Characterizing quantum circuits with qubit functional configurations

Hu, Zixuan; Kais, Sabre

doi:10.1038/s41598-023-31980-3

Title: Characterizing quantum circuits with qubit functional configurations

Journal Article · 03 April 2023 · Scientific Reports

DOI: https://doi.org/10.1038/s41598-023-31980-3 · OSTI ID:1968515

Hu, Zixuan; Kais, Sabre

Abstract We develop a systematic framework for characterizing all quantum circuits with qubit functional configurations. The qubit functional configuration is a mathematical structure that can classify the properties and behaviors of quantum circuits collectively. Major benefits of classifying quantum circuits in this way include: 1. All quantum circuits can be classified into corresponding types; 2. Each type characterizes important properties (such as circuit complexity) of the quantum circuits belonging to it; 3. Each type contains a huge collection of possible quantum circuits allowing systematic investigation of their common properties. We demonstrate the theory’s application to analyzing the hardware-efficient ansatzes of variational quantum algorithms. For potential applications, the functional configuration theory may allow systematic understanding and development of quantum algorithms based on their functional configuration types.

View Journal Article

Cite

Export

Save

Research Organization:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0019215

OSTI ID:: 1968515

Journal Information:: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 13; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United Kingdom

Language:: English

References (44)

Quantum Information and Computation for Chemistry Kais, Sabre Advances in Chemical Physics https://doi.org/10.1002/9781118742631	book	February 2014
Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum‐Classical Algorithms Sim, Sukin; Johnson, Peter D.; Aspuru‐Guzik, Alán Advanced Quantum Technologies, Vol. 2, Issue 12 https://doi.org/10.1002/qute.201900070	journal	October 2019
Characterization of Quantum States Based on Creation Complexity Hu, Zixuan; Kais, Sabre Advanced Quantum Technologies, Vol. 3, Issue 9 https://doi.org/10.1002/qute.202000043	journal	August 2020
The Quantum Condition Space Hu, Zixuan; Kais, Sabre Advanced Quantum Technologies, Vol. 5, Issue 4 https://doi.org/10.1002/qute.202100158	journal	February 2022
Superconducting quantum computing: a review Huang, He-Liang; Wu, Dachao; Fan, Daojin Science China Information Sciences, Vol. 63, Issue 8 https://doi.org/10.1007/s11432-020-2881-9	journal	July 2020
Hybrid quantum-classical convolutional neural networks Liu, Junhua; Lim, Kwan Hui; Wood, Kristin L. Science China Physics, Mechanics & Astronomy, Vol. 64, Issue 9 https://doi.org/10.1007/s11433-021-1734-3	journal	August 2021
The Variational Quantum Eigensolver: A review of methods and best practices Tilly, Jules; Chen, Hongxiang; Cao, Shuxiang Physics Reports, Vol. 986 https://doi.org/10.1016/j.physrep.2022.08.003	journal	November 2022
Quantum Computation and Quantum Information Nielsen, Michael A.; Chuang, Isaac L. Cambridge University Press https://doi.org/10.1017/CBO9780511976667	book	January 2011
Quantum Chemistry in the Age of Quantum Computing Cao, Yudong; Romero, Jonathan; Olson, Jonathan P. Chemical Reviews, Vol. 119, Issue 19 https://doi.org/10.1021/acs.chemrev.8b00803	journal	August 2019
Quantum Simulation of the Radical Pair Dynamics of the Avian Compass Zhang, Yiteng; Hu, Zixuan; Wang, Yuchen The Journal of Physical Chemistry Letters, Vol. 14, Issue 3 https://doi.org/10.1021/acs.jpclett.2c03617	journal	January 2023
Quantum machine learning Biamonte, Jacob; Wittek, Peter; Pancotti, Nicola Nature, Vol. 549, Issue 7671 https://doi.org/10.1038/nature23474	journal	September 2017
Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan Nature, Vol. 549, Issue 7671 https://doi.org/10.1038/nature23879	journal	September 2017
A variational eigenvalue solver on a photonic quantum processor Peruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5213	journal	July 2014
Quantum simulations with trapped ions Blatt, R.; Roos, C. F. Nature Physics, Vol. 8, Issue 4 https://doi.org/10.1038/nphys2252	journal	April 2012
Evidence for quantum annealing with more than one hundred qubits Boixo, Sergio; Rønnow, Troels F.; Isakov, Sergei V. Nature Physics, Vol. 10, Issue 3 https://doi.org/10.1038/nphys2900	journal	February 2014
Quantum algorithms: an overview Montanaro, Ashley npj Quantum Information, Vol. 2, Issue 1 https://doi.org/10.1038/npjqi.2015.23	journal	January 2016
Quantum machine learning for electronic structure calculations Xia, Rongxin; Kais, Sabre Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-06598-z	journal	October 2018
Quantum convolutional neural networks Cong, Iris; Choi, Soonwon; Lukin, Mikhail D. Nature Physics, Vol. 15, Issue 12 https://doi.org/10.1038/s41567-019-0648-8	journal	August 2019
Quantum approximate optimization of non-planar graph problems on a planar superconducting processor Harrigan, Matthew P.; Sung, Kevin J.; Neeley, Matthew Nature Physics, Vol. 17, Issue 3 https://doi.org/10.1038/s41567-020-01105-y	journal	February 2021
Supervised learning with quantum-enhanced feature spaces Havlíček, Vojtěch; Córcoles, Antonio D.; Temme, Kristan Nature, Vol. 567, Issue 7747 https://doi.org/10.1038/s41586-019-0980-2	journal	March 2019
Quantum supremacy using a programmable superconducting processor Arute, Frank; Arya, Kunal; Babbush, Ryan Nature, Vol. 574, Issue 7779 https://doi.org/10.1038/s41586-019-1666-5	journal	October 2019
A quantum algorithm for evolving open quantum dynamics on quantum computing devices Hu, Zixuan; Xia, Rongxin; Kais, Sabre Scientific Reports, Vol. 10, Issue 1 https://doi.org/10.1038/s41598-020-60321-x	journal	February 2020
Relaxation of stationary states on a quantum computer yields a unique spectroscopic fingerprint of the computer’s noise Smart, Scott E.; Hu, Zixuan; Kais, Sabre Communications Physics, Vol. 5, Issue 1 https://doi.org/10.1038/s42005-022-00803-8	journal	January 2022
Variational quantum algorithms Cerezo, M.; Arrasmith, Andrew; Babbush, Ryan Nature Reviews Physics, Vol. 3, Issue 9 https://doi.org/10.1038/s42254-021-00348-9	journal	August 2021
Decomposition of unitary matrices for finding quantum circuits: Application to molecular Hamiltonians Daskin, Anmer; Kais, Sabre The Journal of Chemical Physics, Vol. 134, Issue 14 https://doi.org/10.1063/1.3575402	journal	April 2011
Trapped-ion quantum computing: Progress and challenges Bruzewicz, Colin D.; Chiaverini, John; McConnell, Robert Applied Physics Reviews, Vol. 6, Issue 2 https://doi.org/10.1063/1.5088164	journal	June 2019
Quantum computations: algorithms and error correction Kitaev, A. Yu Russian Mathematical Surveys, Vol. 52, Issue 6 https://doi.org/10.1070/RM1997v052n06ABEH002155	journal	December 1997
Experimental comparison of two quantum computing architectures Linke, Norbert M.; Maslov, Dmitri; Roetteler, Martin Proceedings of the National Academy of Sciences, Vol. 114, Issue 13 https://doi.org/10.1073/pnas.1618020114	journal	March 2017
On the controlled-NOT complexity of controlled-NOT–phase circuits Amy, Matthew; Azimzadeh, Parsiad; Mosca, Michele Quantum Science and Technology, Vol. 4, Issue 1 https://doi.org/10.1088/2058-9565/aad8ca	journal	September 2018
Quantum algorithm for simulating the dynamics of an open quantum system Wang, Hefeng; Ashhab, S.; Nori, Franco Physical Review A, Vol. 83, Issue 6 https://doi.org/10.1103/PhysRevA.83.062317	journal	June 2011
Experimental Quantum Generative Adversarial Networks for Image Generation Huang, He-Liang; Du, Yuxuan; Gong, Ming Physical Review Applied, Vol. 16, Issue 2 https://doi.org/10.1103/PhysRevApplied.16.024051	journal	August 2021
Variational Quantum Gibbs State Preparation with a Truncated Taylor Series Wang, Youle; Li, Guangxi; Wang, Xin Physical Review Applied, Vol. 16, Issue 5 https://doi.org/10.1103/PhysRevApplied.16.054035	journal	November 2021
Quantum Algorithm for Linear Systems of Equations Harrow, Aram W.; Hassidim, Avinatan; Lloyd, Seth Physical Review Letters, Vol. 103, Issue 15 https://doi.org/10.1103/PhysRevLett.103.150502	journal	October 2009
Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices Smart, Scott E.; Mazziotti, David A. Physical Review Letters, Vol. 126, Issue 7 https://doi.org/10.1103/PhysRevLett.126.070504	journal	February 2021
Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators Schlimgen, Anthony W.; Head-Marsden, Kade; Sager, LeeAnn M. Physical Review Letters, Vol. 127, Issue 27 https://doi.org/10.1103/PhysRevLett.127.270503	journal	December 2021
Quantum simulation Georgescu, I. M.; Ashhab, S.; Nori, Franco Reviews of Modern Physics, Vol. 86, Issue 1 https://doi.org/10.1103/RevModPhys.86.153	journal	March 2014
Adiabatic quantum computation Albash, Tameem; Lidar, Daniel A. Reviews of Modern Physics, Vol. 90, Issue 1 https://doi.org/10.1103/RevModPhys.90.015002	journal	January 2018
Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning Amy, Matthew; Maslov, Dmitri; Mosca, Michele IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 33, Issue 10 https://doi.org/10.1109/TCAD.2014.2341953	journal	October 2014
Universal linear optics Carolan, J.; Harrold, C.; Sparrow, C. Science, Vol. 349, Issue 6249 https://doi.org/10.1126/science.aab3642	journal	July 2015
Quantum computational advantage using photons Zhong, Han-Sen; Wang, Hui; Deng, Yu-Hao Science, Vol. 370, Issue 6523 https://doi.org/10.1126/science.abe8770	journal	December 2020
Quantum walks on a programmable two-dimensional 62-qubit superconducting processor Gong, Ming; Wang, Shiyu; Zha, Chen Science, Vol. 372, Issue 6545 https://doi.org/10.1126/science.abg7812	journal	May 2021
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer Shor, Peter W. SIAM Journal on Computing, Vol. 26, Issue 5 https://doi.org/10.1137/S0097539795293172	journal	October 1997
Quantum Computing in the NISQ era and beyond Preskill, John Quantum, Vol. 2 https://doi.org/10.22331/q-2018-08-06-79	journal	August 2018
A general quantum algorithm for open quantum dynamics demonstrated with the Fenna-Matthews-Olson complex Hu, Zixuan; Head-Marsden, Kade; Mazziotti, David A. Quantum, Vol. 6 https://doi.org/10.22331/q-2022-05-30-726	journal	May 2022

Similar Records

The unitary dependence theory for characterizing quantum circuits and states

Journal Article · 2023 · Communications Physics · OSTI ID:1969580

Hu, Zixuan; Kais, Sabre

Recognizing small-circuit structure in two-qubit operators

Journal Article · 2004 · Physical Review. A · OSTI ID:20643882

Shende, Vivek V; Bullock, Stephen S; Markov, Igor L

Characterization of Quantum States Based on Creation Complexity

Journal Article · 2020 · Advanced Quantum Technologies · OSTI ID:1668089

Hu, Zixuan; Kais, Sabre

Related Subjects

97 MATHEMATICS AND COMPUTING
Science & Technology - Other Topics

Title: Characterizing quantum circuits with qubit functional configurations

Citation Formats

References (44)

Similar Records

Related Subjects