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…

Variational Quantum Algorithms for Computational Fluid Dynamics

Dieter Jaksch, Peyman Givi, Andrew J. Daley, Thomas Rung. Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required hardware, but also in identifying the most promising application areas and developing the corresponding quantum algorithms. The availability…

Hybrid discrete-continuous compilation of trapped-ion quantum circuits with deep reinforcement learning

Francesco Preti, Michael Schilling, Sofiene Jerbi, Lea M. Trenkwalder, Hendrik Poulsen Nautrup, Felix Motzoi, Hans J. Briegel. Shortening quantum circuits is crucial to reducing the destructive effect of environmental decoherence and enabling useful algorithms. Here, we demonstrate an improvement in such compilation tasks via a combination of using hybrid discrete-continuous optimization across a continuous gate set, and architecture-tailored implementation. The…

Tensor network reduced order models for wall-bounded flows

Martin Kiffner, Dieter Jaksch. We introduce a widely applicable tensor network-based framework for developing reduced order models describing wall-bounded fluid flows. As a paradigmatic example, we consider the incompressible Navier-Stokes equations and the lid-driven cavity in two spatial dimensions. We benchmark our solution against published reference data for low Reynolds numbers and find excellent agreement. In addition, we investigate the…

Gaining confidence on the correct realization of arbitrary quantum computations

Jose Carrasco, Marc Langer, Antoine Neven, Barbara Kraus. We present verification protocols to gain confidence in the correct performance of the realization of an arbitrary universal quantum computation. The derivation of the protocols is based on the fact that matchgate computations, which are classically efficiently simulable, become universal if supplemented with additional resources. We combine tools from weak simulation, randomized…
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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.