Calculating transition amplitudes by variational quantum deflation

Abstract

Variational quantum eigensolver (VQE) is an appealing candidate for the application of near-term quantum computers. A technique introduced in [Higgot et al., Quantum 3, 156 (2019)], which is named variational quantum deflation (VQD), has extended the ability of the VQE framework for finding excited states of a Hamiltonian. However, no method to evaluate transition amplitudes between the eigenstates found by the VQD without using any costly Hadamard-test-like circuit has been proposed despite its importance for computing properties of the system such as oscillator strengths of molecules. Here we propose a method to evaluate transition amplitudes between the eigenstates obtained by the VQD avoiding any Hadamard-test-like circuit. Our method relies only on the ability to estimate overlap between two states, so it does not restrict to the VQD eigenstates and applies for general situations. To support the significance of our method, we provide a comprehensive comparison of three previously proposed methods to find excited states with numerical simulation of three molecules (lithium hydride, diazene, and azobenzene) in a noiseless situation and find that the VQD method exhibits the best performance among the three methods. Finally, we demonstrate the validity of our method by calculating the oscillator strength of lithium hydride, comparing results from numerical simulations and real-hardware experiments on the cloud enabled quantum computer IBMQ Rome. Our results illustrate the superiority of the VQD to find excited states and widen its applicability to various quantum systems.

12 pages, 7 figures

References in corpus (14)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Recent developments in the PySCF program package
• Hartree-Fock on a superconducting qubit quantum computer
• Mitigating measurement errors in multi-qubit experiments
• Qulacs: a fast and versatile quantum circuit simulator for research purpose
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor
• Tapering off qubits to simulate fermionic Hamiltonians
• Variational algorithms for linear algebra
• Applications of Quantum Computing for Investigations of Electronic Transitions in Phenylsulfonyl-carbazole TADF Emitters
• Penalty methods for variational quantum eigensolver
• Near-term quantum algorithms for linear systems of equations
• Experimental quantum kernel machine learning with nuclear spins in a solid
• Measurement Error Mitigation for Variational Quantum Algorithms

Cited by in corpus (25)

• Qulacs: a fast and versatile quantum circuit simulator for research purpose
• Emerging quantum computing algorithms for quantum chemistry
• Universal quantum circuits for quantum chemistry
• Applications of Quantum Computing for Investigations of Electronic Transitions in Phenylsulfonyl-carbazole TADF Emitters
• Near- and long-term quantum algorithmic approaches for vibrational spectroscopy
• Overhead for simulating a non-local channel with local channels by quasiprobability sampling
• Hybrid quantum-classical algorithm for computing imaginary-time correlation functions
• Quantum-Selected Configuration Interaction: classical diagonalization of Hamiltonians in subspaces selected by quantum computers
• Quantum simulation of excited states from parallel contracted quantum eigensolvers
• Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculations
• HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware
• Accelerated variational quantum eigensolver with joint Bell measurement
• Variational quantum algorithm for ergotropy estimation in quantum many-body batteries
• Excited-state molecular dynamics simulation based on variational quantum algorithms
• Non-adiabatic Quantum Wavepacket Dynamics Simulation Based on Electronic Structure Calculations using the Variational Quantum Eigensolver
• Advancing quantum simulations of nuclear shell model with noise-resilient protocols
• Calculation of core-excited and core-ionized states using variational quantum deflation method and applications to photocatalyst modelling
• Entanglement-assisted phase estimation algorithm for calculating dynamical response functions
• Super-resolution of Green's functions on noisy quantum computers
• Quantum computing of the pairing Hamiltonian at finite temperatures
• Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models
• Almost optimal measurement scheduling of molecular Hamiltonian via finite projective plane
• NISQ algorithm for the matrix elements of a generic observable
• Revisiting semiconductor bulk hamiltonians using quantum computers
• A combined quantum-classical method applied to material design: optimization and discovery of photochromic materials for photopharmacology applications