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arXiv:2207.03473 · Physical Review Research

Simulating one-dimensional quantum chromodynamics on a quantum computer: Real-time evolutions of tetra- and pentaquarks

Y. Y. Atas, Jan F. Haase, Jinglei Zhang, Victor Wei, Sieglinde M.-L. Pfaendler, Randy Lewis, Christine A. Muschik

Published Sep 13, 2023• 58 citations
arXivHTMLPDF

Abstract

Quantum chromodynamics (QCD)---the theory of quarks and gluons---has been studied for decades, but it is yet to be fully understood. A recent example is the prediction and experimental discovery of tetraquarks, which opened a new research field. Crucially, numerous unsolved questions regarding the standard model can exclusively be addressed by nonperturbative calculations. Quantum computers can solve problems for which well-established QCD methods are inapplicable, such as real-time evolution. We take a key step in exploring this possibility by designing a real-time evolution of tetraquark and pentaquark physics in one-dimensional SU(3) gauge theory. We also perform an experiment on a superconducting quantum computer demonstrating an elementary cell consisting of two staggered sites containing quarks and antiquarks with all three colors. This experiment represents an exciting step in quantum computation involving quarks with the gauge group of QCD.

DOI
10.1103/physrevresearch.5.033184

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Quantum chromodynamics (QCD)---the theory of quarks and gluons---has been studied for decades, but it is yet to be fully understood. A recent example is the prediction and experimental discovery of tetraquarks, which opened a new research field. Crucially, numerous unsolved questions regarding the standard model can exclusively be addressed by nonperturbative calculations. Quantum computers can solve problems for which well-established QCD methods are inapplicable, such as real-time evolution. We take a key step in exploring this possibility by designing a real-time evolution of tetraquark and pentaquark physics in one-dimensional SU(3) gauge theory. We also perform an experiment on a superconducting quantum computer demonstrating an elementary cell consisting of two staggered sites containing quarks and antiquarks with all three colors. This experiment represents an exciting step in quantum computation involving quarks with the gauge group of QCD.
Tools necessary for quantum simulations of 1+11+11+1 dimensional quantum chromodynamics are developed. When formulated in axial gauge and with two flavors of quarks, this system requires 12 qubits per spatial site with the gauge fields included via nonlocal interactions. Classical computations and DDD-wave's quantum annealer advantage are used to determine the hadronic spectrum, enabling a decomposition of the masses and a study of quark entanglement. Color ``edge'' states confined within a screening length of the end of the lattice are found. IBM's seven-qubit quantum computers, ibmq_jakarta and ibm_perth, are used to compute dynamics from the trivial vacuum in one-flavor QCD with one spatial site. More generally, the Hamiltonian and quantum circuits for time evolution of 1+11+11+1 dimensional SU(Nc)SU({N}_{c})SU(Nc​) gauge theory with Nf{N}_{f}Nf​ flavors of quarks are developed, and the resource requirements for large-scale quantum simulations are estimated.
We develop a framework for quantum simulations of lattice SU(NcN_cNc​) gauge theory with quarks. Staggered and Wilson lattice fermions are considered in two and three spatial dimensions and a theta angle is included in three dimensions. The physical, gauge-invariant Hilbert space is formulated in a representation basis, where gauge and fermionic degrees of freedom are encoded by irreducible representations of SU(NcN_cNc​) that tensor at each lattice site to contain a singlet. We discuss algorithms for simulating time evolution on quantum computers and carry out noiseless simulations of lattice quantum chromodynamics (Nc=3N_c=3Nc​=3) on small lattices with up to 32 qubits, showcasing theta angle effects, hadronic states, string dynamics, and a baryon chemical potential for the first time in three spatial dimensions.
The quantum chromodynamics (QCD) phase diagram, which reveals the state of strongly interacting matter at different temperatures and densities, is key to answering open questions in physics, ranging from the behaviour of particles in neutron stars to the conditions of the early universe. However, classical simulations of QCD face significant computational barriers, such as the sign problem at finite matter densities. Quantum computing offers a promising solution to overcome these challenges. Here, we take an important step toward exploring the QCD phase diagram with quantum devices by preparing thermal states in one-dimensional non-Abelian gauge theories. We experimentally simulate the thermal states of SU(2) and SU(3) gauge theories at finite densities on a trapped-ion quantum computer using a variational method. This is achieved by introducing two features: Firstly, we add motional ancillae to the existing qubit register to efficiently prepare thermal probability distributions. Secondly, we introduce charge-singlet measurements to enforce colour-neutrality constraints. This work pioneers the quantum simulation of QCD at finite density and temperature for two and three colours, laying the foundation to explore QCD phenomena on quantum platforms. Quantum simulations of the phase diagram of quantum chromodynamics faces hard challenges, such as having to prepare mixed states and enforcing the non-Abelian gauge symmetry constraints. Here, the authors show how to solve the two above problems in a trapped-ion device using motional ancillae and charge-singlet measurements.
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.
Quantum computers are expected to give major speed-ups for the simulation of quantum systems. In this work, we present quantum gates that simulate the colour part of the interactions of quarks and gluons in perturbative quantum chromodynamics (QCD). As a first application, we implement these circuits on a simulated noiseless quantum computer and use them to calculate colour factors for various examples of Feynman diagrams. This work constitutes a first key step towards a quantum simulation of generic scattering processes in perturbative QCD.
Quantum computers have the potential to create important new opportunities for ongoing essential research on gauge theories. They can provide simulations that are unattainable on classical computers such as sign-problem afflicted models or time evolutions. In this work, we variationally prepare the low-lying eigenstates of a non-Abelian gauge theory with dynamically coupled matter on a quantum computer. This enables the observation of hadrons and the calculation of their associated masses. The SU(2) gauge group considered here represents an important first step towards ultimately studying quantum chromodynamics, the theory that describes the properties of protons, neutrons and other hadrons. Our calculations on an IBM superconducting platform utilize a variational quantum eigensolver to study both meson and baryon states, hadrons which have never been seen in a non-Abelian simulation on a quantum computer. We develop a hybrid resource-efficient approach by combining classical and quantum computing, that not only allows the study of an SU(2) gauge theory with dynamical matter fields on present-day quantum hardware, but further lays out the premises for future quantum simulations that will address currently unanswered questions in particle and nuclear physics.