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Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy.
Time in the quantum theory and the uncertainty relation for time and energy
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General theory of fractal path integrals with applications to many-body theories and statistical physics
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Simulating physical phenomena by quantum networks
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Estimation of the local density of states on a quantum computer
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The complexity of the local Hamiltonian problem
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How to perform the most accurate possible phase measurements
D. W. Berry, B. L. Higgins, S. D. Bartlett, M. W. Mitchell, G. J. Pryde, and H. M. Wiseman · 2009
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A variational eigenvalue solver on a photonic quantum processor
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Hamiltonian simulation with nearly optimal dependence on all parameters
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Multilevel monte carlo methods
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Quantum eigenvalue estimation via time series analysis
R. D. Somma · 2019
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Time-dependent hamiltonian simulation with l1-norm scaling
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Quantum simulation via randomized product formulas: Low gate complexity with accuracy guarantees
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A non-orthogonal variational quantum eigensolver
W. J. Huggins, J. Lee, U. Baek, B. O’Gorman, and K. B. Whaley · 2020
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Improved fault-tolerant quantum simulation of condensed-phase correlated electrons via trotterization
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Bayesian inference via rejection filtering
N. Wiebe, C. Granade, A. Kapoor, and K. M. Svore · 2015
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The theory of variational hybrid quantum-classical algorithms
J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik · 2016
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Scalable quantum simulation of molecular energies
P. J. O’Malley, R. Babbush, I. D. Kivlichan, J. Romero, J. R. McClean, R. Barends, J. Kelly, P. Roushan, A. Tranter, N. Ding, et al · 2016
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Fast-forwarding of Hamiltonians and exponentially precise measurements
Y. Atia and D. Aharonov · 2017
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Optimal hamiltonian simulation by quantum signal processing
G. H. Low and I. L. Chuang · 2017
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Encoding electronic spectra in quantum circuits with linear T complexity
R. Babbush, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, A. Paler, A. Fowler, and H. Neven · 2018
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I. D. Kivlichan, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, W. Sun, Z. Jiang, N. Rubin, A. Fowler, A. Aspuru-Guzik, et al · 2020
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Near-optimal ground state preparation
L. Lin and Y. Tong · 2020
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Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems
L. Lin and Y. Tong · 2020
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Algorithms for quantum simulation at finite energies
S. Lu, M. C. Bañuls, and J. I. Cirac · 2020
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Quantum computational chemistry
S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan · 2020
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Error mitigation via verified phase estimation
T. E. O’Brien, S. Polla, N. C. Rubin, W. J. Huggins, S. McArdle, S. Boixo, J. R. McClean, and R. Babbush · 2020
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A. Russo, K. Rudinger, B. Morrison, and A. Baczewski · 2020
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Compilation of fault-tolerant quantum heuristics for combinatorial optimization
Y. R. Sanders, D. W. Berry, P. C. Costa, L. W. Tessler, N. Wiebe, C. Gidney, H. Neven, and R. Babbush · 2020
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A multireference quantum Krylov algorithm for strongly correlated electrons
N. H. Stair, R. Huang, and F. A. Evangelista · 2020
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Nearly tight Trotterization of interacting electrons
Y. Su, H.-Y. Huang, and E. T. Campbell · 2020
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Destructive error interference in product-formula lattice simulation
M. C. Tran, S.-K. Chu, Y. Su, A. M. Childs, and A. V. Gorshkov · 2020
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Focus beyond quadratic speedups for error-corrected quantum advantage
R. Babbush, J. R. McClean, M. Newman, C. Gidney, S. Boixo, and H. Neven · 2021
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Theory of Trotter error with commutator scaling
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First-order Trotter error from a second-order perspective
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