Reducing qubit requirements for quantum simulation using molecular point group symmetries

Abstract

Simulating molecules is believed to be one of the early-stage applications for quantum computers. Current state-of-the-art quantum computers are limited in size and coherence, therefore optimizing resources to execute quantum algorithms is crucial. In this work, we develop the second quantization representation of the spatial-symmetries which are then transformed to their qubit operator representation. These qubit operator representations are used to reduce the number of qubits required for simulating molecules. We present our results for various molecules and elucidate a formal connection of this work with a previous technique that analyzed generic $Z_2$ Pauli symmetries.

References in corpus (16)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum Chemistry in the Age of Quantum Computing
• Error mitigation for short-depth quantum circuits
• Fermionic quantum computation
• A Theory of Fault-Tolerant Quantum Computation
• Extending the computational reach of a noisy superconducting quantum processor
• Gate count estimates for performing quantum chemistry on small quantum computers
• Low-cost error mitigation by symmetry verification
• Error-mitigated digital quantum simulation
• Tapering off qubits to simulate fermionic Hamiltonians
• The Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
• Superfast encodings for fermionic quantum simulation
• Exact and approximate symmetry projectors for the electronic structure problem on a quantum computer
• The Python-based Simulations of Chemistry Framework (PySCF)

Cited by in corpus (55)

• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum computational chemistry
• The Variational Quantum Eigensolver: a review of methods and best practices
• Exploiting symmetry in variational quantum machine learning
• Emerging quantum computing algorithms for quantum chemistry
• Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation
• Towards a Larger Molecular Simulation on the Quantum Computer: Up to 28 Qubits Systems Accelerated by Point Group Symmetry
• Quantum Chemistry Simulations of Dominant Products in Lithium-Sulfur Batteries
• Variational Quantum Eigensolver with Reduced Circuit Complexity
• Simulating Many-Body Systems with a Projective Quantum Eigensolver
• Matrix Model simulations using Quantum Computing, Deep Learning, and Lattice Monte Carlo
• Reducing qubit requirements while maintaining numerical precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach
• A Domain-agnostic, Noise-resistant, Hardware-efficient Evolutionary Variational Quantum Eigensolver
• Resolving Correlated States of Benzyne on a Quantum Computer with an Error-Mitigated Quantum Contracted Eigenvalue Solver
• Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials
• Clifford Circuit Optimization with Templates and Symbolic Pauli Gates
• Quantum-Classical Hybrid Algorithm for the Simulation of All-Electron Correlation
• Variational quantum eigensolver techniques for simulating carbon monoxide oxidation
• Improving quantum measurements by introducing "ghost" Pauli products
• N-electron valence perturbation theory with reference wavefunctions from quantum computing: application to the relative stability of hydroxide anion and hydroxyl radical
• Shallow-circuit variational quantum eigensolver based on symmetry-inspired Hilbert space partitioning for quantum chemical calculations
• Improved algorithms of quantum imaginary time evolution for ground and excited states of molecular systems
• Ab Initio Molecular Dynamics on Quantum Computers
• Challenges in the use of quantum computing hardware-efficient Ansatze in electronic structure theory
• Contextual Subspace Variational Quantum Eigensolver
• Quantum hardware calculations of periodic systems with partition-measurement symmetry verification: simplified models of hydrogen chain and iron crystals
• Prediction of the neutron drip line in oxygen isotopes using quantum computation
• The Basics of Quantum Computing for Chemists
• Quantum simulations of Fermionic Hamiltonians with efficient encoding and ansatz schemes
• Adaptive construction of shallower quantum circuits with quantum spin projection for fermionic systems
• Chemically Aware Unitary Coupled Cluster with ab initio Calculations on System Model H1: A Refrigerant Chemicals Application
• Hierarchical Clifford transformations to reduce entanglement in quantum chemistry wavefunctions
• Using Quantum Annealers to Calculate Ground State Properties of Molecules
• Quantum circuits for the preparation of spin eigenfunctions on quantum computers
• Quantum simulations of molecular systems with intrinsic atomic orbitals
• A stabilizer framework for Contextual Subspace VQE and the noncontextual projection ansatz
• Lowering Tomography Costs in Quantum Simulation with a Symmetry Projected Operator Basis
• Contextual Subspace Variational Quantum Eigensolver Calculation of the Dissociation Curve of Molecular Nitrogen on a Superconducting Quantum Computer
• Simulating a ring-like Hubbard system with a quantum computer
• Simulation of a Diels-Alder Reaction on a Quantum Computer
• Benchmarking Noisy Intermediate Scale Quantum Error Mitigation Strategies for Ground State Preparation of the HCl Molecule
• Clifford Group and Unitary Designs under Symmetry
• Workflow for practical quantum chemical calculations with quantum phase estimation algorithm: electronic ground and π-π* excited states of benzene and its derivatives†
• Local, Expressive, Quantum-Number-Preserving VQE Ansatze for Fermionic Systems
• Entanglement-assisted phase estimation algorithm for calculating dynamical response functions
• Fast gradient-free optimization of excitations in variational quantum eigensolvers
• The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems
• Extending Quantum Computing through Subspace, Embedding and Classical Molecular Dynamics Techniques
• Simulating polaritonic ground states on noisy quantum devices
• The Electronic Structure of the Hydrogen Molecule: A Tutorial Exercise in Classical and Quantum Computation
• Non-unitary Coupled Cluster Enabled by Mid-circuit Measurements on Quantum Computers
• Quantum Simulations of Chemical Reactions: Achieving Accuracy with NISQ Devices
• Electronic Structure Theory with Molecular Point Group Symmetries on Quantum Annealers
• Clifford Transformations for Fermionic Quantum Systems: From Paulis to Majoranas to Fermions
• Resource Estimation for VQE on Small Molecules: Impact of Fermion Mappings and Hamiltonian Reductions