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J. Klassen, M. Marvian, S. Piddock, M. Ioannou, I. Hen, and B. Terhal, Hardness and Ease of Curing the Sign Problem for Two-Local Qubit Hamiltonians , (2019), arXiv:1906.08800
Original
1906
Earlier work this paper cites.
G. Torlai, J. Carrasquilla, M. T. Fishman, R. G. Melko, and M. P. A. Fisher, Wavefunction positivization via automatic differentiation , (2019), arXiv:1906.04654
Original
1906
Earlier work this paper cites.
R. Levy and B. K. Clark, Mitigating the Sign Problem Through Basis Rotations , (2019), arXiv:1907.02076
Original
1907
Earlier work this paper cites.
A. J. Kim, P. Werner, and R. Valentí, Alleviating the Sign Problem in Quantum Monte Carlo Simulations of Spin-Orbit-Coupled Multi-Orbital Hubbard Models , (2019), arXiv:1907.11298
Original
1907
Earlier work this paper cites.
J. E. Hirsch, R. L. Sugar, D. J. Scalapino, and R. Blankenbecler, Monte Carlo simulations of one-dimensional fermion systems , Phys. Rev. B 26
1982
Earlier work this paper cites.
F. Barahona, On the computational complexity of Ising spin glass models , J. Phys. A 15
1982
Earlier work this paper cites.
N. Hatano and M. Suzuki, Representation basis in quantum Monte Carlo calculations and the negative-sign problem , Physics Letters A 163
1992
Earlier work this paper cites.
W. Bietenholz, A. Pochinsky, and U. J. Wiese, Meron-Cluster Simulation of the θ \theta Vacuum in the 2D O(3) Model , Phys. Rev. Lett. 75
1995
Earlier work this paper cites.
E. Dagotto and T. M. Rice, Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials , Science 271
1996
Earlier work this paper cites.
M. Takano, Spin ladder compounds , Physica C: Superconductivity Proceedings of the International Symposium on Frontiers of High - Tc Superconductivity, 263
1996
Earlier work this paper cites.
T. Nakamura, Vanishing of the negative-sign problem of quantum Monte Carlo simulations in one-dimensional frustrated spin systems , Phys. Rev. B 57
1998
Earlier work this paper cites.
S. Chandrasekharan and U.-J. Wiese, Meron-cluster solution of fermion sign problems , Phys. Rev. Lett. 83
1999
Earlier work this paper cites.
P. Henelius and A. W. Sandvik, Sign problem in Monte Carlo simulations of frustrated quantum spin systems , Phys. Rev. B 62
2000
Earlier work this paper cites.
D. P. Landau and K. Binder, A guide to Monte Carlo simulations in statistical physics (Cambridge University Press, 2000)
2000
Earlier work this paper cites.
K. N. Anagnostopoulos and J. Nishimura, New approach to the complex-action problem and its application to a nonperturbative study of superstring theory , Phys. Rev. D 66
2002
Earlier work this paper cites.
M. Troyer, F. Alet, S. Trebst, and S. Wessel, Non-local Updates for Quantum Monte Carlo Simulations , AIP Conf. Proc. 690
2003
Earlier work this paper cites.
C. Wu, J.-P. Hu, and S.-C. Zhang, Exact SO(5) Symmetry in the Spin- 3 / 2 Fermionic System , Phys. Rev. Lett. 91
2003
Earlier work this paper cites.
H.-J. Mikeska and A. K. Kolezhuk, in Quantum Magnetism , Lecture Notes in Physics, edited by U. Schollwöck, J. Richter, D. J. J. Farnell, and R. F. Bishop (Springer Berlin Heidelberg, Berlin, Heidelberg, 2004) pp. 1–83
2004
Earlier work this paper cites.
M. Troyer and U.-J. Wiese, Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations , Phys. Rev. Lett. 94
2005
Earlier work this paper cites.
C. M. Dawson, H. L. Haselgrove, A. P. Hines, D. Mortimer, M. A. Nielsen, and T. J. Osborne, Quantum computing and polynomial equations over the finite field Z_2 , Quant. Inf. Comp. 5
2005
Earlier work this paper cites.
M. A. Levin and X.-G. Wen, String-net condensation: A physical mechanism for topological phases , Phys. Rev. B 71
2005
Earlier work this paper cites.

Similar

M. Schmidt, G. Fung, and R. Rosales, Fast Optimization Methods for L1 Regularization: A Comparative Study and Two New Approaches , in Machine Learning: ECML 2007 , Lecture Notes in Computer Science, edited by J. N. Kok, J. Koronacki, R. L. d. Mantaras, S. Matwin, D. Mladenic, and A. Skowron (Springer Berlin Heidelberg, 2007) pp. 286–297
2007
Cited alongside, same era.
M. Nyfeler, F.-J. Jiang, F. Kämpfer, and U.-J. Wiese, Nested Cluster Algorithm for Frustrated Quantum Antiferromagnets , Phys. Rev. Lett. 100
Original
2008
Cited alongside, same era.
S. Bravyi, D. P. DiVincenzo, R. I. Oliveira, and B. M. Terhal, The Complexity of Stoquastic Local Hamiltonian Problems , Quant. Inf. Comp. 8
2008
Cited alongside, same era.
T. Abrudan, J. Eriksson, and V. Koivunen, Conjugate gradient algorithm for optimization under unitary matrix constraint , Signal Processing 89
2009
Cited alongside, same era.

Then

J. Carrasquilla, Z. Hao, and R. G. Melko, A two-dimensional spin liquid in quantum kagome ice , Nature Communications 6
Original
2015
Later among the works it cites.
H. Pashayan, J. J. Wallman, and S. D. Bartlett, Estimating outcome probabilities of quantum circuits using quasiprobabilities , Phys. Rev. Lett. 115
Original
2015
Later among the works it cites.
Z.-X. Li, Y.-F. Jiang, and H. Yao, Majorana-Time-Reversal Symmetries: A Fundamental Principle for Sign-Problem-Free Quantum Monte Carlo Simulations , Phys. Rev. Lett. 117
Original
2016
Later among the works it cites.
F. Alet, K. Damle, and S. Pujari, Sign-Problem-Free Monte Carlo Simulation of Certain Frustrated Quantum Magnets , Phys. Rev. Lett. 117
Original
2016
Later among the works it cites.
A. Honecker, S. Wessel, R. Kerkdyk, T. Pruschke, F. Mila, and B. Normand, Thermodynamic properties of highly frustrated quantum spin ladders: Influence of many-particle bound states , Phys. Rev. B 93

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2019

Easing the Monte Carlo sign problem

Hangleiter, Dominik, Roth, Ingo, Nagaj, Daniel et al.

Understand

Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems -- their phase transitions, ground and thermal state properties.

However, in many interesting situations QMC methods are faced with a sign problem, causing the severe limitation of an exponential increase in the sampling complexity and hence the run-time of the QMC algorithm.
In this work, we develop a systematic, generally applicable, and practically feasible methodology for easing the sign problem by efficiently computable basis changes and use it to rigorously assess the sign problem.
Our framework introduces measures of non-stoquasticity that -- as we demonstrate analytically and numerically -- at the same time provide a practically relevant and efficiently computable figure of merit for the severity of the sign problem.

Built on

J. Klassen, M. Marvian, S. Piddock, M. Ioannou, I. Hen, and B. Terhal, Hardness and Ease of Curing the Sign Problem for Two-Local Qubit Hamiltonians , (2019), arXiv:1906.08800
Original
1906
Earlier work this paper cites.
G. Torlai, J. Carrasquilla, M. T. Fishman, R. G. Melko, and M. P. A. Fisher, Wavefunction positivization via automatic differentiation , (2019), arXiv:1906.04654
Original
1906
Earlier work this paper cites.
R. Levy and B. K. Clark, Mitigating the Sign Problem Through Basis Rotations , (2019), arXiv:1907.02076
Original
1907
Earlier work this paper cites.
A. J. Kim, P. Werner, and R. Valentí, Alleviating the Sign Problem in Quantum Monte Carlo Simulations of Spin-Orbit-Coupled Multi-Orbital Hubbard Models , (2019), arXiv:1907.11298
Original
1907
Earlier work this paper cites.
J. E. Hirsch, R. L. Sugar, D. J. Scalapino, and R. Blankenbecler, Monte Carlo simulations of one-dimensional fermion systems , Phys. Rev. B 26
1982
Earlier work this paper cites.
F. Barahona, On the computational complexity of Ising spin glass models , J. Phys. A 15
1982
Earlier work this paper cites.
N. Hatano and M. Suzuki, Representation basis in quantum Monte Carlo calculations and the negative-sign problem , Physics Letters A 163
1992
Earlier work this paper cites.
W. Bietenholz, A. Pochinsky, and U. J. Wiese, Meron-Cluster Simulation of the θ \theta Vacuum in the 2D O(3) Model , Phys. Rev. Lett. 75
1995
Earlier work this paper cites.
E. Dagotto and T. M. Rice, Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials , Science 271
1996
Earlier work this paper cites.
M. Takano, Spin ladder compounds , Physica C: Superconductivity Proceedings of the International Symposium on Frontiers of High - Tc Superconductivity, 263
1996
Earlier work this paper cites.
T. Nakamura, Vanishing of the negative-sign problem of quantum Monte Carlo simulations in one-dimensional frustrated spin systems , Phys. Rev. B 57
1998
Earlier work this paper cites.
S. Chandrasekharan and U.-J. Wiese, Meron-cluster solution of fermion sign problems , Phys. Rev. Lett. 83
1999
Earlier work this paper cites.
P. Henelius and A. W. Sandvik, Sign problem in Monte Carlo simulations of frustrated quantum spin systems , Phys. Rev. B 62
2000
Earlier work this paper cites.
D. P. Landau and K. Binder, A guide to Monte Carlo simulations in statistical physics (Cambridge University Press, 2000)
2000
Earlier work this paper cites.
K. N. Anagnostopoulos and J. Nishimura, New approach to the complex-action problem and its application to a nonperturbative study of superstring theory , Phys. Rev. D 66
2002
Earlier work this paper cites.
M. Troyer, F. Alet, S. Trebst, and S. Wessel, Non-local Updates for Quantum Monte Carlo Simulations , AIP Conf. Proc. 690
2003
Earlier work this paper cites.
C. Wu, J.-P. Hu, and S.-C. Zhang, Exact SO(5) Symmetry in the Spin- 3 / 2 Fermionic System , Phys. Rev. Lett. 91
2003
Earlier work this paper cites.
H.-J. Mikeska and A. K. Kolezhuk, in Quantum Magnetism , Lecture Notes in Physics, edited by U. Schollwöck, J. Richter, D. J. J. Farnell, and R. F. Bishop (Springer Berlin Heidelberg, Berlin, Heidelberg, 2004) pp. 1–83
2004
Earlier work this paper cites.
M. Troyer and U.-J. Wiese, Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations , Phys. Rev. Lett. 94
2005
Earlier work this paper cites.
C. M. Dawson, H. L. Haselgrove, A. P. Hines, D. Mortimer, M. A. Nielsen, and T. J. Osborne, Quantum computing and polynomial equations over the finite field Z_2 , Quant. Inf. Comp. 5
2005
Earlier work this paper cites.
M. A. Levin and X.-G. Wen, String-net condensation: A physical mechanism for topological phases , Phys. Rev. B 71
2005
Earlier work this paper cites.

Similar

M. Schmidt, G. Fung, and R. Rosales, Fast Optimization Methods for L1 Regularization: A Comparative Study and Two New Approaches , in Machine Learning: ECML 2007 , Lecture Notes in Computer Science, edited by J. N. Kok, J. Koronacki, R. L. d. Mantaras, S. Matwin, D. Mladenic, and A. Skowron (Springer Berlin Heidelberg, 2007) pp. 286–297
2007
Cited alongside, same era.
M. Nyfeler, F.-J. Jiang, F. Kämpfer, and U.-J. Wiese, Nested Cluster Algorithm for Frustrated Quantum Antiferromagnets , Phys. Rev. Lett. 100
Original
2008
Cited alongside, same era.
S. Bravyi, D. P. DiVincenzo, R. I. Oliveira, and B. M. Terhal, The Complexity of Stoquastic Local Hamiltonian Problems , Quant. Inf. Comp. 8
2008
Cited alongside, same era.
T. Abrudan, J. Eriksson, and V. Koivunen, Conjugate gradient algorithm for optimization under unitary matrix constraint , Signal Processing 89
2009
Cited alongside, same era.

Then

J. Carrasquilla, Z. Hao, and R. G. Melko, A two-dimensional spin liquid in quantum kagome ice , Nature Communications 6
Original
2015
Later among the works it cites.
H. Pashayan, J. J. Wallman, and S. D. Bartlett, Estimating outcome probabilities of quantum circuits using quasiprobabilities , Phys. Rev. Lett. 115
Original
2015
Later among the works it cites.
Z.-X. Li, Y.-F. Jiang, and H. Yao, Majorana-Time-Reversal Symmetries: A Fundamental Principle for Sign-Problem-Free Quantum Monte Carlo Simulations , Phys. Rev. Lett. 117
Original
2016
Later among the works it cites.
F. Alet, K. Damle, and S. Pujari, Sign-Problem-Free Monte Carlo Simulation of Certain Frustrated Quantum Magnets , Phys. Rev. Lett. 117
Original
2016
Later among the works it cites.
A. Honecker, S. Wessel, R. Kerkdyk, T. Pruschke, F. Mila, and B. Normand, Thermodynamic properties of highly frustrated quantum spin ladders: Influence of many-particle bound states , Phys. Rev. B 93

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

S. Bravyi and B. Terhal, Complexity of stoquastic frustration-free Hamiltonians , SIAM J. Comput. 39

Original

2009

Cited alongside, same era.

S. Trotzky, L. Pollet, F. Gerbier, U. Schnorrberger, I. Bloch, N. Prokof’ev, B. Svistunov, and M. Troyer, Suppression of the critical temperature for superfluidity near the Mott transition: validating a quantum simulator , Nature Phys. 6

2010

Cited alongside, same era.

A. W. Sandvik, Computational Studies of Quantum Spin Systems , AIP Conference Proceedings 1297

Original

2010

Cited alongside, same era.

ISO 16269-4:2010, Statistical interpretation of data – Part 4: Detection and treatment of outliers , Standard (International Organization for Standardization, Geneva, CH, 2010)

2010

Cited alongside, same era.

S. P. Jordan, D. Gosset, and P. J. Love, Quantum-Merlin-Arthur–complete problems for stoquastic Hamiltonians and Markov matrices , Phys. Rev. A 81

Original

2010

Cited alongside, same era.

L. Pollet, Recent developments in Quantum Monte-Carlo simulations with applications for cold gases , Rep. Prog. Phys. 75

Original

2012

Cited alongside, same era.

J. S. Spencer, N. S. Blunt, and W. M. Foulkes, The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method , The Journal of Chemical Physics 136

Original

2012

Cited alongside, same era.

S. Foucart and H. Rauhut, A Mathematical Introduction to Compressive Sensing , Applied and Numerical Harmonic Analysis (Springer New York, New York, NY, 2013)

2013

Cited alongside, same era.

Original

2016