Heisenberg-Limited Ground-State Energy Estimation for Early Fault-Tolerant Quantum Computers

Lin, Lin; Tong, Yu

doi:10.1103/PRXQuantum.3.010318

Title: Heisenberg-Limited Ground-State Energy Estimation for Early Fault-Tolerant Quantum Computers

Journal Article · 02 February 2022 · PRX Quantum

DOI: https://doi.org/10.1103/PRXQuantum.3.010318 · OSTI ID:1843533

;

Not Available

View Journal Article

Cite

Export

Save

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0017867

OSTI ID:: 1843533

Journal Information:: PRX Quantum, Journal Name: PRX Quantum Journal Issue: 1 Vol. 3; ISSN 2691-3399; ISSN PQRUAG

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (55)

The Complexity of the Local Hamiltonian Problem Kempe, Julia; Kitaev, Alexei; Regev, Oded FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science https://doi.org/10.1007/978-3-540-30538-5_31	book	January 2004
The Power of Quantum Systems on a Line Aharonov, Dorit; Gottesman, Daniel; Irani, Sandy Communications in Mathematical Physics, Vol. 287, Issue 1 https://doi.org/10.1007/s00220-008-0710-3	journal	January 2009
Multilevel Monte Carlo methods Giles, Michael B. Acta Numerica, Vol. 24 https://doi.org/10.1017/S096249291500001X	journal	April 2015
A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons Stair, Nicholas H.; Huang, Renke; Evangelista, Francesco A. Journal of Chemical Theory and Computation, Vol. 16, Issue 4 https://doi.org/10.1021/acs.jctc.9b01125	journal	February 2020
Quantum Chemistry on Quantum Computers: A Method for Preparation of Multiconfigurational Wave Functions on Quantum Computers without Performing Post-Hartree–Fock Calculations Sugisaki, Kenji; Nakazawa, Shigeaki; Toyota, Kazuo ACS Central Science, Vol. 5, Issue 1 https://doi.org/10.1021/acscentsci.8b00788	journal	December 2018
Entanglement-free Heisenberg-limited phase estimation Higgins, B. L.; Berry, D. W.; Bartlett, S. D. Nature, Vol. 450, Issue 7168 https://doi.org/10.1038/nature06257	journal	November 2007
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
Advances in quantum metrology Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo Nature Photonics, Vol. 5, Issue 4 https://doi.org/10.1038/nphoton.2011.35	journal	March 2011
Fast-forwarding of Hamiltonians and exponentially precise measurements Atia, Yosi; Aharonov, Dorit Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-01637-7	journal	November 2017
Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution Motta, Mario; Sun, Chong; Tan, Adrian T. K. Nature Physics, Vol. 16, Issue 2 https://doi.org/10.1038/s41567-019-0704-4	journal	November 2019
Faster ground state preparation and high-precision ground energy estimation with fewer qubits Ge, Yimin; Tura, Jordi; Cirac, J. Ignacio Journal of Mathematical Physics, Vol. 60, Issue 2 https://doi.org/10.1063/1.5027484	journal	February 2019
General theory of fractal path integrals with applications to many‐body theories and statistical physics Suzuki, Masuo Journal of Mathematical Physics, Vol. 32, Issue 2 https://doi.org/10.1063/1.529425	journal	February 1991
Quantum information and precision measurement Childs, Andrew M.; Preskill, John; Renes, Joseph Journal of Modern Optics, Vol. 47, Issue 2-3 https://doi.org/10.1080/09500340008244034	journal	February 2000
The theory of variational hybrid quantum-classical algorithms McClean, Jarrod R.; Romero, Jonathan; Babbush, Ryan New Journal of Physics, Vol. 18, Issue 2 https://doi.org/10.1088/1367-2630/18/2/023023	journal	February 2016
Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments O’Brien, Thomas E.; Tarasinski, Brian; Terhal, Barbara M. New Journal of Physics, Vol. 21, Issue 2 https://doi.org/10.1088/1367-2630/aafb8e	journal	February 2019
Quantum eigenvalue estimation via time series analysis Somma, Rolando D. New Journal of Physics, Vol. 21, Issue 12 https://doi.org/10.1088/1367-2630/ab5c60	journal	December 2019
A non-orthogonal variational quantum eigensolver Huggins, William J.; Lee, Joonho; Baek, Unpil New Journal of Physics, Vol. 22, Issue 7 https://doi.org/10.1088/1367-2630/ab867b	journal	July 2020
Early fault-tolerant simulations of the Hubbard model Campbell, Earl T. Quantum Science and Technology, Vol. 7, Issue 1 https://doi.org/10.1088/2058-9565/ac3110	journal	November 2021
Classical and Quantum Computation Kitaev, A.; Shen, A.; Vyalyi, M. https://doi.org/10.1090/gsm/047	book	January 2002
Quantum algorithms revisited Cleve, R.; Ekert, A.; Macchiavello, C. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 454, Issue 1969 https://doi.org/10.1098/rspa.1998.0164	journal	January 1998
Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization Sanders, Yuval R.; Berry, Dominic W.; Costa, Pedro C. S. PRX Quantum, Vol. 1, Issue 2 https://doi.org/10.1103/PRXQuantum.1.020312	journal	November 2020
Focus beyond Quadratic Speedups for Error-Corrected Quantum Advantage Babbush, Ryan; McClean, Jarrod R.; Newman, Michael PRX Quantum, Vol. 2, Issue 1 https://doi.org/10.1103/PRXQuantum.2.010103	journal	March 2021
Time in the Quantum Theory and the Uncertainty Relation for Time and Energy Aharonov, Y.; Bohm, D. Physical Review, Vol. 122, Issue 5 https://doi.org/10.1103/PhysRev.122.1649	journal	June 1961
Simulating physical phenomena by quantum networks Somma, R.; Ortiz, G.; Gubernatis, J. E. Physical Review A, Vol. 65, Issue 4 https://doi.org/10.1103/PhysRevA.65.042323	journal	April 2002
Measuring energy, estimating Hamiltonians, and the time-energy uncertainty relation Aharonov, Y.; Massar, S.; Popescu, S. Physical Review A, Vol. 66, Issue 5 https://doi.org/10.1103/PhysRevA.66.052107	journal	November 2002
Estimation of the local density of states on a quantum computer Emerson, Joseph; Lloyd, Seth; Poulin, David Physical Review A, Vol. 69, Issue 5 https://doi.org/10.1103/PhysRevA.69.050305	journal	May 2004
Optimal quantum measurements of expectation values of observables Knill, Emanuel; Ortiz, Gerardo; Somma, Rolando D. Physical Review A, Vol. 75, Issue 1 https://doi.org/10.1103/PhysRevA.75.012328	journal	January 2007
Parameter estimation with mixed-state quantum computation Boixo, Sergio; Somma, Rolando D. Physical Review A, Vol. 77, Issue 5 https://doi.org/10.1103/PhysRevA.77.052320	journal	May 2008
How to perform the most accurate possible phase measurements Berry, D. W.; Higgins, B. L.; Bartlett, S. D. Physical Review A, Vol. 80, Issue 5 https://doi.org/10.1103/PhysRevA.80.052114	journal	November 2009
Ultimate limits to quantum metrology and the meaning of the Heisenberg limit Zwierz, Marcin; Pérez-Delgado, Carlos A.; Kok, Pieter Physical Review A, Vol. 85, Issue 4 https://doi.org/10.1103/PhysRevA.85.042112	journal	April 2012
Chemical basis of Trotter-Suzuki errors in quantum chemistry simulation Babbush, Ryan; McClean, Jarrod; Wecker, Dave Physical Review A, Vol. 91, Issue 2 https://doi.org/10.1103/PhysRevA.91.022311	journal	February 2015
Preparing Ground States of Quantum Many-Body Systems on a Quantum Computer Poulin, David; Wocjan, Pawel Physical Review Letters, Vol. 102, Issue 13 https://doi.org/10.1103/PhysRevLett.102.130503	journal	April 2009
Sampling from the Thermal Quantum Gibbs State and Evaluating Partition Functions with a Quantum Computer Poulin, David; Wocjan, Pawel Physical Review Letters, Vol. 103, Issue 22 https://doi.org/10.1103/PhysRevLett.103.220502	journal	November 2009
General Optimality of the Heisenberg Limit for Quantum Metrology Zwierz, Marcin; Pérez-Delgado, Carlos A.; Kok, Pieter Physical Review Letters, Vol. 105, Issue 18 https://doi.org/10.1103/PhysRevLett.105.180402	journal	October 2010
Optimal Hamiltonian Simulation by Quantum Signal Processing Low, Guang Hao; Chuang, Isaac L. Physical Review Letters, Vol. 118, Issue 1 https://doi.org/10.1103/PhysRevLett.118.010501	journal	January 2017
Quantum Simulation of Electronic Structure with Linear Depth and Connectivity Kivlichan, Ian D.; McClean, Jarrod; Wiebe, Nathan Physical Review Letters, Vol. 120, Issue 11 https://doi.org/10.1103/PhysRevLett.120.110501	journal	March 2018
Accelerated Variational Quantum Eigensolver Wang, Daochen; Higgott, Oscar; Brierley, Stephen Physical Review Letters, Vol. 122, Issue 14 https://doi.org/10.1103/PhysRevLett.122.140504	journal	April 2019
Nearly Optimal Lattice Simulation by Product Formulas Childs, Andrew M.; Su, Yuan Physical Review Letters, Vol. 123, Issue 5 https://doi.org/10.1103/PhysRevLett.123.050503	journal	August 2019
Random Compiler for Fast Hamiltonian Simulation Campbell, Earl Physical Review Letters, Vol. 123, Issue 7 https://doi.org/10.1103/PhysRevLett.123.070503	journal	August 2019
Destructive Error Interference in Product-Formula Lattice Simulation Tran, Minh C.; Chu, Su-Kuan; Su, Yuan Physical Review Letters, Vol. 124, Issue 22 https://doi.org/10.1103/PhysRevLett.124.220502	journal	June 2020
Semiclassical Fourier Transform for Quantum Computation Griffiths, Robert B.; Niu, Chi-Sheng Physical Review Letters, Vol. 76, Issue 17 https://doi.org/10.1103/PhysRevLett.76.3228	journal	April 1996
Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors Abrams, Daniel S.; Lloyd, Seth Physical Review Letters, Vol. 83, Issue 24 https://doi.org/10.1103/PhysRevLett.83.5162	journal	December 1999
Quantum Metrology Giovannetti, Vittorio; Lloyd, Seth; Maccone, Lorenzo Physical Review Letters, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevLett.96.010401	journal	January 2006
Scalable Quantum Simulation of Molecular Energies O’Malley, P. J. J.; Babbush, R.; Kivlichan, I. D. Physical Review X, Vol. 6, Issue 3 https://doi.org/10.1103/PhysRevX.6.031007	journal	July 2016
Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity Babbush, Ryan; Gidney, Craig; Berry, Dominic W. Physical Review X, Vol. 8, Issue 4 https://doi.org/10.1103/PhysRevX.8.041015	journal	October 2018
Quantum computational chemistry McArdle, Sam; Endo, Suguru; Aspuru-Guzik, Alán Reviews of Modern Physics, Vol. 92, Issue 1 https://doi.org/10.1103/RevModPhys.92.015003	journal	March 2020
Theory of Trotter Error with Commutator Scaling Childs, Andrew M.; Su, Yuan; Tran, Minh C. Physical Review X, Vol. 11, Issue 1 https://doi.org/10.1103/physrevx.11.011020	journal	February 2021
Quantum Computation and Quantum Information Nielsen, Michael A.; Chuang, Isaac; Grover, Lov K. American Journal of Physics, Vol. 70, Issue 5 https://doi.org/10.1119/1.1463744	journal	May 2002
Unbiased Estimation with Square Root Convergence for SDE Models Rhee, Chang-Han; Glynn, Peter W. Operations Research, Vol. 63, Issue 5 https://doi.org/10.1287/opre.2015.1404	journal	October 2015
Hamiltonian Simulation by Qubitization Low, Guang Hao; Chuang, Isaac L. Quantum, Vol. 3 https://doi.org/10.22331/q-2019-07-12-163	journal	July 2019
Time-dependent Hamiltonian simulation with L 1 -norm scaling Berry, Dominic W.; Childs, Andrew M.; Su, Yuan Quantum, Vol. 4 https://doi.org/10.22331/q-2020-04-20-254	journal	April 2020
Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization Kivlichan, Ian D.; Gidney, Craig; Berry, Dominic W. Quantum, Vol. 4 https://doi.org/10.22331/q-2020-07-16-296	journal	July 2020
Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems Lin, Lin; Tong, Yu Quantum, Vol. 4 https://doi.org/10.22331/q-2020-11-11-361	journal	November 2020
Near-optimal ground state preparation Lin, Lin; Tong, Yu Quantum, Vol. 4 https://doi.org/10.22331/q-2020-12-14-372	journal	December 2020
Fast amplification of QMA Nagaj, D.; Wocjan, P.; Zhang, Y. Quantum Information and Computation, Vol. 9, Issue 11&12 https://doi.org/10.26421/QIC9.11-12-8	journal	November 2009

Similar Records

Ground-State Preparation and Energy Estimation on Early Fault-Tolerant Quantum Computers via Quantum Eigenvalue Transformation of Unitary Matrices

Journal Article · 2022 · PRX Quantum · OSTI ID:1892087

Dong, Yulong; Lin, Lin; Tong, Yu

Assessment of quantum phase estimation protocols for early fault-tolerant quantum computers

Journal Article · 2024 · Physical Review A · OSTI ID:2474573

Nelson, Jacob S.; Baczewski, Andrew D.

Fault-tolerant quantum computation with cluster states

Journal Article · 2005 · Physical Review. A · OSTI ID:20653280

Nielsen, Michael A; Dawson, Christopher M

Title: Heisenberg-Limited Ground-State Energy Estimation for Early Fault-Tolerant Quantum Computers

Citation Formats

References (55)

Similar Records

Related Subjects