QCFD Publications

Quantum-Inspired Tensor-Network Fractional-Step Method for Incompressible Flow in Curvilinear Coordinates

We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed tensor representations of the flow fields and the differential operators and discuss the numerical implementation of the tensor operations required for computing fluid flows in detail.…

Disentangling fermionic Gaussian states and entanglement transitions in unitary circuit games wtih matchgates

In unitary circuit games, two competing parties, an "entangler" and a "disentangler", can induce an entanglement phase transition in a quantum many-body system. The transition occurs at a certain rate at which the disentangler acts. We analyze such games within the context of matchgate dynamics, which equivalently corresponds to evolutions of non-interacting fermions. We first investigate general entanglement properties of…

Publications, QCFD Publications June 17, 2025

Dynamical quantum phase transitions on random networks

We investigate two types of dynamical quantum phase transitions (DQPTs) in the transverse-field Ising model on ensembles of Erdős–Rényi networks of size N. These networks consist of vertices connected randomly with probability p (0<p⩽1). Using analytical derivations and numerical techniques, we compare the characteristics of the transitions for p < 1 against the fully connected network (p = 1). We analytically show that the overlap between the wave…

News, Publications, QCFD Publications March 11, 2025

Tensor-Programmable Quantum Circuits for Solving Differential Equations

Pia Siegl, Greta Sophie Reese, Tomohiro Hashizume, Nis-Luca van Hülst, Dieter Jaksch We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of unitary operators. Hence, it allows for the direct implementation of a broad class of differential equations governing…

Publications, QCFD Publications January 31, 2025

Tensor networks enable the calculation of turbulence probability distributions

Nikita Gourianov, Peyman Givi, Dieter Jaksch, Stephen B. Pope. Predicting the dynamics of turbulent fluid flows has long been a central goal of science and engineering. Yet, even with modern computing technology, accurate simulation of all but the simplest turbulent flow-fields remains impossible: the fields are too chaotic and multi-scaled to directly store them in memory and perform time-evolution. An…

Publications, QCFD Publications January 16, 2025

Efficient Estimation and Sequential Optimization of Cost Functions in Variational Quantum Algorithms

Muhammad Umer, Eleftherios Mastorakis, Dimitris G. Angelakis Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its derivatives, coupled with their effective utilization, facilitates faster convergence by enabling smooth navigation through complex landscapes, ensuring the algorithm's…

Publications, QCFD Publications November 25, 2024

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-…

Publications, QCFD Publications October 30, 2024

Self-Adaptive Physics-Informed Quantum Machine Learning for Solving Differential Equations

Abhishek Setty, Rasul Abdusalamov, Felix Motzoi. Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum machine learning setting for a variety of problems, including the 2D Poisson's equation, second-order differential equation, system of…

Publications, QCFD Publications October 29, 2024

Tensor Train Multiplication (TTM)

Alexios A Michailidis, Christian Fenton, Martin Kiffner. We present the Tensor Train Multiplication (TTM) algorithm for the elementwise multiplication of two tensor trains with bond dimension χ. The computational complexity and memory requirements of the TTM algorithm scale as χ3 and χ2, respectively. This represents a significant improvement compared with the conventional approach, where the computational complexity scales as χ4 and memory requirements scale as χ3.We benchmark…

Publications, QCFD Publications, Uncategorized October 25, 2024

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…