Review on Quantum Computing for Lattice Field Theory

Abstract

In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the conventional Monte Carlo approach, such as the sign-problem afflicted regimes of finite baryon density, topological terms, and out-of-equilibrium dynamics. First proof-of-concept quantum computations of lattice gauge theories in (1+1) dimensions have been accomplished, and first resource-efficient quantum algorithms for lattice gauge theories in (1+1) and (2+1) dimensions have been developed. The path towards quantum computations of (3+1)-dimensional lattice gauge theories, including Lattice QCD, requires many incremental steps of improving both quantum hardware and quantum algorithms. After reviewing these requirements and recent advances, we discuss the main challenges and future directions.

Qudit-based quantum computing with SRF cavities at Fermilab

“…Therefore, the second term implies that the qubit's frequency depends on the photon number of the storage mode. For instance, the qubit frequency 𝜔 (0) 𝑞 = 𝜔 𝑞 when the storage is in its ground state |0⟩ changes to 𝜔 (1) 𝑞 = 𝜔 𝑞 + 𝜒 𝑠 when the storage is excited to |1⟩. In general, if there are 𝑛 photons in the storage, the effective qubit frequency is given by…”

“…Despite the great success of classical numerical methods, several problems become intractable under certain important parameter regimes due to the so-called sign problem. Recent theoretical studies have proposed that these obstacles can be circumvented by utilizing quantum algorithms [1,2]. For example, several resource-efficient quantum algorithms for (1+1), (2+1) and (3+1) dimensional gauge theories have been developed [3][4][5][6][7][8][9][10].…”

First-Order Phase Transition of the Schwinger Model with a Quantum Computer

“…Thus, variations of the conventional MC approach have been proposed to tackle this obstacle [11], but so far only with limited success. Hence, there is great interest in al-ternative methods that bypass the issue, such as tensor networks and quantum computing [14][15][16][17]. In particular, quantum computing offers a promising alternative route [15,16,18], with already a number of successful demonstrations [19][20][21][22][23][24][25][26].…”

Implementation of bond weighting method for the Grassmann tensor renormalization group

“…In the high-energy community, the Grassmann TRG was first applied to the Schwinger model [3]. Since fermions obey Pauli's excursion rule, fermionic systems are well suited to be represented by tensor networks or qubits [4,5]. In the case of the path-integral formalism, fermions are described by the Grassmann numbers and we can immediately express the given fermionic path integral as a Grassmann tensor network.…”