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.