A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry

Abstract

The ability to perform classically intractable electronic structure calculations is often cited as one of the principal applications of quantum computing. A great deal of theoretical algorithmic development has been performed in support of this goal. Most techniques require a scheme for mapping electronic states and operations to states of and operations upon qubits. The two most commonly used techniques for this are the Jordan-Wigner transformation and the Bravyi-Kitaev transformation. However, comparisons of these schemes have previously been limited to individual small molecules. In this paper we discuss resource implications for the use of the Bravyi-Kitaev mapping scheme, specifically with regard to the number of quantum gates required for simulation. We consider both small systems which may be simulatable on near-future quantum devices, and systems sufficiently large for classical simulation to be intractable. We use 86 molecular systems to demonstrate that the use of the Bravyi-Kitaev transformation is typically at least approximately as efficient as the canonical Jordan-Wigner transformation, and results in substantially reduced gate count estimates when performing limited circuit optimisations.

arXiv comment46 pages, 11 figures

References in corpus (22)

• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• The theory of variational hybrid quantum-classical algorithms
• Simulated Quantum Computation of Molecular Energies
• Fermionic quantum computation
• Scalable Quantum Simulation of Molecular Energies
• Towards Quantum Chemistry on a Quantum Computer
• Elucidating Reaction Mechanisms on Quantum Computers
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Quantum measurements and the Abelian Stabilizer Problem
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Finding Exponential Product Formulas of Higher Orders
• Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation
• 0.5 Petabyte Simulation of a 45-Qubit Quantum Circuit
• Exploiting locality in quantum computation for quantum chemistry
• Calculating the Thermal Rate Constant with Exponential Speed-Up on a Quantum Computer
• qHiPSTER: The Quantum High Performance Software Testing Environment
• Operator Locality in Quantum Simulation of Fermionic Models
• Bravyi-Kitaev Superfast simulation of fermions on a quantum computer
• Quantum Algorithm for Molecular Properties and Geometry Optimization
• Quantum Information and Computation for Chemistry

Cited by in corpus (70)

• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum computational chemistry
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• The Variational Quantum Eigensolver: a review of methods and best practices
• Quantum Computer Systems for Scientific Discovery
• A perspective on the current state-of-the-art of quantum computing for drug discovery applications
• Measurement reduction in variational quantum algorithms
• Quantum Power Method by a Superposition of Time-Evolved States
• Calculating energy derivatives for quantum chemistry on a quantum computer
• Quantum computing of the ${}^6$Li nucleus via ordered unitary coupled clusters
• A Feasible Approach for Automatically Differentiable Unitary Coupled-Cluster on Quantum Computers
• Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in VQE
• Quantum simulation of electronic structure with a transcorrelated Hamiltonian: improved accuracy with a smaller footprint on the quantum computer
• Variational approaches to constructing the many-body nuclear ground state for quantum computing
• Single-particle digitization strategy for quantum computation of a ${\varphi }^4$ scalar field theory
• Mutual information-assisted Adaptive Variational Quantum Eigensolver
• Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters
• Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure
• Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches
• A Quantum Algorithm to Calculate Band Structure at the EOM Level of Theory
• Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials
• How many quantum gates do gauge theories require?
• Effective calculation of the Green's function in the time domain on near-term quantum processors
• Self-healing of Trotter error in digital adiabatic state preparation
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• Hamiltonian simulation-based quantum-selected configuration interaction for large-scale electronic structure calculations with a quantum computer
• Bootstrap Embedding on a Quantum Computer
• Quantum Algorithm for Simulating Hamiltonian Dynamics with an Off-diagonal Series Expansion
• Optimization of CNOT circuits on limited connectivity architecture
• Post-Hartree-Fock method in Quantum Chemistry for Quantum Computer
• Quantum algorithms for scientific computing
• A unified framework of transformations based on the Jordan-Wigner transformation
• Q${}^2$Chemistry: A quantum computation platform for quantum chemistry
• Accurate and Efficient Quantum Computations of Molecular Properties Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against Experimental Data
• Learning How to Dynamically Decouple
• Neural network enhanced measurement efficiency for molecular groundstates
• Lowering Tomography Costs in Quantum Simulation with a Symmetry Projected Operator Basis
• Discovering optimal fermion-qubit mappings through algorithmic enumeration
• Exactly solving the Kitaev chain and generating Majorana-zero-modes out of noisy qubits
• PauliComposer: Compute Tensor Products of Pauli Matrices Efficiently
• Quantum Chemistry Calculations using Energy Derivatives on Quantum Computers
• A framework for efficient ab initio electronic structure with Gaussian Process States
• Quantum-machine-assisted Drug Discovery
• Analysis of Superfast Encoding Performance for Electronic Structure Simulations
• Deep Quantum Circuit Simulations of Low-Energy Nuclear States
• Ultrafast Hybrid Fermion-to-Qubit mapping
• Scalable quantum computation with fast gates in two-dimensional microtrap arrays of trapped ions
• A Comprehensive Cross-Model Framework for Benchmarking the Performance of Quantum Hamiltonian Simulations
• Fast gradient-free optimization of excitations in variational quantum eigensolvers
• A Hybrid Qubit Encoding: Splitting Fock Space into Fermionic and Bosonic Subspaces
• Projective Quantum Phase Difference Estimation Algorithm for the Direct Computation of Eigenenergy Gaps on a Quantum Computer
• Size-consistency and orbital-invariance issues revealed by VQE-UCCSD calculations with the FMO scheme
• Quantum computational study of chloride ion attack on chloromethane for chemical accuracy and quantum noise effects with UCCSD and k-UpCCGSD ansatzes
• Roadmap for quantum simulation of the fractional quantum Hall effect
• Fermihedral: On the Optimal Compilation for Fermion-to-Qubit Encoding
• A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations
• Quantum Computing in Pharma: A Multilayer Embedding Approach for Near Future Applications
• Clifford circuit based heuristic optimization of fermion-to-qubit mappings
• Parallelization techniques for quantum simulation of fermionic systems
• Transforming Collections of Pauli Operators into Equivalent Collections of Pauli Operators over Minimal Registers
• The Electronic Structure of the Hydrogen Molecule: A Tutorial Exercise in Classical and Quantum Computation
• Harnessing Quantum Computing for Energy Materials: Opportunities and Challenges
• Phase estimation with partially randomized time evolution
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Does the full configuration interaction method based on quantum phase estimation with Trotter decomposition satisfy the size consistency condition?
• A simple quantum simulation algorithm with near-optimal precision scaling
• A quantum Monte Carlo algorithm for arbitrary high-spin Hamiltonians
• Quantum-Classical Computing for Time-Dependent Ion-Atom Collision Dynamics: Applications to Charge Transfer Cross Section Simulations
• Resource-Optimized Grouping Shadow for Efficient Energy Estimation
• Resource Estimation for VQE on Small Molecules: Impact of Fermion Mappings and Hamiltonian Reductions