arXiv subjects

Erez Zohar

Publications and source records attributed to Erez Zohar.

At least 37 records · Page 2Linked to original sources

arXiv2023

Finding the ground state of a lattice gauge theory with fermionic tensor networks: a $2+1d$ $\mathbb{Z}_2$ demonstration

Tensor network states, and in particular Projected Entangled Pair States (PEPS) have been a strong ansatz for the variational study of complicated quantum many-body systems, thanks to their built-in entanglement entropy area law. In this work, we use a special kind of PEPS - Gauged Gaussian Fermionic PEPS (GGFPEPS) to find the ground state of $2+1d$ dimensional pure $\mathbb{Z}_2$ lattice gauge theories for a wide range of coupling constants. We do so by combining PEPS methods with Monte-Carlo computations, allowing for efficient contraction of the PEPS and computation of correlation functions. Previously, such numerical computations involved the calculation of the Pfaffian of a matrix scaling with the system size, forming a severe bottleneck; in this work we show how to overcome this problem. This paves the way for applying the method we propose and benchmark here to other gauge groups, higher dimensions, and models with fermionic matter, in an efficient, sign-problem-free way.

quant-ph↗

arXiv2022

Tunable photon-mediated interactions between spin-1 systems

The exchange of virtual photons between quantum optical emitters in cavity QED or quantum nanophotonic setups induces interactions between them which can be harnessed for quantum information and simulation purposes. So far, these interactions have been mostly characterized for two-level emitters, which restrict their application to engineering quantum gates among qubits or simulating spin-1/2 quantum many-body models. Here, we show how to harness multi-level emitters with several optical transitions to engineer a wide class of photon-mediated interactions between effective spin-1 systems. We characterize their performance through analytical and numerical techniques, and provide specific implementations based on the atomic level structure of Alkali atoms. Our results expand the quantum simulation toolbox available in such cavity QED and quantum nanophotonic setups, and open up new ways of engineering entangling gates among qutrits.

quant-ph↗

arXiv2022

Approximating Relativistic Quantum Field Theories with Continuous Tensor Networks

We present a continuous tensor-network construction for the states of quantum fields called cPEPS (continuous projected entangled pair state), which enjoys the same spatial and global symmetries of ground-states of relativistic field theories. We explicitly show how such a state can approximate and eventually converge to the free field theory vacuum and suggest a regularization-independent way of estimating the convergence via a universal term in the fidelity per-site. We also present a detailed bottom-up construction of the cPEPS as the continuum limit of the conventional lattice Projected Entangled Pair State (PEPS).

quant-ph↗

arXiv2021

Photon-mediated Stroboscopic Quantum Simulation of a $\mathbb{Z}_{2}$ Lattice Gauge Theory

Quantum simulation of lattice gauge theories (LGTs), aiming at tackling non-perturbative particle and condensed matter physics, has recently received a lot of interest and attention, resulting in many theoretical proposals, as well as several experimental implementations. One of the current challenges is to go beyond 1+1 dimensions, where four-body (plaquette) interactions, not contained naturally in quantum simulating devices, appear. In this Letter, we propose a method to obtain them based on a combination of stroboscopic optical atomic control and the non-local photon-mediated interactions appearing in nanophotonic or cavity QED setups. We illustrate the method for a $\mathbb{Z}_{2}$ lattice Gauge theory. We also show how to prepare the ground state and measure Wilson loops using state-of-the-art techniques in atomic physics.

quant-ph↗

arXiv2021

Wilson Loops and Area Laws in Lattice Gauge Theory Tensor Networks

Tensor network states have been a very prominent tool for the study of quantum many-body physics, thanks to their physically relevant entanglement properties and their ability to encode symmetries. In the last few years, the formalism has been extended and applied to theories with local symmetries to - lattice gauge theories. In the contraction of tensor network states as well as correlation functions of physical observables with respect to them, one uses the so-called transfer operator, whose local properties dictate the long-range behaviour of the state. In this work we study transfer operators of tensor network states (in particular, PEPS - projected entangled pair states) in the context of lattice gauge theories, and consider the implications of the local symmetry on their structure and properties. We focus on the Wilson loop - a nonlocal, gauge-invariant observable which is central to pure gauge theories, whose long range decay behaviour probes the confinement or deconfinement of static charges. Using the symmetry, we show how to handle its contraction, and formulate conditions relating local properties to its decay fashion.

quant-ph↗

arXiv2021

Duality as a Feasible Physical Transformation

Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, and offer numerous advantages for the study of many-body physics. In this work, we suggest a method which shall introduce them to the world of quantum simulation too: a feasible scheme for implementing duality transformations as physical operations, mapping between dual quantum states showing the same observable physics, rather than just a mathematical trick. Demonstrating with Abelian lattice models, we show how duality transformations could be implemented in the laboratory as sequences of single- and two-body operations - unitaries and measurements.

quant-ph↗

arXiv2021

Engineering a U(1) lattice gauge theory in classical electric circuits

Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter, and quantum information science. Their local symmetries enforce the charge conservation observed in the laws of physics. Impressive experimental progress has demonstrated that they can be engineered in table-top experiments using synthetic quantum systems. However, the challenges posed by the scalability of such lattice gauge simulators are pressing, thereby making the exploration of different experimental setups desirable. Here, we realize a U(1) lattice gauge theory with five matter sites and four gauge links in classical electric circuits employing nonlinear elements connecting LC oscillators. This allows for probing previously inaccessible spectral and transport properties in a multi-site system. We directly observe Gauss's law, known from electrodynamics, and the emergence of long-range interactions between massive particles in full agreement with theoretical predictions. Our work paves the way for investigations of increasingly complex gauge theories on table-top classical setups, and demonstrates the precise control of nonlinear effects within metamaterial devices.

cond-mat.mes-hall↗

arXiv2021

Non-Abelian gauge invariance from dynamical decoupling

Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter or quantum information theory. The recent progress in the control of artificial quantum systems already allows for studying Abelian lattice gauge theories in table-top experiments. However, the realization of non-Abelian models remains challenging. Here, we employ a coherent quantum control scheme to enforce non-Abelian gauge invariance, and discuss this idea in detail for a one dimensional SU(2) lattice gauge system. Finally, we comment on how to extend our scheme to other non-Abelian gauge symmetries and higher spatial dimensions, which summarized, provides a promising route for the quantum simulation of non-Abelian lattice gauge theories.

quant-ph↗

arXiv2021

Quantum Simulation of Lattice Gauge Theories in more than One Space Dimension -- Requirements, Challenges, Methods

Over the recent years, the relatively young field of quantum simulation of lattice gauge theories - aiming at implementing simulators of gauge theories with quantum platforms, has gone through a rapid development process. It is now of interest not only to people in the quantum information and technology community, but also seen as a valid tool for tackling hard, nonperturbative gauge theory physics by more and more particle and nuclear physicists. Along the theoretical progress, nowadays more and more experiments which actually implement such simulators are being reported, manifesting beautiful results, but mostly on $1+1$ dimensional physics. In this paper, we review the essential ingredients and requirements of lattice gauge theories in more dimensions, discuss their meanings, the challenges they impose and how they could be dealt with, potentially, aiming at the next steps of this field towards simulating challenging physical problems.

quant-ph↗

arXiv2021

Cold atoms meet lattice gauge theory

The central idea of this review is to consider quantum field theory models relevant for particle physics and replace the fermionic matter in these models by a bosonic one. This is mostly motivated by the fact that bosons are more ``accessible'' and easier to manipulate for experimentalists, but this ``substitution'' also leads to new physics and novel phenomena. It allows us to gain new information about among other things confinement and the dynamics of the deconfinement transition. We will thus consider bosons in dynamical lattices corresponding to the bosonic Schwinger or Z$_2$ Bose-Hubbard models. Another central idea of this review concerns atomic simulators of paradigmatic models of particle physics theory such as the Creutz-Hubbard ladder, or Gross-Neveu-Wilson and Wilson-Hubbard models. Finally, we will briefly describe our efforts to design experimentally friendly simulators of these and other models relevant for particle physics.

cond-mat.quant-gas↗

arXiv2020

A gauge redundancy-free formulation of compact QED with dynamical matter for quantum and classical computations

We introduce a way to express compact quantum electrodynamics with dynamical matter on two- and three-dimensional spatial lattices in a gauge redundancy-free manner while preserving translational invariance. By transforming to a rotating frame, where the matter is decoupled from the gauge constraints, we can express the gauge field operators in terms of dual operators. In two space dimensions, the dual representation is completely free of any local constraints. In three space dimensions, local constraints among the dual operators remain but involve only the gauge field degrees of freedom (and not the matter degrees of freedom). These formulations, which reduce the required Hilbert space dimension, could be useful for both numerical (classical) Hamiltonian computations and quantum simulation or computation.

quant-ph↗

arXiv2020

Real-time dynamics in 2+1d compact QED using complex periodic Gaussian states

We introduce a class of variational states to study ground state properties and real-time dynamics in (2+1)-dimensional compact QED. These are based on complex Gaussian states which are made periodic in order to account for the compact nature of the $U(1)$ gauge field. Since the evaluation of expectation values involves infinite sums, we present an approximation scheme for the whole variational manifold. We calculate the ground state energy density for lattice sizes up to $20 \times 20$ and extrapolate to the thermodynamic limit for the whole coupling region. Additionally, we study the string tension both by fitting the potential between two static charges and by fitting the exponential decay of spatial Wilson loops. As the ansatz does not require a truncation in the local Hilbert spaces, we analyze truncation effects which are present in other approaches. The variational states are benchmarked against exact solutions known for the one plaquette case and exact diagonalization results for a $\mathbb{Z}_3$ lattice gauge theory. Using the time-dependent variational principle, we study real-time dynamics after various global quenches, e.g. the time evolution of a strongly confined electric field between two charges after a quench to the weak-coupling regime. Up to the points where finite size effects start to play a role, we observe equilibrating behavior.

hep-th↗

arXiv2020

From the Jaynes-Cummings model to non-Abelian gauge theories: a guided tour for the quantum engineer

The design of quantum many body systems, which have to fulfill an extensive number of constraints, appears as a formidable challenge within the field of quantum simulation. Lattice gauge theories are a particular important class of quantum systems with an extensive number of local constraints and play a central role in high energy physics, condensed matter and quantum information. Whereas recent experimental progress points towards the feasibility of large-scale quantum simulation of Abelian gauge theories, the quantum simulation of non-Abelian gauge theories appears still elusive. In this paper we present minimal non-Abelian lattice gauge theories, whereby we introduce the necessary formalism in well-known Abelian gauge theories, such as the Jaynes-Cumming model. In particular, we show that certain minimal non-Abelian lattice gauge theories can be mapped to three or four level systems, for which the design of a quantum simulator is standard with current technologies. Further we give an upper bound for the Hilbert space dimension of a one dimensional SU(2) lattice gauge theory, and argue that the implementation with current digital quantum computer appears feasible.

quant-ph↗

arXiv2020

Variational Monte Carlo simulation with tensor networks of a pure $\mathbb{Z}_3$ gauge theory in (2+1)d

Variational minimization of tensor network states enables the exploration of low energy states of lattice gauge theories. However, the exact numerical evaluation of high-dimensional tensor network states remains challenging in general. In [E. Zohar, J. I. Cirac, Phys. Rev. D 97, 034510 (2018)] it was shown how, by combining gauged Gaussian projected entangled pair states with a variational Monte Carlo procedure, it is possible to efficiently compute physical observables. In this paper we demonstrate how this approach can be used to investigate numerically the ground state of a lattice gauge theory. More concretely, we explicitly carry out the variational Monte Carlo procedure based on such contraction methods for a pure gauge Kogut-Susskind Hamiltonian with a $\mathbb{Z}_3$ gauge field in two spatial dimensions. This is a first proof of principle to the method, which provides an inherent way to increase the number of variational parameters and can be readily extended to systems with physical fermions.

quant-ph↗

arXiv2019

Gauss Law, Minimal Coupling and Fermionic PEPS for Lattice Gauge Theories

In these lecture notes, we review some recent works on Hamiltonian lattice gauge theories, that involve, in particular, tensor network methods. The results reviewed here are tailored together in a slightly different way from the one used in the contexts where they were first introduced, by looking at the Gauss law from two different points of view: for the gauge field it is a differential equation, while from the matter point of view, on the other hand, it is a simple, explicit algebraic equation. We will review and discuss what these two points of view allow and do not allow us to do, in terms of unitarily gauging a pure-matter theory and eliminating the matter from a gauge theory, and relate that to the construction of PEPS (Projected Entangled Pair States) for lattice gauge theories.

quant-ph↗

arXiv2019

Local Manipulation and Measurement of Nonlocal Many-Body Operators in Lattice Gauge Theory Quantum Simulators

Lattice Gauge Theories form a very successful framework for studying nonperturbative gauge field physics, in particular in Quantum Chromodynamics. Recently, their quantum simulation on atomic and solid-state platforms has been discussed, aiming at overcoming some of the difficulties still faced by the conventional approaches (such as the sign problem and real time evolution). While the actual implementations of a lattice gauge theory on a quantum simulator may differ in terms of the simulating system and its properties, they are all directed at studying similar physical phenomena, requiring the measurement of nonlocal observables, due to the local symmetry of gauge theories. In this work, general schemes for measuring such nonlocal observables (Wilson loops and mesonic string operators) in general lattice gauge theory quantum simulators that are based merely on local operations are proposed.

quant-ph↗

arXiv2019

Quantum Simulation of the Abelian-Higgs Lattice Gauge Theory with Ultracold Atoms

We present a quantum simulation scheme for the Abelian-Higgs lattice gauge theory using ultracold bosonic atoms in optical lattices. The model contains both gauge and Higgs scalar fields, and exhibits interesting phases related to confinement and the Higgs mechanism. The model can be simulated by an atomic Hamiltonian, by first mapping the local gauge symmetry to an internal symmetry of the atomic system, the conservation of hyperfine angular momentum in atomic collisions. By including auxiliary bosons in the simulation, we show how the Abelian-Higgs Hamiltonian emerges effectively. We analyze the accuracy of our method in terms of different experimental parameters, as well as the effect of the finite number of bosons on the quantum simulator. Finally, we propose possible experiments for studying the ground state of the system in different regimes of the theory, and measuring interesting high energy physics phenomena in real time.

quant-ph↗

arXiv2019

Opportunities for Nuclear Physics & Quantum Information Science

This whitepaper is an outcome of the workshop Intersections between Nuclear Physics and Quantum Information held at Argonne National Laboratory on 28-30 March 2018 [www.phy.anl.gov/npqi2018/]. The workshop brought together 116 national and international experts in nuclear physics and quantum information science to explore opportunities for the two fields to collaborate on topics of interest to the U.S. Department of Energy (DOE) Office of Science, Office of Nuclear Physics, and more broadly to U.S. society and industry. The workshop consisted of 22 invited and 10 contributed talks, as well as three panel discussion sessions. Topics discussed included quantum computation, quantum simulation, quantum sensing, nuclear physics detectors, nuclear many-body problem, entanglement at collider energies, and lattice gauge theories.

nucl-th↗