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arXiv:2001.03044 · Scientific Reports

Confinement and entanglement dynamics on a digital quantum computer

Joseph Vovrosh, Johannes Knolle

Published Jun 2, 2021• 74 citations
arXivHTMLPDF

Abstract

Confinement describes the phenomenon when the attraction between two particles grows with their distance, most prominently found in quantum chromodynamics (QCD) between quarks. In condensed matter physics, confinement can appear in quantum spin chains, for example, in the one dimensional transverse field Ising model (TFIM) with an additional longitudinal field, famously observed in the quantum material cobalt niobate or in optical lattices. Here, we establish that state-of-the-art quantum computers have reached capabilities to simulate confinement physics in spin chains. We report quantitative confinement signatures of the TFIM on an IBM quantum computer observed via two distinct velocities for information propagation from domain walls and their mesonic bound states. We also find the confinement induced slow down of entanglement spreading by implementing randomized measurement protocols for the second order Rényi entanglement entropy. Our results are a crucial step for probing non-perturbative interacting quantum phenomena on digital quantum computers beyond the capabilities of classical hardware.

DOI
10.1038/s41598-021-90849-5

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Confinement describes the phenomenon when the attraction between two particles grows with their distance, most prominently found in quantum chromodynamics (QCD) between quarks. In condensed matter physics, confinement can appear in quantum spin chains, for example, in the one dimensional transverse field Ising model (TFIM) with an additional longitudinal field, famously observed in the quantum material cobalt niobate or in optical lattices. Here, we establish that state-of-the-art quantum computers have reached capabilities to simulate confinement physics in spin chains. We report quantitative confinement signatures of the TFIM on an IBM quantum computer observed via two distinct velocities for information propagation from domain walls and their mesonic bound states. We also find the confinement induced slow down of entanglement spreading by implementing randomized measurement protocols for the second order Rényi entanglement entropy. Our results are a crucial step for probing non-perturbative interacting quantum phenomena on digital quantum computers beyond the capabilities of classical hardware.
Abstract Confinement describes the phenomenon when the attraction between two particles grows with their distance, most prominently found in quantum chromodynamics (QCD) between quarks. In condensed matter physics, confinement can appear in quantum spin chains, for example, in the one dimensional transverse field Ising model (TFIM) with an additional longitudinal field, famously observed in the quantum material cobalt niobate or in optical lattices. Here, we establish that state-of-the-art quantum computers have reached quantum simulation capabilities to explore confinement physics in spin chains. We report quantitative confinement signatures of the TFIM on an IBM quantum computer observed via two distinct velocities for information propagation from domain walls and their mesonic bound states. We also find the confinement induced slow down of entanglement spreading by implementing randomized measurement protocols for the second order Renyi entanglement entropy. Our results are a crucial step for probing non-perturbative interacting quantum phenomena on digital quantum computers beyond the capabilities of classical hardware.
The study of confinement in quantum spin chains has seen a large surge of interest in recent years.It is not only important for understanding a range of effective one-dimensional condensed-matter realizations but it also shares some of the nonperturbative physics with quantum chromodynamics (QCD), which makes it a prime target for current quantum simulation efforts.In analogy to QCD, the confinementinduced two-particle bound states that appear in these models are dubbed mesons.Here, we study scattering events due to meson collisions in a quantum spin chain with long-range interactions such that two mesons have an extended interaction.We show how novel hadronic bound states, e.g., with four constituent particles akin to tetraquarks, may form dynamically in fusion events.In a natural collision their signal is weak, as elastic meson scattering dominates.However, we propose two controllable protocols that allow for a clear observation of dynamical hadron formation.We discuss how this physics can be simulated in trapped-ion or Rydberg-atom setups.
Abstract Universal quantum computers are potentially an ideal setting for simulating many-body quantum dynamics that is out of reach for classical digital computers. We use state-of-the-art IBM quantum computers to study paradigmatic examples of condensed matter physics—we simulate the effects of disorder and interactions on quantum particle transport, as well as correlation and entanglement spreading. Our benchmark results show that the quality of the current machines is below what is necessary for quantitatively accurate continuous-time dynamics of observables and reachable system sizes are small comparable to exact diagonalization. Despite this, we are successfully able to demonstrate clear qualitative behaviour associated with localization physics and many-body interaction effects.
We investigate the dynamics of the quantum Ising model on two-dimensional square lattices up to 16 $\ifmmode\times\else\texttimes\fi{}$ 16 spins. In the ordered phase, the model exhibits dynamically constrained dynamics, leading to confinement of elementary excitations and slow thermalization. After demonstrating the signatures of confinement, we probe the dynamics of interfaces in the constrained regime through sudden quenches of product states with domains of opposite magnetization. We find that the nature of excitations can be captured by perturbation theory throughout the confining regime and identify the crossover to the deconfining regime. We systematically explore the effect of the transverse field on the modes propagating along flat interfaces and investigate the crossover from resonant to diffusive melting of a square of flipped spins embedded in a larger lattice.
Due to the mechanism of confinement, as known from quantum chromodynamics, it is difficult to observe individual particles carrying fractional quantum number (e.g., quark with fractional electric charge). A condensed-matter example of fractionalized particles is spinons in quasi-one-dimensional spin systems, which are domain walls in the background of N\'eel configurations carrying spin-12\frac{1}{2}21​. Using the time-evolving block decimation algorithm, we visualize the nontrivial spinon dynamics induced by the confine mechanism in a two-leg spin-12\frac{1}{2}21​ ladder. It can be illustrated by a simple single-particle picture of Bloch oscillation, not only qualitatively but also quantitatively. We propose the experimental realization and the real time detection of the spinon dynamics in the ultracold boson systems of 87{}^{87}87Rb.
Matter under extreme conditions behaves as a non-equilibrium, strongly-interacting quantum system. Such systems are in the non-perturbative regime of quantum chromodynamics (QCD), where their time evolution is classically intractable. Quantum computing offers a promising alternative, but present-day devices are limited in qubit count and circuit depth, so efficient formulations and algorithms are key to scaling toward experimentally relevant QCD simulations. A scalable framework is established for simulating energy loss and hadronization in 1+1-dimensional SU(2) lattice gauge theory, in which a heavy quark traverses a lattice of light quarks. Classical lattice QCD methods are translated into physics-informed circuits to prepare the interacting ground state. The evolution is run on IBM's quantum processor ibm_pittsburgh, where the charge distribution and energy loss are measured. A further study develops the quantum simulation of the fully gauge-fixed SU(2) Hamiltonian in a mixed basis, a formulation that is expected to remain efficient at all gauge couplings. Digitizing the continuous gauge fields with as few as three qubits per plaquette reproduces low-energy observables with 10−310^{-3}10−3 precision. Scaling to larger systems is limited by resource overhead, which motivates truncations that preserve the relevant observables. Sequency Hierarchy Truncation (SeqHT) exploits the hierarchy in basis-operator contributions. Demonstrated on the adiabatic preparation of the λφ4λφ^4λφ4 ground state on ibm_sherbrooke, SeqHT reduces circuit depth by ~30%, suppressing hardware noise in the extracted observables. All simulations in this dissertation are validated on quantum hardware against classical benchmarks. These studies advance quantum simulations of real-time QCD dynamics.