Quantum circuits for the preparation of spin eigenfunctions on quantum computers

Abstract

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wavefunctions that are relevant in the behavior of the system under study. Hamiltonian symmetries are an important instrument, to classify relevant many-particle wavefunctions, and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on 3- and 5-spin systems on graphs with triangle connectivity.

arXiv comment15 pages, 14 figures, 6 tables

References in corpus (49)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• A variational eigenvalue solver on a quantum processor
• Elementary gates for quantum computation
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum Simulation
• The theory of variational hybrid quantum-classical algorithms
• Quantum Spin Liquids
• Quantum Chemistry in the Age of Quantum Computing
• Error mitigation for short-depth quantum circuits
• Evaluating analytic gradients on quantum hardware
• Zoo of quantum-topological phases of matter
• Extending the computational reach of a noisy superconducting quantum processor
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• An RVB phase in the triangular lattice quantum dimer model
• Quantum algorithms for quantum chemistry and quantum materials science
• Validating quantum computers using randomized model circuits
• Multipartite entanglement and high precision metrology
• A Theory of Trotter Error
• Quantum Natural Gradient
• Cloud Quantum Computing of an Atomic Nucleus
• Evidence for a Gapped Spin-Liquid Ground State in a Kagome Heisenberg Antiferromagnet
• Mitigating measurement errors in multi-qubit experiments
• Excitations in the field-induced quantum spin liquid state of alpha-RuCl3
• Repeated Quantum Error Detection in a Surface Code
• Experimental realization of Dicke states of up to six qubits for multiparty quantum networking
• Quantum dimer model on the kagome lattice: solvable dimer liquid and Ising gauge theory
• Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
• Option Pricing using Quantum Computers
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography
• Quantum phases of Rydberg atoms on a kagome lattice
• Tapering off qubits to simulate fermionic Hamiltonians
• Nearly optimal lattice simulation by product formulas
• Emerging quantum computing algorithms for quantum chemistry
• Doubling the size of quantum simulators by entanglement forging
• Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms
• Reducing qubit requirements for quantum simulation using molecular point group symmetries
• Deterministic Preparation of Dicke States
• Spin-selective reactions of radical pairs act as quantum measurements
• A Feasible Approach for Automatically Differentiable Unitary Coupled-Cluster on Quantum Computers
• Theory of analytical energy derivatives for the variational quantum eigensolver
• Penalty methods for variational quantum eigensolver
• A necessary and sufficient condition to play games in quantum mechanical settings
• Simulating quantum chemistry in the seniority-zero space on qubit-based quantum computers
• Lindblad Tomography of a Superconducting Quantum Processor
• Exchange interactions in transition metal oxides: The role of oxygen spin polarization
• Experimental Realization of Classical ${\mathbb{Z}}_2$ Spin Liquids in a Programmable Quantum Device

Cited by in corpus (8)

• Measuring Electron Correlation. The Impact of Symmetry and Orbital Transformations
• Quantum simulations of molecular systems with intrinsic atomic orbitals
• Spin coupling is all you need: Encoding strong electron correlation in molecules on quantum computers
• Multireference error mitigation for quantum computation of chemistry
• Calculation of the moscovium ground-state energy by quantum algorithms
• Ground state energy and magnetization curve of a frustrated magnetic system from real-time evolution on a digital quantum processor
• Preparation of the single-spinon wave function on a quantum computer
• Accelerated spin-adapted ground state preparation with non-variational quantum algorithms