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Quantized gravitational responses, the sign problem, and quantum complexity.
Zohar Ringel1,2, Dmitry L Kovrizhin1,3
1Rudolf Peierls Centre for Theoretical Physics, Keble Road, Oxford OX1 3NP, UK.
Science Advances
|September 30, 2017
Summary
Quantized gravitational responses obstruct sign-free quantum Monte Carlo (QMC) simulations for bosonic systems. This finding impacts condensed matter physics and quantum simulations, especially those with broken time-reversal symmetry.
Area of Science:
- Quantum physics
- Condensed matter physics
- Computational physics
Background:
- Efficient classical simulation of quantum systems is a major challenge.
- The sign problem in quantum Monte Carlo (QMC) simulations prevents sign-free calculations for many important quantum systems.
- The existence of a fundamental obstruction to sign-free representations in generic quantum systems is an open question.
Purpose of the Study:
- To investigate obstructions to local sign-free QMC simulations in systems with bosonic degrees of freedom.
- To explore the connection between quantized gravitational responses and the sign problem.
- To examine these phenomena in condensed matter systems and models with broken time-reversal symmetry.
Main Methods:
- Analysis of systems with bosonic degrees of freedom.
- Identification of quantized gravitational responses as obstructions.
- Application of arguments to condensed matter systems like fractional quantum Hall effects.
- Examination of systems with spontaneously broken time-reversal (TR) symmetry, including perturbed quantum Kagome antiferromagnets.
- Study of vertex models where TR symmetry is preserved.
Main Results:
- Quantized gravitational responses are identified as obstructions to local sign-free QMC.
- These responses are linked to phenomena such as fractional quantum Hall effects in condensed matter.
- Similar obstructions are shown to exist in systems with broken time-reversal symmetry.
- The connection between gravitational responses and the sign problem is also observed in vertex models with preserved TR symmetry.
Conclusions:
- Quantized gravitational responses present a fundamental obstruction to sign-free QMC simulations for certain quantum systems.
- This finding clarifies limitations in simulating quantum systems classically, particularly those involving bosonic degrees of freedom.
- The results have implications for understanding phenomena in condensed matter physics and developing more efficient quantum simulation algorithms.