Towards Variational Quantum Algorithms for generalized linear and nonlinear transport phenomena

Sergio Bengoechea, Paul Over, Dieter Jaksch, Thomas Rung This article proposes a Variational Quantum Algorithm (VQA) to solve linear and nonlinear thermofluid dynamic transport equations. The hybrid classical-quantum framework is applied to problems governed by the heat, wave, and Burgers' equation in combination with different engineering boundary conditions. Topics covered include the consideration of non-constant material properties and upwind-biased first-…

Quantum Algorithm for the Advection-Diffusion Equation with Optimal Success Probability

Paul Over, Sergio Bengoechea, Peter Brearley, Sylvain Laizet, Thomas Rung. A quantum algorithm for simulating multidimensional scalar transport problems using a time-marching strategy is presented. After discretization, the explicit time-marching operator is separated into an advection-like component and a corrective shift operator. The advection-like component is mapped to a Hamiltonian simulation problem and is combined with the shift operator through…

Landscape approximation of low energy solutions to binary optimization problems

Benjamin Y.L. Tan, Beng Yee Gan, Daniel Leykam, and Dimitris G. Angelakis. We show how the localization landscape, originally introduced to bound low energy eigenstates of disordered wave media and many-body quantum systems, can form the basis for hardware efficient quantum algorithms for solving binary optimization problems. Many binary optimization problems can be cast as finding low-energy eigenstates of Ising…

Nonlinear Quantum Dynamics in Superconducting NISQ Processors

Muhammad Umer, Eleftherios Mastorakis, Sofia Evangelou, Dimitris G. Angelakis. A recently proposed variational quantum algorithm has expanded the horizon of variational quantum computing to nonlinear physics and fluid dynamics. In this work, we employ this algorithm to find the ground state of the nonlinear Schrödinger equation with a quadratic potential and implement it on the cloud superconducting quantum processors. We…

Partitioned Quantum Subspace Expansion

Tom O'Leary, Lewis W. Anderson, Dieter Jaksch, Martin Kiffner. We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given Krylov subspace requires the same quantum resources in both the single step and sequential cases. We…

Boundary Treatment for Variational Quantum Simulations of Partial Differential Equations on Quantum Computers

Paul Over, Sergio Bengoechea, Thomas Rung, Francesco Clerici, Leonardo Scandurra, Eugene de Villiers, Dieter Jaksch. The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum computers of the current noisy intermediate-scale quantum era. The partial differential equation is initially translated into an optimal control problem with…

Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer

Chong Hian Chee, Daniel Leykam, Adrian M. Mak, and Dimitris G. Angelakis. Fermionic Ansatz state preparation is a critical subroutine in many quantum algorithms such as the variational quantum eigensolver for quantum chemistry and condensed-matter applications. The shallowest circuit depth needed to prepare Slater determinants and correlated states to date scales at least linearly with respect to the system size \(N\). Inspired by…
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The QCFD (Quantum Computational Fluid Dynamics) project is funded under the European Union’s Horizon Programme (HORIZON-CL4-2021-DIGITAL-EMERGING-02-10), Grant Agreement 101080085 QCFD.