Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theor
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Received: January 5, Revised: May 26, Accepted: July 28, Published: August 28,
2020 2020 2020 2020
Xiaopeng Cui,a Yu Shia,1 and Ji-Chong Yanga,b a
Department of Physics & State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China b Department of Physics, Liaoning Normal University, Dalian 116029, China
E-mail: [email protected], [email protected], [email protected] 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. Keywords: Confinement, Lattice Quantum Field Theory, Spontaneous Symmetry Breaking, Topological States of Matter ArXiv ePrint: 1910.08020 1
Corresponding author.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP08(2020)160
JHEP08(2020)160
Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theory
Contents 1 Introduction
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5 5 7 11 13 14 14
3 Results of pseudoquantum simulation 3.1 Wegner-Wilson loops 3.2 Critical points and duality 3.3 Densities of states 3.4 Orders of quantum phase transitions 3.5 Topology
15 16 17 20 22 25
4 Summary
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1
Introduction
Quantum simulation and quantum computation can efficiently solve some problems that cannot be efficiently solved in classical computers [1–4], and is under extensive studies worldwide, thanks to the rapid development of quantum science and technology. A controllable quantum system, which may even be universal or programmable, simulates various quantum systems, whose physical properties can be conveniently investigated with various parameter values. Even with only tens of qubits, far less than those in full fault-tolerant quantum comp
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