Digitization of scalar fields for quantum computing
Abstract
Qubit, operator, and gate resources required for the digitization of lattice λΦ4 scalar field theories onto quantum computers are considered, building upon the foundational work by Jordan et al. [Quantum Inf. Comput. 14, 1014 (2014); Science 336, 1130 (2012)], with a focus towards noisy intermediate-scale quantum devices. The Nyquist-Shannon sampling theorem, introduced in this context by Macridin et al. [Phys. Rev. A 98, 042312 (2018)] building on the work of Somma [Quantum Inf. Comput. 16, 1125 (2016)], provides a guide with which to evaluate the efficacy of two field-space bases, the eigenstates of the field operator, as used by Jordan et al., and eigenstates of a harmonic oscillator, to describe ( 0 + 1 )- and ( d + 1 )-dimensional scalar field theory. We show how techniques associated with improved actions, which are heavily utilized in lattice QCD calculations to systematically reduce lattice-spacing artifacts, can be used to reduce the impact of the field digitization in λΦ4, but are found to be inferior to a complete digitization improvement of the Hamiltonian using a quantum Fourier transform. When the Nyquist-Shannon sampling theorem is satisfied, digitization errors scale as | log | log | εdig| | | ~ n Q (numbermore »
- Authors:
-
- Univ. of Washington, Seattle, WA (United States)
- Publication Date:
- Research Org.:
- Univ. of Washington, Seattle, WA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1609315
- Alternate Identifier(s):
- OSTI ID: 1515572
- Grant/Contract Number:
- FG02-00ER41132; ERKJ335; ERKJ333
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review A
- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 5; Journal ID: ISSN 2469-9926
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Optics; Physics
Citation Formats
Klco, Natalie, and Savage, Martin J. Digitization of scalar fields for quantum computing. United States: N. p., 2019.
Web. doi:10.1103/physreva.99.052335.
Klco, Natalie, & Savage, Martin J. Digitization of scalar fields for quantum computing. United States. https://doi.org/10.1103/physreva.99.052335
Klco, Natalie, and Savage, Martin J. Thu .
"Digitization of scalar fields for quantum computing". United States. https://doi.org/10.1103/physreva.99.052335. https://www.osti.gov/servlets/purl/1609315.
@article{osti_1609315,
title = {Digitization of scalar fields for quantum computing},
author = {Klco, Natalie and Savage, Martin J.},
abstractNote = {Qubit, operator, and gate resources required for the digitization of lattice λΦ4 scalar field theories onto quantum computers are considered, building upon the foundational work by Jordan et al. [Quantum Inf. Comput. 14, 1014 (2014); Science 336, 1130 (2012)], with a focus towards noisy intermediate-scale quantum devices. The Nyquist-Shannon sampling theorem, introduced in this context by Macridin et al. [Phys. Rev. A 98, 042312 (2018)] building on the work of Somma [Quantum Inf. Comput. 16, 1125 (2016)], provides a guide with which to evaluate the efficacy of two field-space bases, the eigenstates of the field operator, as used by Jordan et al., and eigenstates of a harmonic oscillator, to describe ( 0 + 1 )- and ( d + 1 )-dimensional scalar field theory. We show how techniques associated with improved actions, which are heavily utilized in lattice QCD calculations to systematically reduce lattice-spacing artifacts, can be used to reduce the impact of the field digitization in λΦ4, but are found to be inferior to a complete digitization improvement of the Hamiltonian using a quantum Fourier transform. When the Nyquist-Shannon sampling theorem is satisfied, digitization errors scale as | log | log | εdig| | | ~ n Q (number of qubits describing the field at a given spatial site) for the low-lying states, leaving the familiar power-law lattice-spacing and finite-volume effects that scale as | log | εlatt| | ~ NQ (total number of qubits in the simulation). For localized (delocalized) field-space wave functions, it is found that nQ ~ 4 ( 7 ) qubits per spatial lattice site are sufficient to reduce theoretical digitization errors below error contributions associated with approximation of the time-evolution operator and noisy implementation on near-term quantum devices. Only classical computing resources have been used to obtain the results presented in this work.},
doi = {10.1103/physreva.99.052335},
journal = {Physical Review A},
number = 5,
volume = 99,
place = {United States},
year = {Thu May 23 00:00:00 EDT 2019},
month = {Thu May 23 00:00:00 EDT 2019}
}
Web of Science
Works referenced in this record:
Continuum limit and improved action in lattice theories
journal, September 1983
- Symanzik, K.
- Nuclear Physics B, Vol. 226, Issue 1
Proposal for a minimal surface code experiment
text, January 2017
- Wootton, James R.; Peter, Andreas; Winkler, János R.
- American Physical Society
Efficient basis formulation for 1+1 dimensional SU(2) lattice gauge theory: Spectral calculations with matrix product states
text, January 2017
- Bañuls, Mari Carmen; Cichy, Krzysztof; Cirac, J. Ignacio
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Quantum Algorithms for Quantum Field Theories
journal, May 2012
- Jordan, S. P.; Lee, K. S. M.; Preskill, J.
- Science, Vol. 336, Issue 6085
Quantum simulation of quantum field theory using continuous variables
journal, December 2015
- Marshall, Kevin; Pooser, Raphael; Siopsis, George
- Physical Review A, Vol. 92, Issue 6
Real-Time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks
journal, March 2016
- Pichler, T.; Dalmonte, M.; Rico, E.
- Physical Review X, Vol. 6, Issue 1
Atomic Quantum Simulation of Dynamical Gauge Fields Coupled to Fermionic Matter: From String Breaking to Evolution after a Quench
journal, October 2012
- Banerjee, D.; Dalmonte, M.; Müller, M.
- Physical Review Letters, Vol. 109, Issue 17
Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
journal, September 2012
- Chatrchyan, S.; Khachatryan, V.; Sirunyan, A. M.
- Physics Letters B, Vol. 716, Issue 1
Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices
journal, December 2015
- Zohar, Erez; Cirac, J. Ignacio; Reznik, Benni
- Reports on Progress in Physics, Vol. 79, Issue 1
Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
journal, September 2012
- Aad, G.; Abajyan, T.; Abbott, B.
- Physics Letters B, Vol. 716, Issue 1
Machine learning method for state preparation and gate synthesis on photonic quantum computers
journal, January 2019
- Arrazola, Juan Miguel; Bromley, Thomas R.; Izaac, Josh
- Quantum Science and Technology, Vol. 4, Issue 2
Quantum-classical computation of Schwinger model dynamics using quantum computers
journal, September 2018
- Klco, N.; Dumitrescu, E. F.; McCaskey, A. J.
- Physical Review A, Vol. 98, Issue 3
Partial-symmetries of weak interactions
journal, February 1961
- Glashow, Sheldon L.
- Nuclear Physics, Vol. 22, Issue 4
Simulating lattice gauge theories on a quantum computer
journal, February 2006
- Byrnes, Tim; Yamamoto, Yoshihisa
- Physical Review A, Vol. 73, Issue 2
Efficient Basis Formulation for ( )-Dimensional SU(2) Lattice Gauge Theory: Spectral Calculations with Matrix Product States
journal, November 2017
- Bañuls, Mari Carmen; Cichy, Krzysztof; Cirac, J. Ignacio
- Physical Review X, Vol. 7, Issue 4
Quantum simulation of the Abelian-Higgs lattice gauge theory with ultracold atoms
journal, June 2017
- González-Cuadra, Daniel; Zohar, Erez; Cirac, J. Ignacio
- New Journal of Physics, Vol. 19, Issue 6
Quantum computation of scattering amplitudes in scalar quantum electrodynamics
journal, February 2018
- Yeter-Aydeniz, Kübra; Siopsis, George
- Physical Review D, Vol. 97, Issue 3
Digital quantum simulation of lattice gauge theories in three spatial dimensions
journal, September 2018
- Bender, Julian; Zohar, Erez; Farace, Alessandro
- New Journal of Physics, Vol. 20, Issue 9
Gauge-invariant implementation of the Abelian-Higgs model on optical lattices
journal, October 2015
- Bazavov, A.; Meurice, Y.; Tsai, S. -W.
- Physical Review D, Vol. 92, Issue 7
Improved continuum limit lattice action for QCD with wilson fermions
journal, September 1985
- Sheikholeslami, B.; Wohlert, R.
- Nuclear Physics B, Vol. 259, Issue 4
Exploiting Locality in Quantum Computation for Quantum Chemistry
journal, December 2014
- McClean, Jarrod R.; Babbush, Ryan; Love, Peter J.
- The Journal of Physical Chemistry Letters, Vol. 5, Issue 24
Cloud Quantum Computing of an Atomic Nucleus
journal, May 2018
- Dumitrescu, E. F.; McCaskey, A. J.; Hagen, G.
- Physical Review Letters, Vol. 120, Issue 21
Low-distance surface codes under realistic quantum noise
journal, December 2014
- Tomita, Yu; Svore, Krysta M.
- Physical Review A, Vol. 90, Issue 6
New optimization methods for converging perturbative series with a field cutoff
journal, February 2004
- Kessler, B.; Li, L.; Meurice, Y.
- Physical Review D, Vol. 69, Issue 4
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator
journal, July 2018
- Hempel, Cornelius; Maier, Christine; Romero, Jonathan
- Physical Review X, Vol. 8, Issue 3
Two-baryon systems with twisted boundary conditions
journal, April 2014
- Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C.
- Physical Review D, Vol. 89, Issue 7
State preservation by repetitive error detection in a superconducting quantum circuit
journal, March 2015
- Kelly, J.; Barends, R.; Fowler, A. G.
- Nature, Vol. 519, Issue 7541
Circuit complexity in quantum field theory
journal, October 2017
- Jefferson, Robert A.; Myers, Robert C.
- Journal of High Energy Physics, Vol. 2017, Issue 10
Gate-count estimates for performing quantum chemistry on small quantum computers
journal, August 2014
- Wecker, Dave; Bauer, Bela; Clark, Bryan K.
- Physical Review A, Vol. 90, Issue 2
Fermion-Fermion Scattering in Quantum Field Theory with Superconducting Circuits
journal, February 2015
- García-Álvarez, L.; Casanova, J.; Mezzacapo, A.
- Physical Review Letters, Vol. 114, Issue 7
U(1) Wilson lattice gauge theories in digital quantum simulators
journal, October 2017
- Muschik, Christine; Heyl, Markus; Martinez, Esteban
- New Journal of Physics, Vol. 19, Issue 10
�ber das Paulische �quivalenzverbot
journal, September 1928
- Jordan, P.; Wigner, E.
- Zeitschrift f�r Physik, Vol. 47, Issue 9-10
Fault-tolerant quantum computation with few qubits
journal, September 2018
- Chao, Rui; Reichardt, Ben W.
- npj Quantum Information, Vol. 4, Issue 1
Simulating the performance of a distance-3 surface code in a linear ion trap
journal, April 2018
- Trout, Colin J.; Li, Muyuan; Gutiérrez, Mauricio
- New Journal of Physics, Vol. 20, Issue 4
Chiral symmetry and O(a) improvement in lattice QCD
journal, October 1996
- Lüscher, M.
- Nuclear Physics B, Vol. 478, Issue 1-2
Aharonov–Bohm effect and nucleon–nucleon phase shifts on the lattice
journal, July 2004
- Bedaque, Paulo F.
- Physics Letters B, Vol. 593, Issue 1-4
Continuum limit and improved action in lattice theories
journal, September 1983
- Symanzik, K.
- Nuclear Physics B, Vol. 226, Issue 1
Twisted boundary conditions in lattice simulations
journal, March 2005
- Sachrajda, C. T.; Villadoro, G.
- Physics Letters B, Vol. 609, Issue 1-2
Scalar quantum field theories as a benchmark for near-term quantum computers
journal, March 2019
- Yeter-Aydeniz, Kübra; Dumitrescu, Eugene F.; McCaskey, Alex J.
- Physical Review A, Vol. 99, Issue 3
Quantum algorithms for fermionic simulations
journal, July 2001
- Ortiz, G.; Gubernatis, J. E.; Knill, E.
- Physical Review A, Vol. 64, Issue 2
Quantum Monte Carlo simulations of the BCS-BEC crossover at finite temperature
journal, August 2008
- Bulgac, Aurel; Drut, Joaquín E.; Magierski, Piotr
- Physical Review A, Vol. 78, Issue 2
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
journal, June 2016
- Martinez, Esteban A.; Muschik, Christine A.; Schindler, Philipp
- Nature, Vol. 534, Issue 7608
Proposal for a minimal surface code experiment
journal, September 2017
- Wootton, James R.; Peter, Andreas; Winkler, János R.
- Physical Review A, Vol. 96, Issue 3
The theory of variational hybrid quantum-classical algorithms
journal, February 2016
- McClean, Jarrod R.; Romero, Jonathan; Babbush, Ryan
- New Journal of Physics, Vol. 18, Issue 2
Fermionic Quantum Computation
journal, May 2002
- Bravyi, Sergey B.; Kitaev, Alexei Yu.
- Annals of Physics, Vol. 298, Issue 1
BQP-completeness of scattering in scalar quantum field theory
journal, January 2018
- Jordan, Stephen P.; Krovi, Hari; Lee, Keith S. M.
- Quantum, Vol. 2
Elucidating reaction mechanisms on quantum computers
journal, July 2017
- Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.
- Proceedings of the National Academy of Sciences, Vol. 114, Issue 29
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
Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
text, January 2018
- Akgun, B.; Azzolini, V.; Calamba, A.
- Figshare
Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories
journal, July 2013
- Wiese, U. ‐J.
- Annalen der Physik, Vol. 525, Issue 10-11
Observation of a new Boson at a mass of 125 gev with the cms Experiment at the lhc
conference, March 2015
- Mariotti, Chiara
- Proceedings of the MG13 Meeting on General Relativity, The Thirteenth Marcel Grossmann Meeting
Lattice Monte Carlo calculations for unitary fermions in a finite box
journal, February 2013
- Endres, Michael G.; Kaplan, David B.; Lee, Jong-Wan
- Physical Review A, Vol. 87, Issue 2
Digital quantum computation of fermion-boson interacting systems
journal, October 2018
- Macridin, Alexandru; Spentzouris, Panagiotis; Amundson, James
- Physical Review A, Vol. 98, Issue 4
Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991
- Lüscher, Martin
- Nuclear Physics B, Vol. 354, Issue 2-3
Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms
journal, June 2001
- Lin, C.; Zong, F. H.; Ceperley, D. M.
- Physical Review E, Vol. 64, Issue 1
Quantum computations on a topologically encoded qubit
journal, June 2014
- Nigg, D.; Muller, M.; Martinez, E. A.
- Science, Vol. 345, Issue 6194
Holographic Fermi liquids in a spontaneously generated lattice
journal, May 2016
- Alsup, James; Papantonopoulos, Eleftherios; Siopsis, George
- Physical Review D, Vol. 93, Issue 10
Phenomenological Lagrangians
journal, April 1979
- Weinberg, Steven
- Physica A: Statistical Mechanics and its Applications, Vol. 96, Issue 1-2
Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
journal, September 2017
- Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan
- Nature, Vol. 549, Issue 7671
Two-dimensional lattice gauge theories with superconducting quantum circuits
journal, December 2014
- Marcos, D.; Widmer, P.; Rico, E.
- Annals of Physics, Vol. 351
Quantum Simulation of the Universal Features of the Polyakov Loop
journal, November 2018
- Zhang, Jin; Unmuth-Yockey, J.; Zeiher, J.
- Physical Review Letters, Vol. 121, Issue 22
Simulating physical phenomena by quantum networks
journal, April 2002
- Somma, R.; Ortiz, G.; Gubernatis, J. E.
- Physical Review A, Vol. 65, Issue 4
Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
journal, March 2018
- Kivlichan, Ian D.; McClean, Jarrod; Wiebe, Nathan
- Physical Review Letters, Vol. 120, Issue 11
Scalable Quantum Simulation of Molecular Energies
journal, July 2016
- O’Malley, P. J. J.; Babbush, R.; Kivlichan, I. D.
- Physical Review X, Vol. 6, Issue 3
Simple Method to Make Asymptotic Series of Feynman Diagrams Converge
journal, March 2002
- Meurice, Y.
- Physical Review Letters, Vol. 88, Issue 14
A Model of Leptons
journal, November 1967
- Weinberg, Steven
- Physical Review Letters, Vol. 19, Issue 21
Quantum Monte Carlo Simulations of the BCS-BEC Crossover at Finite Temperature
text, January 2008
- Bulgac, Aurel; Drut, Joaquin E.; Magierski, Piotr
- arXiv
Lattice Monte Carlo calculations for unitary fermions in a finite box
text, January 2012
- Endres, Michael G.; Kaplan, David B.; Lee, Jong-Wan
- arXiv
Atomic Quantum Simulation of Dynamical Gauge Fields coupled to Fermionic Matter: From String Breaking to Evolution after a Quench
text, January 2012
- Banerjee, D.; Dalmonte, M.; Müller, M.
- arXiv
Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
text, January 2013
- Wiese, U. -J.
- arXiv
Gate count estimates for performing quantum chemistry on small quantum computers
text, January 2013
- Wecker, Dave; Bauer, Bela; Clark, Bryan K.
- arXiv
Low-distance Surface Codes under Realistic Quantum Noise
text, January 2014
- Tomita, Yu; Svore, Krysta M.
- arXiv
Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation
text, January 2014
- Babbush, Ryan; McClean, Jarrod; Wecker, Dave
- arXiv
State preservation by repetitive error detection in a superconducting quantum circuit
text, January 2014
- Kelly, J.; Barends, R.; Fowler, A. G.
- arXiv
Quantum simulation of quantum field theory using continuous variables
text, January 2015
- Marshall, Kevin; Pooser, Raphael; Siopsis, George
- arXiv
Gauge-invariant implementation of the Abelian Higgs model on optical lattices
text, January 2015
- Bazavov, Alexei; Meurice, Yannick; Tsai, Shan-Wen
- arXiv
Scalable Quantum Simulation of Molecular Energies
text, January 2015
- O'Malley, P. J. J.; Babbush, R.; Kivlichan, I. D.
- arXiv
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
text, January 2016
- Martinez, E. A.; Muschik, C. A.; Schindler, P.
- arXiv
Digital lattice gauge theories
text, January 2016
- Zohar, Erez; Farace, Alessandro; Reznik, Benni
- arXiv
Quantum Computation of Scattering Amplitudes in Scalar Quantum Electrodynamics
text, January 2017
- Yeter-Aydeniz, Kübra; Siopsis, George
- arXiv
Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory
text, January 2017
- Moosavian, Ali Hamed; Jordan, Stephen
- arXiv
Cloud Quantum Computing of an Atomic Nucleus
text, January 2018
- Dumitrescu, E. F.; McCaskey, A. J.; Hagen, G.
- arXiv
Electron-Phonon Systems on a Universal Quantum Computer
text, January 2018
- Macridin, Alexandru; Spentzouris, Panagiotis; Amundson, James
- arXiv
Quantum-Classical Computation of Schwinger Model Dynamics using Quantum Computers
text, January 2018
- Klco, N.; Dumitrescu, E. F.; McCaskey, A. J.
- arXiv
Learning the quantum algorithm for state overlap
text, January 2018
- Cincio, Lukasz; Subaşı, Yiğit; Sornborger, Andrew T.
- arXiv
Quantum simulation of the universal features of the Polyakov loop
text, January 2018
- Zhang, Jin; Unmuth-Yockey, J.; Zeiher, J.
- arXiv
Digital quantum computation of fermion-boson interacting systems
text, January 2018
- Macridin, Alexandru; Spentzouris, Panagiotis; Amundson, James
- arXiv
Machine learning method for state preparation and gate synthesis on photonic quantum computers
text, January 2018
- Arrazola, Juan Miguel; Bromley, Thomas R.; Izaac, Josh
- arXiv
Twisted Boundary Conditions in Lattice Simulations
text, January 2004
- Sachrajda, C. T.; Villadoro, G.
- arXiv
Chiral symmetry and O(a) improvement in lattice QCD
text, January 1996
- Luescher, Martin; Sint, Stefan; Sommer, Rainer
- arXiv
A Simple Method to Make Asymptotic Series of Feynman Diagrams Converge
text, January 2001
- Meurice, Y.
- arXiv
New Optimization Methods for Converging Perturbative Series with a Field Cutoff
text, January 2003
- Kessler, B.; Li, L.; Meurice, Y.
- arXiv
Aharonov-Bohm effect and nucleon-nucleon phase shifts on the lattice
text, January 2004
- Bedaque, Paulo F.
- arXiv
Simulating Physical Phenomena by Quantum Networks
text, January 2001
- Somma, R.; Ortiz, G.; Gubernatis, J. E.
- arXiv
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- npj Quantum Information, Vol. 5, Issue 1
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journal, January 2020
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- Reports on Progress in Physics, Vol. 83, Issue 2
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text, January 2019
- Lamm, Henry; Lawrence, Scott; Yamauchi, Yukari
- arXiv
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- McCaskey, Alexander J.; Parks, Zachary P.; Jakowski, Jacek
- arXiv
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- Alexandru, Andrei; Bedaque, Paulo F.; Harmalkar, Siddhartha
- arXiv
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- Bañuls, Mari Carmen; Cichy, Krzysztof
- arXiv
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journal, February 2021
- Zhang, Dan-Bo; Xing, Hongxi; Yan, Hui
- Chinese Physics B, Vol. 30, Issue 2