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arXiv:2209.10781 · Physical review. D/Physical review. D.

Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. II. Single-baryon β -decay in real time

Roland C. Farrell, Ivan A. Chernyshev, Sarah J. M. Powell, Nikita A. Zemlevskiy, Marc Illa, Martin J. Savage A

Published Mar 30, 2023• 76 citations
arXivHTMLPDF

Abstract

A framework for quantum simulations of real-time weak decays of hadrons and nuclei in a two-flavor lattice theory in one spatial dimension is presented. A single generation of the Standard Model is found to require 16 qubits per spatial lattice site after mapping to spin operators via the Jordan-Wigner transformation. Both quantum chromodynamics and flavor-changing weak interactions are included in the dynamics, the latter through four-Fermi effective operators. Quantum circuits that implement time evolution in this lattice theory are developed and run on Quantinuum's H1-1 20-qubit trapped ion system to simulate the $\ensuremath{\beta}$-decay of a single baryon on one lattice site. These simulations include the initial state preparation and are performed for both one and two Trotter time steps. The potential intrinsic error-correction properties of this type of lattice theory are discussed, and the leading lattice Hamiltonian required to simulate $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay of nuclei induced by a neutrino Majorana mass term is provided.

DOI
10.1103/physrevd.107.054513

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Quantum computing has long been an experimental technology with the potential to simulate, at scale, phenomena which on classical devices would be too expensive to simulate at any but the smallest scales. Over the last several years, however, it has entered the NISQ era, where the number of qubits are sufficient for quantum advantage but substantial noise on hardware stands in the way of this achievement. This thesis details NISQ device-centered improvements to techniques of quantum simulation of the out-of-equilbrium real-time dynamics of lattice quantum chromodynamics (LQCD) and of dense 3-flavor neutrino systems on digital quantum devices. The first project concerning LQCD is a comparison of methods for implementing the variational quantum eigensolver (VQE) that initializes the ground state of an SU(3) plaquette-chain. The thesis then pivots to a 1+1D lattice of quarks interacting with an SU(3) gauge-field. A VQE-based state-preparation for the vacua and a Trotterized time-evolution circuit is designed and applied to the problems of simulating beta and neutrinoless double beta decay. Finally, these circuits are adapted to a version useable on quantum devices with nearest-neighbor connectivity with minimal overhead, with an eye towards utilizing the higher qubit count of such devices for hadron dynamics and scattering. This thesis covers two projects that concern dense 3-flavor neutrino systems. The first details design and testing of Trotterized time-evolution circuits on state-of-the-art quantum devices. The second, motivated by the Gottesman-Knill theorem's result that deviation from stabilizer states ("magic") is necessary for a problem to exhibit quantum advantage, details results with implications for the Standard Model in general that the 3 flavor ultradense neutrino systems with the highest, most-persistent magic are those that start with neutrinos in all 3 flavors.

arXiv:2502.02502•Feb 4, 2025•0 citations
A framework for quantum simulations of real-time weak decays of hadrons and nuclei in a two-flavor lattice theory in one spatial dimension is presented. A single generation of the Standard Model is found to require 16 qubits per spatial lattice site after mapping to spin operators via the Jordan-Wigner transformation. Both quantum chromodynamics and flavor-changing weak interactions are included in the dynamics, the latter through four-Fermi effective operators. Quantum circuits that implement time evolution in this lattice theory are developed and run on Quantinuum's H1-1 20-qubit trapped ion system to simulate the \ensuremathβ\ensuremath{\beta}\ensuremathβ-decay of a single baryon on one lattice site. These simulations include the initial state preparation and are performed for both one and two Trotter time steps. The potential intrinsic error-correction properties of this type of lattice theory are discussed, and the leading lattice Hamiltonian required to simulate 0\ensuremathν\ensuremathβ\ensuremathβ0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}0\ensuremathν\ensuremathβ\ensuremathβ-decay of nuclei induced by a neutrino Majorana mass term is provided.
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.
Simulations of energy loss and hadronization are essential for understanding a range of phenomena in non-equilibrium strongly-interacting matter. We establish a framework for performing such simulations on a quantum computer and apply it to a heavy quark moving across a modest-sized 1+1D SU(2) lattice of light quarks. Conceptual advances with regard to simulations of non-Abelian versus Abelian theories are developed, allowing for the evolution of the energy in light quarks, of their local non-Abelian charge densities, and of their multi-partite entanglement to be computed. The non-trivial action of non-Abelian charge operators on arbitrary states suggests mapping the heavy quarks to qubits alongside the light quarks, and limits the heavy-quark motion to discrete steps among spatial lattice sites. Further, the color entanglement among the heavy quarks and light quarks is implemented using hadronic operators, and Domain Decomposition is shown to be effective in quantum state preparation. Scalable quantum circuits that account for the heterogeneity of non-Abelian charge sectors across the lattice are used to prepare the interacting ground-state wavefunction in the presence of heavy quarks. The discrete motion of heavy quarks between adjacent spatial sites is implemented using fermionic SWAP operations. Quantum simulations of the dynamics of a system on L=3L=3L=3 spatial sites are performed using IBM's ibm_pittsburgh{\tt ibm\_pittsburgh}ibm_pittsburgh quantum computer using 18 qubits, for which the circuits for state preparation, motion, and one second-order Trotter step of time evolution have a two-qubit depth of 398. A suite of error mitigation techniques are used to extract the observables from the simulations, providing results that are in good agreement with classical simulations. The framework presented here generalizes straightforwardly to other non-Abelian groups, including SU(3) for quantum chromodynamics.
We study quantum simulation of SU(3) non-Abelian gauge theory dynamically coupled with fundamental fermions in 3+13+13+1 dimensions by employing the lattice Hamiltonian in axial gauge that avoids Gauss's law constraints. The temporal component of the gauge field is analytically solved in terms of independent field degrees of freedom and a lattice regulated Green's function. The axial gauge condition is trivially maintained in time evolution, even under Trotterization. The gauge field degrees of freedom are expressed in the local field basis and can be efficiently transformed into the canonical conjugate momentum basis by local quantum Fourier transforms. We prove the number of qubits needed for describing all states up to an energy EEE with an accuracy εεε on a lattice of volume VVV at bare coupling ggg is bounded as 16nAV+12nfV16n_A V + 12n_f V16nA​V+12nf​V, where $n_A \approx \log_2 (\frac{64 E' V^{4/3}}{π^2ε} + \frac{32\sqrt{2}g n_f E'^{1/2} V^{7/6}}{\sqrt{3}π^3ε^{1/2}} ) $ is the number of qubits needed for each independent gauge field per site with a shifted energy E′E'E′, and nfn_fnf​ denotes the number of fermion flavors. We then analyze a quantum algorithm for time evolution that is based on Trotterization, quantum Fourier transform, and Jordan-Wigner transformation, for which quantum circuits can be explicitly constructed under arbitrary gauge field truncation and digitization. We find the numbers of CNOT and single-qubit rotation gates both scale as O(nA4V4/3)+O(V5/3)O(n_A^4 V^{4/3}) + O(V^{5/3})O(nA4​V4/3)+O(V5/3) per Trotter step for fixed nf≤6n_f\leq 6nf​≤6. We conclude that quantum resources needed for simulating real-time dynamics of lattice QCD scale polynomially with volume, energy, time, accuracy, and bare Hamiltonian parameters.
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 computing has long been an experimental technology with the potential to simulate, at scale, phenomena which on classical devices would be too expensive to simulate at any but the smallest scales. Over the last several years, however, it has entered the NISQ era, where the number of qubits are sufficient for quantum advantage but substantial noise on hardware stands in the way of this achievement. This thesis details NISQ device-centered improvements to techniques of quantum simulation of the out-of-equilbrium real-time dynamics of lattice quantum chromodynamics (LQCD) and of dense 3-flavor neutrino systems on digital quantum devices. The first project concerning LQCD is a comparison of methods for implementing the variational quantum eigensolver (VQE) that initializes the ground state of an SU(3) plaquette-chain. The thesis then pivots to a 1+1D lattice of quarks interacting with an SU(3) gauge-field. A VQE-based state-preparation for the vacua and a Trotterized time-evolution circuit is designed and applied to the problems of simulating beta and neutrinoless double beta decay. Finally, these circuits are adapted to a version useable on quantum devices with nearest-neighbor connectivity with minimal overhead, with an eye towards utilizing the higher qubit count of such devices for hadron dynamics and scattering. This thesis covers two projects that concern dense 3-flavor neutrino systems. The first details design and testing of Trotterized time-evolution circuits on state-of-the-art quantum devices. The second, motivated by the Gottesman-Knill theorem's result that deviation from stabilizer states ("magic") is necessary for a problem to exhibit quantum advantage, details results with implications for the Standard Model in general that the 3 flavor ultradense neutrino systems with the highest, most-persistent magic are those that start with neutrinos in all 3 flavors.