Quantum systems engineering

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.

Abstract:

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

Abstract:

Understanding spatial and temporal order in many-body systems is a key challenge, particularly in out-of-equilibrium settings. A major hurdle is developing controlled model systems to study these phases. We propose an experiment with a driven quantum gas coupled to a dissipative optical cavity, realizing a non-equilibrium phase diagram featuring both spatial and temporal order. The system’s control parameter is the detuning between the drive frequency and cavity resonance. Negative detunings yield a spatially ordered phase, while positive detunings produce phases with both spatial order and persistent oscillations, forming dissipative spatio-temporal lattices. We also identify a phase where the dynamics dephase, leading to chaotic behavior. Numerical and analytical evidence supports these superradiant phases, showing that the spatio-temporal lattice originates from cavity dissipation. The atoms experience accelerated transport, either via uniform acceleration or abrupt momentum transitions. Our work provides insights into temporal phases of matter not possible at equilibrium.