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Title: 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:
 [1];  [1];  [1];  [1]
  1. 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):
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 Volume: 20; Journal Issue: 11; Journal ID: ISSN 1367-2630
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:10.1088/1367-2630/aae94a.
Cincio, Lukasz, Subaşı, Yiğit, Sornborger, Andrew T., & Coles, Patrick J. Learning the quantum algorithm for state overlap. United States. doi:10.1088/1367-2630/aae94a.
Cincio, Lukasz, Subaşı, Yiğit, Sornborger, Andrew T., and Coles, Patrick J. Thu . "Learning the quantum algorithm for state overlap". United States. doi:10.1088/1367-2630/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},
journal = {New Journal of Physics},
issn = {1367-2630},
number = 11,
volume = 20,
place = {United States},
year = {2018},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1088/1367-2630/aae94a

Citation Metrics:
Cited by: 12 works
Citation information provided by
Web of Science

Figures / Tables:

Figure 1. Figure 1.: Machine-learning approach to discovering and optimizing quantum algorithms.Weoptimize an algorithm for a given set of resources, which includes input resources (ancilla and data qubits) and measurement resources (i.e. which qubits can be measured). The algorithm is then determined by the quantum gate sequence and the classical post-processing ofmore » the measurement results. To find the algorithm that computes the function $x$→$f$ ($x$),we minimize a cost function that quantifies the discrepancy between the desired output $f$ ($x$( $i$)) and the actual output $y$( $i$) for a set of training data inputs {$x$( $i$) }. If the training data are sufficiently general, the algorithm that minimizes the cost should be a general algorithm that computes $f$ ($x$) for any input $x$.« less

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