Ultrafast Hybrid Fermion-to-Qubit mapping

Abstract

Fermion-to-qubit mappings play a crucial role in representing fermionic interactions on a quantum computer. Efficient mappings translate fermionic modes of a system to qubit interactions with a high degree of locality while using few auxiliary resources. We present a family of locality-preserving fermion-to-qubit mappings that require fewer auxiliary qubits than all existing schemes known to date. One instance requires only 1.016 qubits-per-fermion compared to 1.25 for the best-known locality-preserving mapping by Y.-A. Chen and Y. Xu [PRX Quantum 4, 010326 (2023)]. Our family of mappings (parameterised by integer $n$) establishes a direct trade-off between the number of auxiliary qubits ($\frac{1}{n^2}$) and the circuit length ($O(\log n)$). Furthermore, we present a non-local variant that combines the strengths of the Jordan-Wigner and Bravyi-Kitaev mappings to give 98\% shorter circuits than the Jordan-Wigner mapping. This is achieved by applying seemly incompatible mappings at different scales, making it possible for their respective strengths to complement each other.

References in corpus (22)

• The theory of variational hybrid quantum-classical algorithms
• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• Fermionic quantum computation
• Elucidating Reaction Mechanisms on Quantum Computers
• Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Simulating Lattice Gauge Theories within Quantum Technologies
• Digital quantum simulation of fermionic models with a superconducting circuit
• Quantum Algorithms for Fermionic Simulations
• Mapping local Hamiltonians of fermions to local Hamiltonians of spins
• A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry
• A Compact Fermion to Qubit Mapping
• Superfast encodings for fermionic quantum simulation
• Operator Locality in Quantum Simulation of Fermionic Models
• Exact bosonization in two spatial dimensions and a new class of lattice gauge theories
• Quantum codes for quantum simulation of Fermions on a square lattice of qubits
• Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure
• Equivalence between fermion-to-qubit mappings in two spatial dimensions
• Discovering optimal fermion-qubit mappings through algorithmic enumeration
• Strong-Weak Duality via Jordan-Wigner Transformation: Using Fermionic Methods for Strongly Correlated $su(2)$ Spin Systems

Cited by in corpus (4)

• Quantum algorithms for scientific computing
• Local Jordan-Wigner transformations on the torus
• Clifford circuit based heuristic optimization of fermion-to-qubit mappings
• Resource Estimation for VQE on Small Molecules: Impact of Fermion Mappings and Hamiltonian Reductions