Inverse iteration quantum eigensolvers assisted with a continuous variable

Abstract

The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse power iteration method. A key ingredient is to construct an inverse Hamiltonian as a linear combination of coherent Hamiltonian evolution. We first consider a continuous-variable quantum mode~(qumode) for realizing such a linear combination as an integral, with weights being encoded into a qumode resource state. We demonstrate the quantum algorithm with numeral simulations under finite squeezing, for a range of physical systems including molecules and quantum many-body models. We also discuss a hybrid quantum-classical algorithm that directly sums up Hamiltonian evolution with different durations for comparison. It is revealed that continuous-variable resources are valuable for reducing coherent evolution time of Hamiltonians in quantum algorithms.

Simulation of optimal work extraction for quantum systems with work storage

“…[20,[44][45][46] In this regard, the whole system consists of both discrete-variable qubits and one continuous-variable, and it is conventional to simulate it with a hybrid-variable quantum circuit. [1,[47][48][49] With a work storage, the energy can be transferred from the system to the work storage, and therefore energy conservation can be considered in this setup. We investigate energy conservation in two scenarios.…”

Quantum Inverse Algorithm via Adaptive Variational Quantum Linear Solver: Applications to General Eigenstates

“…in 2017 is an alternative approach that uses Fourier transformation to expand the Hamiltonian inverse power . This approach has been recently applied to ground state calculations of molecules by other authors, , but its numerical integration is sensitive to the condition number in the Hamiltonian Ĥ . Consequently, the approximation requires a long evolution time to offer a stable inverse power with large condition numbers, making it challenging to use for excited-state calculations in QInverse.…”