Sign Problems in Quantum Field Theory: Classical and Quantum Approaches
- URL: http://arxiv.org/abs/2006.03683v2
- Date: Mon, 22 Jun 2020 02:28:11 GMT
- Title: Sign Problems in Quantum Field Theory: Classical and Quantum Approaches
- Authors: Scott Lawrence
- Abstract summary: lattice field computation theory provides non-perturbative access to equilibrium physics of quantum fields.
When applied to certain fermionic systems, or to the calculation of out-of-equilibrium physics, Monte Carlo calculations encounter the so-called sign problem.
This thesis details two methods for mitigating or avoiding the sign problem.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Monte Carlo calculations in the framework of lattice field theory provide
non-perturbative access to the equilibrium physics of quantum fields. When
applied to certain fermionic systems, or to the calculation of
out-of-equilibrium physics, these methods encounter the so-called sign problem,
and computational resource requirements become impractically large. These
difficulties prevent the calculation from first principles of the equation of
state of quantum chromodynamics, as well as the computation of transport
coefficients in quantum field theories, among other things.
This thesis details two methods for mitigating or avoiding the sign problem.
First, via the complexification of the field variables and the application of
Cauchy's integral theorem, the difficulty of the sign problem can be changed.
This requires searching for a suitable contour of integration. Several methods
of finding such a contour are discussed, as well as the procedure for
integrating on it. Two notable examples are highlighted: in one case, a contour
exists which entirely removes the sign problem, and in another, there is
provably no contour available to improve the sign problem by more than a
(parametrically) small amount.
As an alternative, physical simulations can be performed with the aid of a
quantum computer. The formal elements underlying a quantum computation - that
is, a Hilbert space, unitary operators acting on it, and Hermitian observables
to be measured - can be matched to those of a quantum field theory. In this way
an error-corrected quantum computer may be made to serve as a well controlled
laboratory. Precise algorithms for this task are presented, specifically in the
context of quantum chromodynamics.
Related papers
- What is computable and non-computable in the quantum domain: 7 statements and 3 conjectures [0.7892577704654171]
There is no universal approach that helps to define a scope of problems that quantum computers are able to speed up.
On the one hand, the class of quantum states that is of interest for quantum computing should be complex.
On the other hand, such quantum states should be reachable on a practical quantum computer.
arXiv Detail & Related papers (2024-03-25T15:47:35Z) - Simulating 2D lattice gauge theories on a qudit quantum computer [2.2246996966725305]
We present a quantum computation of the properties of the basic building block of two-dimensional lattice quantum electrodynamics.
This is made possible by the use of a trapped-ion qudit quantum processor.
Qudits are ideally suited for describing gauge fields, which are naturally high-dimensional.
arXiv Detail & Related papers (2023-10-18T17:06:35Z) - Quantum algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
The anticipated applications of quantum computers span across science and industry.
We present a survey of several potential application areas of quantum algorithms.
We outline the challenges and opportunities in each area in an "end-to-end" fashion.
arXiv Detail & Related papers (2023-10-04T17:53:55Z) - General quantum algorithms for Hamiltonian simulation with applications
to a non-Abelian lattice gauge theory [44.99833362998488]
We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers.
The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions.
The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
arXiv Detail & Related papers (2022-12-28T18:56:25Z) - Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
We study the problem of designing worst-case to average-case reductions for quantum algorithms.
We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
arXiv Detail & Related papers (2022-12-06T22:01:49Z) - Quantum Computing Quantum Monte Carlo [8.69884453265578]
We propose a hybrid quantum-classical algorithm that integrates quantum computing and quantum Monte Carlo.
Our work paves the way to solving practical problems with intermediatescale and early-fault tolerant quantum computers.
arXiv Detail & Related papers (2022-06-21T14:26:24Z) - Interactive Protocols for Classically-Verifiable Quantum Advantage [46.093185827838035]
"Interactions" between a prover and a verifier can bridge the gap between verifiability and implementation.
We demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer.
arXiv Detail & Related papers (2021-12-09T19:00:00Z) - Quantum variational solving of the Wheeler-DeWitt equation [0.0]
We propose and investigate a new method of solving the Wheeler-DeWitt equation, which employs a variational quantum computing approach.
For this purpose, the gravitational system is regularized, by performing spherical compactification of the phase space.
This makes the system's Hilbert space finite-dimensional and allows to use $SU(2)$ variables, which are easy to handle in quantum computing.
arXiv Detail & Related papers (2021-11-04T17:44:49Z) - Sampling and the complexity of nature [0.0]
I investigate the complexity-theoretic and physical foundations of quantum sampling algorithms.
I shed light on how and under which conditions quantum sampling devices can be tested or verified.
An overarching theme of the thesis is the quantum sign problem which arises due to destructive interference between paths.
arXiv Detail & Related papers (2020-12-14T19:35:27Z) - Quantum Statistical Complexity Measure as a Signalling of Correlation
Transitions [55.41644538483948]
We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions.
We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain.
We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
arXiv Detail & Related papers (2020-02-05T00:45:21Z) - Quantum computation of thermal averages in the presence of a sign
problem [45.82374977939355]
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system.
We show how quantum algorithms completely solve the problem, and discuss how this can apply to more complex systems of physical interest.
arXiv Detail & Related papers (2020-01-15T14:01:11Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.