The Simulation of Quantum Systems

Steven Kenneth Kauffmann

Using the results of a recent earlier article, it is pointed out that homogeneously linear, strictly oscillatory, conservative classical dynamical systems that have N degrees of freedom automatically simulate N-state quantum systems. Because the simulating oscillatory classical system is not subject to the information-destroying constraints which are imposed on the simulated quantum system by its probability interpretation, that simulating classical system actually has a greater information-bearing capacity than the N-state quantum system which it simulates. In addition, it is easy to ensure that the simulating oscillatory classical system is robust against the “decoherence" problems which typically beset the simulated N-state quantum system. Though it therefore might seem tempting to classically simulate two-state quantum systems, namely the much-discussed qubits, it appears to be far more advantageous to use cavity electromagnetic standing-wave modes to simulate N-state quantum systems for which N is as large as possible. A single such cavity-mode simulated \long qubyte" might even suffice as the random access memory for an entire computer.

Christof Zalka

We show that the time evolution of the wave function of a quantum–mechanical many–particle system can be simulated precisely and efficiently on a quantum computer. The time needed for such a simulation is comparable to the time of a conventional simulation of the corresponding classical system, a performance which can't be expected from any classical simulation of a quantum system. We then show how quantities of interest, like the energy spectrum of a system, can be obtained. We also indicate that ultimately the simulation of quantum field theory might be possible on large quantum computers.

Vijayarangan Natarajan

Hans A. De Raedt, Kristel F. L. Michielsen, Anthony Hams +2 more

Xue-Er Gao, Dai-Li Li, Zhihang Liu +1 more

Quantum simulation is one of the main contents of quantum information science, aiming to simulate and investigate poorly controllable or unobtainable quantum systems by using controllable quantum systems. Quantum simulation can be implemented in quantum computers, quantum simulators, and small quantum devices. Non-Hermitian systems have aroused research interest increasingly in recent two decades. On one hand, non-Hermitian quantum theories can be seen as the complex extensions of the conventional quantum mechanics, and are closely related to open systems and dissipative systems. On the other hand, both quantum systems and classical systems can be constructed as non-Hermitian systems with novel properties, which can be used to improve the precision of precise measurements. However, a non-Hermitian system is more difficult to simulate than a Hermitian system in that the time evolution of it is no longer unitary. In this review, we introduce recent research progress of quantum simulations of non-Hermitian systems. We mainly introduce theoretical researches to simulate typical non-Hermitian quantum systems by using the linear combinations of unitaries, briefly showing the advantages and limitations of each proposal, and we briefly mention other theoretical simulation methods, such as quantum random walk, space embedded and dilation. Moreover, we briefly introduce the experimental quantum simulations of non-Hermitian systems and novel phenomena in nuclear magnetic resonance, quantum optics and photonics, classical systems, etc. The recent progress of the combinations of quantum simulation and non-Hermitian physics has promoted the development of the non-Hermitian theories, experiments and applications, and expand the scope of application of quantum simulations and quantum computers.