Real-time lattice gauge theory actions: Unitarity, convergence, and path integral contour deformations

Kanwar, Gurtej; Wagman, Michael L.

doi:10.1103/physrevd.104.014513

Cited by 18 publications

(6 citation statements)

References 115 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The path integral approach to real-time system is formulated by Schwinger and Keldysh [6,7] and its lattice version is discussed in [9,10,14,15]. In the following we consider 1+1 dimensional lattice system, whose coordinate is denoted as…”

Section: Closed-time Formalismmentioning

confidence: 99%

A novel method to evaluate real-time path integral for scalar $\phi^4$ theory

Takeda

2022

Proceedings of the 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)

View full text Add to dashboard Cite

We present a new scheme which numerically evaluates the real-time path integral for ϕ 4 real scalar field theory in a lattice version of the closed-time formalism. First step of the scheme is to rewrite the path integral in an explicitly convergent form by applying Cauchy's integral theorem to each scalar field. In the step an integration path for the scalar field is deformed on a complex plane such that the ϕ 4 term becomes a damping factor in the path integral. Secondly the integrations of the complexified scalar fields are discretized by the Gauss-Hermite quadrature and then the path integral turns out to be a multiple sum. Finally in order to efficiently evaluate the summation we apply information compression technique using the singular value decomposition to the discretized path integral, then a tensor network representation for the path integral is obtained after integrating the discretized fields. As a demonstration, by using the resulting tensor network we numerically evaluate the time-correlator in 1+1 dimensional system. For confirmation, we compare our result with the exact one at small spatial volume. Furthermore, we show the correlator in relatively large volume using a coarse-graining scheme and verify that the result is stable against changes of a truncation order for the coarse-graining scheme.

show abstract

Section: Closed-time Formalismmentioning

confidence: 99%

A novel method to evaluate real-time path integral for scalar $\phi^4$ theory

Takeda

2022

Proceedings of the 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)

View full text Add to dashboard Cite

show abstract

“…In the end, we have found a unitary one-step scheme, namely, equation (18) with the choices of equations ( 27) and (30), which generates the two-step scheme of unitary fermions.…”

Section: The 'Underlying' Unitary One-step Schemementioning

confidence: 99%

“…Lately, real-time LGT has entered a new era with the advent of quantum simulation [13] and quantum computation [14], which reduce exponentially the cost in simulating many-body quantum systems. As above, there are two types of real-time LGTs: (a) real-time Hamiltonian LGT, where time is either kept continuous (with the perspective of analog quantum simulations [15][16][17][18]) or discretized (with the perspective of digital quantum simulations [19,20] and quantum algorithms [21][22][23][24][25][26][27][28][29]), and (b) real-time Lagrangian LGT, where time is discretized but spacetime is not Wick-rotated [30]. Our paper combines both perspectives.…”

Section: Introductionmentioning

confidence: 99%

A single-particle framework for unitary lattice gauge theory in discrete time

Arnault

Cedzich

2022

New J. Phys.

View full text Add to dashboard Cite

We construct a real-time lattice-gauge-theory-type action for a spin-1/2 matter field of a single particle on a (1+1)-dimensional spacetime lattice. The framework is based on a discrete-time quantum walk, and is hence inherently unitary and strictly local, i.e., transition amplitudes exactly vanish outside of a lightcone on the lattice. We then provide a lattice Noether's theorem for internal symmetries of this action. We further couple this action to an electromagnetic field by a minimal substitution on the lattice. Finally, we suggest a real-time lattice-gauge-theory-type action for the electromagnetic field in arbitrary spacetime dimensions, and derive its classical equations of motion, which are lattice versions of Maxwell's equations.

show abstract

“…However, LQCD has been unable to predict dynamical quantities such as inelastic scattering cross-sections above four particle inelastic thresholds and real-time dynamics due to sign problems [3]. While recent work has been done to address these problems [4][5][6][7][8], quantum computing provides an avenue for advantage over classical computing by circumventing this signal-tonoise problem entirely [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Noise Improvements in Quantum Simulations of sQED using Qutrits

Gustafson

2022

Preprint

View full text Add to dashboard Cite

We present an argument for the advantages of using qudits over qubits for scalar Quantum Electrodynamics in (1 + 1)d. We measure the mass gap using an out of time correlator as a function of noise coming from an amplitude damping error channel and a generalized Pauli channel decoherence channel for both qubits and qutrits. For the same error in determination of the mass, the qutrit simulations can tolerate 10 to 100x larger gate noise than a qubit simulations. We find that 20 per-cent accuracy on the mass gap could be possible in the near future with a qutrits but is infeasible using qubits.

show abstract

Real-time lattice gauge theory actions: Unitarity, convergence, and path integral contour deformations

Cited by 18 publications

References 115 publications

A novel method to evaluate real-time path integral for scalar $\phi^4$ theory

A novel method to evaluate real-time path integral for scalar $\phi^4$ theory

A single-particle framework for unitary lattice gauge theory in discrete time

Noise Improvements in Quantum Simulations of sQED using Qutrits

Contact Info

Product

Resources

About