First-quantized eigensolver for ground and excited states of electrons under a uniform magnetic field

Abstract

First-quantized eigensolver (FQE) is a recently proposed framework of quantum computation for obtaining the ground state of an interacting electronic system based on probabilistic imaginary-time evolution. In this study, we propose a method for introducing a uniform magnetic field to an FQE calculation. We demonstrate via resource estimation that the additional circuit responsible for the magnetic field can be implemented with a liner depth in terms of the number of qubits assigned to each electron, giving rise to no impact on the leading order of whole computational cost. We confirm the validity of our method via numerical simulations for ground and excited states by employing the filtration circuits for energy eigenstates. We also provide the generic construction of derivative circuits together with measurement-based formulae. As a special case of them, we can obtain the electric-current density in an electronic system to get insights into the microscopic origin of magnetic response.

References in corpus (9)

• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Simulating chemistry efficiently on fault-tolerant quantum computers
• Quantum Krylov subspace algorithms for ground and excited state energy estimation
• Quantum simulation of the single-particle Schrodinger equation
• Grid-based methods for chemistry simulations on a quantum computer
• Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation
• Improved reversible and quantum circuits for Karatsuba-based integer multiplication
• Exhaustive search for optimal molecular geometries using imaginary-time evolution on a quantum computer
• Resource-frugal Hamiltonian eigenstate preparation via repeated quantum phase estimation measurements

Cited by in corpus (4)

• Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer
• Accelerating quantum imaginary-time evolution with random measurements
• First-quantized adiabatic time evolution for the ground state of a many-electron system and the optimal nuclear configuration
• Encoded probabilistic imaginary-time evolution on a trapped-ion quantum computer for ground and excited states of spin qubits