Quantum simulation of confinement dynamics

Abstract

Quantum computers have generated much excitement over recent years due to their potential to outperform classical computers in many difficult problems. While a fully fault tolerant quantum device is yet to be built, there has been much work pushing for noisy intermediate-scale quantum (NISQ) devices to achieve quantum advantage. One of the most promising fields to accomplish this is in quantum simulation of quantum many-body systems. A classical computer is able to simulate a general quantum system but suffers from exponential memory requirements in system size. Thus, for exact results, classical computers are limited to simulating just tens of particles whereas realistic quantum systems are comprised of $\sim 10^{23}$. Quantum computers are able to reduce this memory cost to polynomial growth making them key to understand the physics of many-body systems. One area that is notably difficult to simulate is confinement physics. Confinement is the phenomenon in which the energy of two particles grows indefinitely with their separation - most prominently found between quarks in quantum chromodynamics (QCD). In this work we will consider the application of quantum devices to simulate such phenomena. In particular, we consider simple condensed matter systems, namely variations of the Ising model, that exhibit confinement physics. In the first half of this work we perform an analytical and numerical study of confinement, and develop a trotterization protocol to enable the quantum simulation of such physics on a digital quantum computer. We present results obtained directly on an IBM quantum computer showing the non-equilibrium effects of confinement in such systems. In order to achieve these results we developed state-of-the-art error mitigation methods to combat the large errors inherently faced in current NISQ devices. In the latter half, we propose physical phenomena that may act as a benchmark for quantum devices in the future. Collisions of mesons (boundstates of two particles) with impurities are considered in which a long-lived metastable state is found to form. Such collisions have potential to be simulated on digital quantum computers in the near future. We then consider collisions of mesons in systems with long-range interactions. We show how collisions of interacting mesons can lead to the formation of hadrons (boundstates of many constituent particles) in a fusion type event. While these proposals are beyond current digital quantum computer capabilities, analogue quantum simulation devices such as trapped ion setups or Rydberg atom experiments are well suited to realise this physics.