Primitive Quantum Gates for an SU(3) Discrete Subgroup: $\Sigma (36\times 3)$

Abstract

We construct the primitive gate set for the digital quantum simulation of the 108-element $\Sigma (36\times 3)$ group. This is the first time a nonabelian crystal-like subgroup of $SU(3)$ has been constructed for quantum simulation. The gauge link registers and necessary primitives -- the inversion gate, the group multiplication gate, the trace gate, and the $\Sigma (36\times 3)$ Fourier transform -- are presented for both an eight-qubit encoding and a heterogeneous three-qutrit plus two-qubit register. For the latter, a specialized compiler was developed for decomposing arbitrary unitaries onto this architecture.

15 pages, 11 Figures, 6 Tables

References in corpus (96)

• A variational eigenvalue solver on a quantum processor
• Elementary gates for quantum computation
• Good Quantum Error-Correcting Codes Exist
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Multiple Particle Interference and Quantum Error Correction
• Prescription for experimental determination of the dynamics of a quantum black box
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Synthesis of Quantum Logic Circuits
• Simple Quantum Error Correcting Codes
• Quantum Algorithms for Quantum Field Theories
• Restrictions on Transversal Encoded Quantum Gate Sets
• Optimal Quantum Circuits for General Two-Qubit Gates
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• Quantum algorithms for algebraic problems
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers
• Simulating Compact Quantum Electrodynamics with ultracold atoms: Probing confinement and nonperturbative effects
• Lattice QCD at Finite Density -- An introductory review
• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation
• Thermalization in Nature and on a Quantum Computer
• QCD as a Quantum Link Model
• General Methods for Digital Quantum Simulation of Gauge Theories
• Digital lattice gauge theories
• Quantum Algorithms for Simulating the Lattice Schwinger Model
• Approaches to the sign problem in lattice field theory
• Hardware efficient quantum simulation of non-abelian gauge theories with qudits on Rydberg platforms
• Efficient synthesis of universal Repeat-Until-Success circuits
• Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories
• Introductory lectures on lattice QCD at nonzero baryon number
• Gluon Field Digitization for Quantum Computers
• Towards Quantum Simulating QCD
• A resource efficient approach for quantum and classical simulations of gauge theories in particle physics
• Gauge-invariant implementation of the Abelian Higgs model on optical lattices
• Digital quantum simulation of lattice gauge theories in three spatial dimensions
• Quantum Simulation of Quantum Field Theory in the Light-Front Formulation
• Quantum simulation of non-equilibrium dynamics and thermalization in the Schwinger model
• Quantum simulation of the universal features of the Polyakov loop
• BQP-completeness of Scattering in Scalar Quantum Field Theory
• On the representation of Boolean and real functions as Hamiltonians for quantum computing
• Solving Gauss's Law on Digital Quantum Computers with Loop-String-Hadron Digitization
• Gluon Field Digitization via Group Space Decimation for Quantum Computers
• Toward scalable simulations of Lattice Gauge Theories on quantum computers
• Synthesis of Multivalued Quantum Logic Circuits by Elementary Gates
• Quantum simulation of scattering in the quantum Ising model
• Lattice QCD at finite temperature and density
• Digitizing Gauge Fields: Lattice Monte Carlo Results for Future Quantum Computers
• Tensor renormalization group study of the non-Abelian Higgs model in two dimensions
• Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT
• Fermion-qudit quantum processors for simulating lattice gauge theories with matter
• Qubit regularization of asymptotic freedom
• Principal series of finite subgroups of SU(3)
• A gauge-invariant, rotor Hamiltonian from dual variables of 3D U(1) gauge theory
• Toward Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States
• A qubit regularization of the $O(3)$ sigma model
• Universal features of the Abelian Polyakov loop in 1+1 dimension
• Fermions at Finite Density in (2+1)d with Sign-Optimized Manifolds
• Quantum and classical spin network algorithms for $q$-deformed Kogut-Susskind gauge theories
• Synthesis of multi-qudit Hybrid and d-valued Quantum Logic Circuits by Decomposition
• Simulating Hadronic Physics on NISQ devices using Basis Light-Front Quantization
• Primitive Quantum Gates for Dihedral Gauge Theories
• Framework for simulating gauge theories with dipolar spin systems
• Improved Hamiltonians for Quantum Simulations
• Light-Front Field Theory on Current Quantum Computers
• Toward Quantum Simulations of ${\mathbb{Z}}_2$ Gauge Theory Without State Preparation
• Quantum simulation of quantum field theories as quantum chemistry
• Prospects for Simulating a Qudit Based Model of (1+1)d Scalar QED
• The spectrum of qubitized QCD: glueballs in a $S(1080)$ gauge theory
• Accelerating lattice quantum field theory calculations via interpolator optimization using NISQ-era quantum computing
• Photon-mediated Stroboscopic Quantum Simulation of a ${\mathbb{Z}}_2$ Lattice Gauge Theory
• Real-time simulation of (2+1)-dimensional lattice gauge theory on qubits
• Digitising SU(2) Gauge Fields and the Freezing Transition
• How many quantum gates do gauge theories require?
• Constructive Quantum Shannon Decomposition from Cartan Involutions
• Variational thermal quantum simulation of the lattice Schwinger model
• Variational quantum simulation of U(1) lattice gauge theories with qudit systems
• Quantum Simulation of Z2 Lattice Gauge theory with minimal resources
• From square plaquettes to triamond lattices for SU(2) gauge theory
• A Family of Quantum Codes with Exotic Transversal Gates
• State preparation and measurement in a quantum simulation of the O(3) sigma model
• Optimal synthesis of multivalued quantum circuit
• Qu8its for Quantum Simulations of Lattice Quantum Chromodynamics
• Gauge Theory Couplings on Anisotropic Lattices
• Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group
• Robustness of gauge-invariant dynamics against defects in ultracold-atom gauge theories
• Gluon Digitization via Character Expansion for Quantum Computers
• Quantum computation of thermal averages in the presence of a sign problem
• Fuzzy gauge theory for quantum computers
• Spacetime-Efficient Low-Depth Quantum State Preparation with Applications
• Protecting local and global symmetries in simulating 1+1-D non-abelian gauge theories
• The $2T$-qutrit, a two-mode bosonic qutrit
• Qcompiler: quantum compilation with CSD method
• Dihedral Lattice Gauge Theories on a Quantum Annealer
• Quantum mean estimation for lattice field theory
• Quantum Gate Sets for Lattice QCD in the strong coupling limit: $N_f=1$

Cited by in corpus (10)

• Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques
• Qutrit and Qubit Circuits for Three-Flavor Collective Neutrino Oscillations
• Improved Honeycomb and Hyperhoneycomb Lattice Hamiltonians for Quantum Simulations of Non-Abelian Gauge Theories
• Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to ${\mathbb{D}}_8$
• Field digitization scaling in a ${\mathbb{Z}}_N\subset U(1)$ symmetric model
• Disorder-Free Localization and Fragmentation in a Non-Abelian Lattice Gauge Theory
• Quantum circuit for ${\mathbb{Z}}_3$ lattice gauge theory at nonzero baryon density
• Synthesis of Single Qutrit Circuits from Clifford+R
• Perturbation theory, irrep truncations, and state preparation methods for quantum simulations of SU(3) lattice gauge theory
• Counting gauge-invariant states with matter fields and finite gauge groups