Quantum simulation of lattice gauge theories in more than one space dimension—requirements, challenges and methods

Over recent years, the relatively young field of quantum simulation of lattice gauge theories, aiming at implementing simulators of gauge theories with quantum platforms, has gone through a rapid development process. Nowadays, it is not only of interest to the quantum information and technology communities. It is also seen as a valid tool for tackling hard, non-perturbative gauge theory problems by particle and nuclear physicists. Along the theoretical progress, nowadays more and more experiments implementing such simulators are being reported, manifesting beautiful results, but mostly on 1 + 1 dimensional physics. In this article, we review the essential ingredients and requirements of lattice gauge theories in more dimensions and discuss their meanings, the challenges they pose and how they could be dealt with, potentially aiming at the next steps of this field towards simulating challenging physical problems in analogue, or analogue-digital ways. This article is part of the theme issue ‘Quantum technologies in particle physics’.

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Z2 lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation

Physical Review B ◽

10.1103/physrevb.104.085138 ◽

2021 ◽

Vol 104 (8) ◽

Author(s):

Lukas Homeier ◽

Christian Schweizer ◽

Monika Aidelsburger ◽

Arkady Fedorov ◽

Fabian Grusdt

Keyword(s):

Gauge Theories ◽

Quantum Simulation ◽

Lattice Gauge ◽

Lattice Gauge Theories ◽

Toric Code

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Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theory

Journal of High Energy Physics ◽

10.1007/jhep08(2020)160 ◽

2020 ◽

Vol 2020 (8) ◽

Author(s):

Xiaopeng Cui ◽

Yu Shi ◽

Ji-Chong Yang

Keyword(s):

Gauge Theory ◽

Particle Physics ◽

Lattice Gauge Theory ◽

Quantum Phase Transitions ◽

Rapid Development ◽

Quantum Simulation ◽

Quantum Processes ◽

Perturbative Approach ◽

Time Dynamics ◽

Lattice Gauge

Abstract Gauge theory is the framework of the Standard Model of particle physics and is also important in condensed matter physics. As its major non-perturbative approach, lattice gauge theory is traditionally implemented using Monte Carlo simulation, consequently it usually suffers such problems as the Fermion sign problem and the lack of real-time dynamics. Hopefully they can be avoided by using quantum simulation, which simulates quantum systems by using controllable true quantum processes. The field of quantum simulation is under rapid development. Here we present a circuit-based digital scheme of quantum simulation of quantum ℤ2 lattice gauge theory in 2 + 1 and 3 + 1 dimensions, using quantum adiabatic algorithms implemented in terms of universal quantum gates. Our algorithm generalizes the Trotter and symmetric decompositions to the case that the Hamiltonian varies at each step in the decomposition. Furthermore, we carry through a complete demonstration of this scheme in classical GPU simulator, and obtain key features of quantum ℤ2 lattice gauge theory, including quantum phase transitions, topological properties, gauge invariance and duality. Hereby dubbed pseudoquantum simulation, classical demonstration of quantum simulation in state-of-art fast computers not only facilitates the development of schemes and algorithms of real quantum simulation, but also represents a new approach of practical computation.

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