized to ρ = σ, quantifies the Renyi entanglement. Here, we find algorithms that have shorter depths than the Swap Test, including one that has a constant depth (independent of problem size). Furthermore, we apply our approach to the hardware-specific connectivity and gate sets used by Rigetti's and IBM's quantum computers and demonstrate that the shorter algorithms that we derive significantly reduce the error—compared to the Swap Test—on these computers.
- Authors:
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE; LANL Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 1482266
- Alternate Identifier(s):
- OSTI ID: 1482937
- Report Number(s):
- LA-UR-18-21984
Journal ID: ISSN 1367-2630
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Journal Article: Published Article
- Journal Name:
- New Journal of Physics
- Additional Journal Information:
- Journal Name: New Journal of Physics Journal Volume: 20 Journal Issue: 11; Journal ID: ISSN 1367-2630
- Publisher:
- IOP Publishing
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Computer Science; Information Science; Mathematics; quantum computing algorithms
Citation Formats
Cincio, Lukasz, Subaşı, Yiğit, Sornborger, Andrew T., and Coles, Patrick J. Learning the quantum algorithm for state overlap. United Kingdom: N. p., 2018.
Web. doi:10.1088/1367-2630/aae94a.
Cincio, Lukasz, Subaşı, Yiğit, Sornborger, Andrew T., & Coles, Patrick J. Learning the quantum algorithm for state overlap. United Kingdom. https://doi.org/10.1088/1367-2630/aae94a
Cincio, Lukasz, Subaşı, Yiğit, Sornborger, Andrew T., and Coles, Patrick J. 2018.
"Learning the quantum algorithm for state overlap". United Kingdom. https://doi.org/10.1088/1367-2630/aae94a.
@article{osti_1482266,
title = {Learning the quantum algorithm for state overlap},
author = {Cincio, Lukasz and Subaşı, Yiğit and Sornborger, Andrew T. and Coles, Patrick J.},
abstractNote = {Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning approach for discovering such algorithms. We apply our method to a ubiquitous primitive: computing the overlap $\mathrm{Tr}(\rho \sigma )$ between two quantum states ρ and σ. The standard algorithm for this task, known as the Swap Test, is used in many applications such as quantum support vector machines, and, when specialized to ρ = σ, quantifies the Renyi entanglement. Here, we find algorithms that have shorter depths than the Swap Test, including one that has a constant depth (independent of problem size). Furthermore, we apply our approach to the hardware-specific connectivity and gate sets used by Rigetti's and IBM's quantum computers and demonstrate that the shorter algorithms that we derive significantly reduce the error—compared to the Swap Test—on these computers.},
doi = {10.1088/1367-2630/aae94a},
url = {https://www.osti.gov/biblio/1482266},
journal = {New Journal of Physics},
issn = {1367-2630},
number = 11,
volume = 20,
place = {United Kingdom},
year = {Thu Nov 01 00:00:00 EDT 2018},
month = {Thu Nov 01 00:00:00 EDT 2018}
}
Web of Science
Figures / Tables:
Works referenced in this record:
Generating three-qubit quantum circuits with neural networks
journal, October 2017
- Swaddle, Michael; Noakes, Lyle; Smallbone, Harry
- Physics Letters A, Vol. 381, Issue 39
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
Entanglement spectroscopy on a quantum computer
journal, November 2017
- Johri, Sonika; Steiger, Damian S.; Troyer, Matthias
- Physical Review B, Vol. 96, Issue 19
Evolutionary Approach to Quantum and Reversible Circuits Synthesis
journal, December 2003
- Lukac, Martin; Perkowski, Marek; Goi, Hilton
- Artificial Intelligence Review, Vol. 20, Issue 3/4
On the CNOT -cost of TOFFOLI gates
journal, May 2009
- Shende, V. V.; Markov, I. L.
- Quantum Information and Computation, Vol. 9, Issue 5&6
A review of procedures to evolve quantum algorithms
journal, February 2009
- Gepp, Adrian; Stocks, Phil
- Genetic Programming and Evolvable Machines, Vol. 10, Issue 2
Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms
journal, February 2005
- Khaneja, Navin; Reiss, Timo; Kehlet, Cindie
- Journal of Magnetic Resonance, Vol. 172, Issue 2
Quantum circuit learning
journal, September 2018
- Mitarai, K.; Negoro, M.; Kitagawa, M.
- Physical Review A, Vol. 98, Issue 3
Basic circuit compilation techniques for an ion-trap quantum machine
journal, February 2017
- Maslov, Dmitri
- New Journal of Physics, Vol. 19, Issue 2
Surface codes: Towards practical large-scale quantum computation
journal, September 2012
- Fowler, Austin G.; Mariantoni, Matteo; Martinis, John M.
- Physical Review A, Vol. 86, Issue 3
swap test and Hong-Ou-Mandel effect are equivalent
journal, May 2013
- Garcia-Escartin, Juan Carlos; Chamorro-Posada, Pedro
- Physical Review A, Vol. 87, Issue 5
A quantum Fredkin gate
journal, March 2016
- Patel, Raj B.; Ho, Joseph; Ferreyrol, Franck
- Science Advances, Vol. 2, Issue 3
Five two-bit quantum gates are sufficient to implement the quantum Fredkin gate
journal, April 1996
- Smolin, John A.; DiVincenzo, David P.
- Physical Review A, Vol. 53, Issue 4
Faster phase estimation
journal, March 2014
- Svore, Krysta M.; Hastings, Matthew B.; Freedman, Michael
- Quantum Information and Computation, Vol. 14, Issue 3&4
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
Implementation of a quantum Fredkin gate using an entanglement resource
conference, May 2013
- Ferreyrol, Franck; Ralph, Timothy C.; Pryde, Geoff J.
- 2013 Conference on Lasers & Electro-Optics Europe & International Quantum Electronics Conference CLEO EUROPE/IQEC
Simulating the transverse Ising model on a quantum computer: Error correction with the surface code
journal, March 2013
- You, Hao; Geller, Michael R.; Stancil, P. C.
- Physical Review A, Vol. 87, Issue 3
A blueprint for demonstrating quantum supremacy with superconducting qubits
journal, April 2018
- Neill, C.; Roushan, P.; Kechedzhi, K.
- Science, Vol. 360, Issue 6385
Programming languages and compiler design for realistic quantum hardware
journal, September 2017
- Chong, Frederic T.; Franklin, Diana; Martonosi, Margaret
- Nature, Vol. 549, Issue 7671
Designing High-Fidelity Single-Shot Three-Qubit Gates: A Machine-Learning Approach
journal, November 2016
- Zahedinejad, Ehsan; Ghosh, Joydip; Sanders, Barry C.
- Physical Review Applied, Vol. 6, Issue 5
Deep Learning for Logic Optimization Algorithms
conference, January 2018
- Haaswijk, Winston; Collins, Edo; Seguin, Benoit
- 2018 IEEE International Symposium on Circuits and Systems (ISCAS)
Quantum Fingerprinting
journal, September 2001
- Buhrman, Harry; Cleve, Richard; Watrous, John
- Physical Review Letters, Vol. 87, Issue 16
Figures / Tables found in this record: