Mathematical Problems of Large Quantum Systems

Jan Philip Solovej

Alexander Nikolaevich Pechen

Leo Van Hove, Nicolaas Marinus Hugenholtz, L. P. Howland

Emanuel Colella, Benjamin A. Baldwin, Shaun Kelso +4 more

The advent of noisy intermediate-scale quantum (NISQ) systems signifies an important stage in quantum computing development. Despite the constraints due to their limited qubit numbers and noise susceptibility, NISQ devices exhibit substantial potential to tackle complex computational challenges via hybrid classical-quantum algorithms. Among the various hybrid algorithms, variational quantum algorithms (VQAs) are gaining increasing attention due to their ability to solve highly complex, large-scale problems where classical algorithms fail. In particular, the variational quantum eigensolver (VQE) shows its potential in calculating the energies and ground states of large systems, where the complexity of solving such problems grows exponentially and becomes intractable for classical computers. At this regard, the aim of this paper is to extend the use of VQE for solving circular waveguide modes to verify their applicability to mathematically complex EM problems. In particular, we propose to calculate the fundamental and the some higher order modes for both transverse electric and transverse magnetic cases in circular waveguides. This is mathematically challenging due to the nature of geometry and the associated boundary conditions of circular structures. The results confirm the possibility of applying VQE for mathematically complex EM problems, announcing its potential to scale up and solve high-dimensional, large-scale EM problems where classical algorithms can fail.

Stefan Chuchkov, Grigor Y. Mihaylov, Teodor B Iliev +3 more

Quantum technologies have recently undergone a second quantum revolution, following the first that triumphed with the creation of quantum mechanics at the beginning of the twentieth century. Quantum computing promises to solve hard mathematical problems exponentially faster than classical supercomputers, and this poses serious threats to classical cryptography, whose security is based on deterministic hard-to-solve mathematical problems such as the factorial of large integers.

Walter E Thirring, Evans M. Harrell