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.
Highlights
Gauge theory is the framework of the Standard Model, describing both electroweak and strong interactions among elementary particles, and is a guide beyond the Standard Model
As a new approach avoiding Fermion sign problem and an ideal avenue to study quantum phase transition (QPT) and real-time quantum dynamics, quantum simulations of LGTs are under study
Implementing quantum adiabatic algorithm in terms of quantum circuit consisting of universal quantum gates of one or two qubits, we present a digital scheme of quantum adiabatic simulation of quantum Z2 LGT, which is important in both high energy physics and condensed matter physics
Summary
For a d-dimensional square lattice with linear size L, the number of links is Nl = dLd, the number of plaquettes is Np = Nl(d − 1)/2 This theory possesses Z2 gauge invariance, similar to Gauss law, dictating that each eigenstate |ψ of H must satisfy. L∈C μ which is a product of σlx pierced by a non-contractible (d − 1)-dimensional surface Cμ on the dual lattice, μ = 1, · · · , d (figure 2). The degeneracy changes when g = 0, with only |Vν = 1, ν = 1, · · · , d remaining as the ground state They represent different topological sectors, because Vμ is conserved while each non-contractible (d − 1)dimensional surface can deform. There is Z2 topological order in the deconfined phase, while the confined phase is trivial, and QPT in this theory is topological [55, 57, 60]
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