Quantum Simulations in Effective Model Spaces (I): Hamiltonian Learning-VQE using Digital Quantum Computers and Application to the Lipkin-Meshkov-Glick Model

Caroline Robin, Martin Savage |

The utility of effective model spaces in quantum simulations of non-relativistic quantum many-body systems is explored in the context of the Lipkin-Meshkov-Glick model of interacting fermions.  We introduce an iterative hybrid-classical-quantum algorithm, Hamiltonian learning variational quantum eigensolver (HL-VQE), that simultaneously optimizes an effective Hamiltonian, thereby rearranging entanglement into the effective model space, and the associated ground-state wavefunction. HL-VQE is found to provide an exponential improvement in Lipkin-Meshkov-Glick model calculations, compared to a naive truncation without Hamiltonian learning, throughout a significant fraction of the Hilbert space.  Quantum simulations are performed to demonstrate the HL-VQE algorithm, using an efficient mapping where the number of qubits scales with the log of the size of the effective model space, rather than the particle number, allowing for the description of large systems with small quantum circuits. Implementations on IBM’s QExperience quantum computers and simulators for 1- and 2-qubit effective model spaces are shown to provide accurate and precise results, reproducing classical predictions.  This work constitutes a step in the development of entanglement-driven quantum algorithms for the description of nuclear systems, that leverages the potential of noisy intermediate-scale quantum (NISQ) devices.

Gauge Invariance of Non-Abelian Field Strength Correlators: the Axial Gauge Puzzle

Bruno Scheihing-Hitschfeld, Xiaojun Yao |

Many transport coefficients of the quark-gluon plasma and nuclear structure functions can be written as gauge invariant correlation functions of non-Abelian field strengths dressed with Wilson lines. We discuss the applicability of axial gauge n.A=0 to calculate them. In particular, we address issues that appear when one attempts to trivialize the Wilson lines in the correlation functions by gauge-fixing. We find it is always impossible to completely remove the gauge fields n.A in Wilson lines that extend to infinity in the n-direction by means of gauge transformations. We show how the obstruction appears in an explicit example of a perturbative calculation, and we also explain it more generally from the perspective of the path integral that defines the theory. Our results explain why the two correlators that define the heavy quark and quarkonium transport coefficients, which are seemingly equal in axial gauge, are actually different physical quantities of the quark-gluon plasma and have different values. Furthermore, our findings provide insights into the difference between two inequivalent gluon parton distribution functions.

Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms

Anthony Ciavarella, Stephan Caspar, Hersh Singh, Martin Savage |

The 1+1D O(3) non-linear σ-model is a model system for future quantum lattice simulations of other
asymptotically-free theories, such as non-Abelian gauge theories. We find that utilizing dimensional reduction
can make efficient use of two-dimensional layouts presently available on cold atom quantum simulators. A
new definition of the renormalized coupling is introduced, which is applicable to systems with open boundary
conditions and can be measured using analog quantum simulators. Monte Carlo and tensor network calculations
are performed to determine the quantum resources required to reproduce perturbative short-distance observables.
In particular, we show that a rectangular array of 48 Rydberg atoms with existing quantum hardware capabilities
should be able to adiabatically prepare low-energy states of the perturbatively-matched theory. These states can
then be used to simulate non-perturbative observables in the continuum limit that lie beyond the reach of classical

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

Xiaojun Yao |

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 gluon in-medium radiation on a small lattice. The Landau-Pomeranchuk-Migdal effect that suppresses the total radiation probability is observed in the quantum simulation results of both the toy model and the gluon case.

Faster spectral density calculation using energy moments

Jeremy Hartse, Alessandro Roggero |

Accurate predictions of inclusive scattering cross sections in the linear response regime require efficient and controllable methods to calculate the spectral density in a strongly-correlated many-body system. In this work we reformulate the recently proposed Gaussian Integral Transform technique in terms of Fourier moments of the system Hamiltonian which can be computed efficiently on a quantum computer. One of the main advantages of this framework is that it allows for an important reduction of the computational cost by exploiting previous knowledge about the energy moments of the spectral density. For a simple model of medium mass nucleus like ⁴⁰Ca and target energy resolution of 1 MeV we find an expected speed-up of ≈ 125 times for the calculation of the giant dipole response and of ≈ 50 times for the simulation of quasi-elastic electron scattering at typical momentum transfers.

Multi-Neutrino Entanglement and Correlations in Dense Neutrino Systems

Marc Illa, Martin J. Savage | 2210.08656 [nucl-th]

The time-evolution of multi-neutrino entanglement and correlations are studied in two-flavor collective neutrino oscillations, relevant for dense neutrino environments, building upon previous works. Specifically, simulations performed of systems with up to 12 neutrinos using Quantinuum’s H1-1 20 qubit trapped-ion quantum computer are used to compute n-tangles, and two- and three-body correlations, probing beyond mean-field descriptions. n-tangle re-scalings are found to converge for large system sizes.

State Preparation in the Heisenberg Model through Adiabatic Spiraling

Anthony Ciavarella, Stephan Caspar, Marc Illa, Martin Savage | 2210.04965 [quant-ph]

An adiabatic state preparation technique, called the adiabatic spiral, is proposed for the Heisenberg model. This technique is suitable for implementation on a number of quantum simulation platforms such as Rydberg atoms, trapped ions, or superconducting qubits. Classical simulations of small systems suggest that it can be successfully implemented in the near future. A comparison to Trotterized time evolution is performed and it is shown that the adiabatic spiral is able to outperform Trotterized adiabatics.

Quantum computation of dynamical quantum phase transitions and entanglement tomography in a lattice gauge theory

Joseph Carolan, Andrew Connelly, Zohreh Davoudi, Eugene Dumitrescu, Niklas Mueller, Kübra Yeter-Aydeniz | 2210.03089 [quant-ph]

Strongly-coupled gauge theories far from equilibrium may exhibit unique features that could illuminate the physics of early universe and of hadron and ion colliders. Studying real-time phenomena has proven challenging with classical-simulation methods, but is a natural application of quantum-simulation devices. To demonstrate this prospect, we quantum compute non-equal time correlation functions and perform entanglement tomography of non-equilibrium states of a simple lattice gauge theory, the Schwinger model, using a trapped-ion quantum computer by IonQ Inc. As an ideal target for near-term devices, a recently-predicted dynamical quantum phase transition in this model is studied by preparing, quenching, and tracking the subsequent non-equilibrium dynamics in three ways: i) overlap echos signaling dynamical transitions, ii) non-equal time correlation functions with an underlying topological nature, and iii) the entanglement structure of non-equilibrium states, including Entanglement Hamiltonians. These results constitute the first observation of a dynamical quantum phase transition in a lattice gauge theory on a quantum computer, and are a first step toward investigating topological phenomena in nuclear and high-energy physics using quantum technologies.

Lattice regularization of Theta-vacua in Grassmannian nonlinear sigma models: Anomalies, sign-problems and qubit models

Hersh Singh, Mendel Nguyen | 2209.12630 [hep-lat]

Anomalies are a powerful way to gain insight into possible lattice regularizations of a quantum field theory. In this work, we consider lattice regularizations of a class of the toy-models of QCD: the 1+1-dimensional asymptotically-free Grassmanian nonlinear sigma models with a theta term. We argue that the continuum anomaly for a given symmetry can be matched by a manifestly symmetric lattice regularization only if (i) the symmetry action is offsite, or (ii) if the continuum anomaly is reproduced exactly on the lattice. Using the Grassmanian nonlinear sigma models as a case study, we provide examples of lattice regularizations in which both possibilities are realized. For possibility (i), we generalize recent work for the  O(3)  NLSM with an arbitrary theta term, where it was regulated using model of qubits with a small extra dimension, solving a sign problem present in conventional formulations of theta vacua. We argue that Grassmannian NLSM can be obtained similarly from SU(N) antiferromagnets with a well-defined continuum limit, reproducing both the IR physics of theta vacua and the UV physics of asymptotic freedom. These results enable the application of new classical algorithms to lattice Monte Carlo studies of these quantum field theories, and provide a viable realization suited for their quantum simulation. On the other hand, we show that, perhaps surprisingly, the conventional lattice regularization of theta vacua due to Berg and Luscher reproduces the anomaly exactly on the lattice, providing a realization of the second possibility.

Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (II) Single-Baryon Beta-Decay in Real Time

Roland Farrell, Ivan Chernyshev, Sarah Powell, Nikita Zemlevskiy, Marc Illa, Martin Savage | 2209.10781 [quant-ph]

A framework for quantum simulations of real-time weak decays of hadrons and nuclei in a 2-flavor lattice theory in one spatial dimension is presented. A single generation of the Standard Model is mapped to spin operators via the Jordan-Wigner transformation, and both quantum chromodynamics and flavor-changing weak interactions are included in the dynamics, the latter through four-Fermi effective operators. This mapping requires 16 qubits per spatial lattice site. Quantum circuits which implement time evolution in this lattice theory are developed and run on Quantinuum’s H1 1 20-qubit trapped ion system to simulate the beta-decay of a single baryon on one lattice site. Simulations of the real-time evolution of a single baryon, including initial state preparation, are performed for both one and two Trotter time steps. We comment on the potential intrinsic error-correction properties of this type of lattice theory.