Quantum systems engineering

Abstract:

Quantum approaches to combinatorial optimization problems (COPs) are often limited by the resource demands of Quadratic Unconstrained Binary Optimization (QUBO) encodings, which enlarge circuits through penalty terms and increase qubit and gate counts. We show that Higher-Order Unconstrained Binary Optimization (HUBO) enables a more resource-efficient formulation. Our method systematically constructs HUBO Hamiltonians and, compared to a QUBO formulation in benchmarks on Gate Assignment (GAP), Maximum k-Colorable Subgraph (MkCS), and Integer Programming (IP) problems, significantly reduces qubit requirements and decreases total CNOT gate counts by at least 89.6% for all tested instances. These results highlight HUBO as a practical alternative for quantum optimization on near-term devices. To promote adoption, we release an open-source Python library that automates HUBO model construction, extends beyond the examples presented in this work, and broadens access to resource-efficient quantum optimization.

Abstract:

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. The applicability of our method is demonstrated by applying it to the paradigm example of steady and transient flows around stationary and rotating cylinders. We find excellent quantitative agreement in comparison to finite difference simulations for Strouhal numbers, forces and velocity fields. The properties of our approach are discussed in terms of reduced order models. We estimate the memory saving and potential runtime advantages in comparison to standard finite difference simulations. We find accurate results with errors of less than 0.3% for flow-field compressions by a factor of up to 20 and differential operators compressed by factors of up to 1000 compared to sparse matrix representations. We provide strong numerical evidence that the runtime scaling advantages of the tensor network approach with system size will provide substantial resource savings when simulating larger systems. Finally, we note that, like other tensor network-based fluid flow simulations, our algorithmic framework is directly portable to a quantum computer leading to further scaling advantages.

Abstract:

This article proposes a variational quantum algorithm 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’ equations in combination with different engineering boundary conditions. Topics covered include the encoding of band matrices, as in the consideration of nonconstant material properties and upwind-biased first-and higher-order approximations, widely used in engineering computational fluid dynamics, by the use of a mask function. Verification examples demonstrate high predictive agreement with classical methods. Furthermore, the scalability analysis shows a polylog scaling of the number of quantum gates with the number of qubits. Remaining challenges refer to the implicit construction of upwind schemes and the identification of an appropriate parameterization strategy of the quantum ansatz.

Abstract:

We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing midcircuit 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 the dynamics of classical and quantum systems. The capabilities of the framework are demonstrated for linear and nonlinear partial differential equations using the example of the linearized Euler equations with absorbing boundaries and the nonlinear Burgers’ equation. For a turbulence data set, we demonstrate potential advantages of the quantum-tensor scheme over its classical counterparts.

Abstract:

Despite its ubiquity, the quantum many-body properties of dispersion remain poorly understood. Here, we investigate the entanglement distribution in assemblies of quantum Drude oscillators, minimal models for dispersion-bound systems. We establish an analytic relationship between entanglement and correlation energy and show how entanglement monogamy determines whether many-body corrections to the pair potential are attractive, repulsive, or zero. These findings, demonstrated in trimers and extended lattices, apply in more general chemical environments where dispersion coexists with other cohesive forces.