Learning the quantum algorithm for state overlap
Abstract
Shortdepth algorithms are crucial for reducing computational error on nearterm quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machinelearning 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 hardwarespecific 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:

 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; LANL Laboratory Directed Research and Development (LDRD) Program
 OSTI Identifier:
 1482266
 Alternate Identifier(s):
 OSTI ID: 1482937
 Report Number(s):
 LAUR1821984
Journal ID: ISSN 13672630
 Grant/Contract Number:
 89233218CNA000001
 Resource Type:
 Journal Article: Published Article
 Journal Name:
 New Journal of Physics
 Additional Journal Information:
 Journal Volume: 20; Journal Issue: 11; Journal ID: ISSN 13672630
 Publisher:
 IOP Publishing
 Country of Publication:
 United States
 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 States: N. p., 2018.
Web. doi:10.1088/13672630/aae94a.
Cincio, Lukasz, Subaşı, Yiğit, Sornborger, Andrew T., & Coles, Patrick J. Learning the quantum algorithm for state overlap. United States. doi:10.1088/13672630/aae94a.
Cincio, Lukasz, Subaşı, Yiğit, Sornborger, Andrew T., and Coles, Patrick J. Thu .
"Learning the quantum algorithm for state overlap". United States. doi:10.1088/13672630/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 = {Shortdepth algorithms are crucial for reducing computational error on nearterm quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machinelearning 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 hardwarespecific 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 = {10.1088/13672630/aae94a},
journal = {New Journal of Physics},
issn = {13672630},
number = 11,
volume = 20,
place = {United States},
year = {2018},
month = {10}
}
Web of Science
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