Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions

Nguyen, Nhung H.; Tran, Minh C.; Zhu, Yingyue; Green, Alaina; Alderete, C. Huerta; Davoudi, Zohreh; Linke, Norbert

doi:10.1103/prxquantum.3.020324

Cited by 78 publications

(15 citation statements)

References 87 publications

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“…Motivated by the dearth of research activity pertaining to DQS of coupled fermion-boson models, as well as the emerging trend of simulating models from highand medium-energy physics [34][35][36][37][38][39][40], in this paper we present a DQS of the nonequilibrium dynamics following a quench [41] of scalar Yukawa interaction [42]. Such coupling -first proposed in the context of interaction between nucleons mediated by pions [43] -involves fermion-, antifermion-, and boson degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

Digital quantum simulation of scalar Yukawa coupling: Dynamics following an interaction quench on IBM Q

Kaldenbach¹,

Heller²,

Alber³

et al. 2022

Preprint

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Motivated by the dearth of studies pertaining to the digital quantum simulation of coupled fermion-boson systems and the revitalized interest in simulating models from medium-and highenergy physics, we investigate the nonequilibrium dynamics following a Yukawa-interaction quench on IBM Q. After adopting -due to current quantum-hardware limitations -a single-site (zerodimensional) version of the scalar Yukawa-coupling model as our point of departure, we design low-depth quantum circuits that emulate its dynamics with up to three bosons. In particular, using advanced circuit-optimization techniques, in the one-boson case we demonstrate circuit compression, i.e. design a shallow (constant-depth) circuit that contains only two CNOT gates, regardless of the total simulation time. In the three-boson case -where such a compression is not possible -we design a circuit in which one Trotter step entails 8 CNOTs, this number being far below the maximal CNOT-cost of a generic three-qubit gate. Using an analogy with the travelling salesman problem, we also provide a CNOT-cost estimate for quantum circuits emulating the system dynamics for higher boson-number truncations. Finally, based on the proposed circuits for one-and three-boson cases, we quantify the system dynamics for several different initial states by evaluating the expected fermion-and boson numbers at an arbitrary time after the quench. We validate our results by finding their good agreement with the exact ones obtained through classical benchmarking.Higgs mechanism, after electroweak symmetry breaking [42]. Finally, it is worthwhile mentioning that interaction mechanism somewhat analogous to Yukawa coupling are of relevance in the context of strongly-correlated systems in condensed-matter physics [56].

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Section: Introductionmentioning

confidence: 99%

Digital quantum simulation of scalar Yukawa coupling: Dynamics following an interaction quench on IBM Q

Kaldenbach¹,

Heller²,

Alber³

et al. 2022

Preprint

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show abstract

“…Therefore, local fermion-to-qubit mappings trade non-locality in the operators for extra qubits and non-locality in the states. To ensure the simulation proceeds in the allowed subspace of the Hilbert space-that is, that the local and non-local constraints are satisfied-strategies similar to preserving (gauge) symmetries in latticegauge-theory simulations [47][48][49][50][51][52][53][54] can be explored.…”

Section: Local Fermion-to-qubit Mappingsmentioning

confidence: 99%

Parallelization techniques for quantum simulation of fermionic systems

Bringewatt

Davoudi

2023

Quantum

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Mapping fermionic operators to qubit operators is an essential step for simulating fermionic systems on a quantum computer. We investigate how the choice of such a mapping interacts with the underlying qubit connectivity of the quantum processor to enable (or impede) parallelization of the resulting Hamiltonian-simulation algorithm. It is shown that this problem can be mapped to a path coloring problem on a graph constructed from the particular choice of encoding fermions onto qubits and the fermionic interactions onto paths. The basic version of this problem is called the weak coloring problem. Taking into account the fine-grained details of the mapping yields what is called the strong coloring problem, which leads to improved parallelization performance. A variety of illustrative analytical and numerical examples are presented to demonstrate the amount of improvement for both weak and strong coloring-based parallelizations. Our results are particularly important for implementation on near-term quantum processors where minimizing circuit depth is necessary for algorithmic feasibility.

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“…For applications in quantum field theory, it has been shown that scalar field theory with the φ 4 (x) interaction can be efficiently simulated on a quantum computer [117][118][119][120]. Later studies investigated fermionic fields [121] and gauge theories in low dimensions [122][123][124][125][126][127][128][129][130]. Quantum simulation has been explored to study open quantum systems in heavy ion collisions such as heavy quarks and jets [131,132].…”

Section: Introductionmentioning

confidence: 99%

Quantum Simulation of Light-Front QCD for Jet Quenching in Nuclear Environments

Yao¹

2022

Preprint

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We develop a framework to simulate jet quenching in nuclear environments on a quantum computer. The formulation is based on the light-front Hamiltonian dynamics of QCD. The Hamiltonian consists of three parts relevant for jet quenching studies: kinetic, diffusion and splitting terms. In the basis made up of n-particle states in momentum space, the kinetic Hamiltonian is diagonal. Matrices representing the diffusion and splitting parts are sparse. The diffusion part of the Hamiltonian depends on classical background gauge fields, which need to be sampled classically before constructing quantum circuits for the time evolution. The cost of the sampling scales linearly with the time length of the evolution and the momentum grid volume. The framework automatically keeps track of quantum interference and thus it can be applied to study the Landau-Pomeranchuk-Migdal effect in cases with more than two splittings, which is beyond the scope of state-of-the-art analyses, no matter whether the medium is static or expanding, thin or thick, hot or cold. We apply this framework to study a toy model and carry out the quantum simulation by using the IBM Qiskit simulator. The Landau-Pomeranchuk-Migdal effect that suppresses the total radiation probability is observed in the quantum simulation results.

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Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions

Cited by 78 publications

References 87 publications

Digital quantum simulation of scalar Yukawa coupling: Dynamics following an interaction quench on IBM Q

Digital quantum simulation of scalar Yukawa coupling: Dynamics following an interaction quench on IBM Q

Parallelization techniques for quantum simulation of fermionic systems

Quantum Simulation of Light-Front QCD for Jet Quenching in Nuclear Environments

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