Numerical Simulations

Stefan Hillmich, Robert Wille

Jincheng Zhang

This paper introduces the Quantum Superposition-Based Complex Numerical Simulation Framework (QCSNF), a novel computational paradigm designed to address the limitations of traditional numerical methods in simulating complex quantum systems. We propose a framework that leverages quantum superposition to enhance numerical accuracy and efficiency. The core mechanism centers around employing quantum entanglement and superposition to guide the simulation process, enabling the resolution of previously intractable problems. This paper details the architecture of QCSNF, explores the theoretical underpinnings of its operation, and provides a preliminary implementation demonstrating the potential for significant improvements in the simulation of specific quantum numerical challenges. The research highlights the advantages of quantum superposition in achieving higher precision and reduced computational complexity.

Scott Kirkpatrick

Shimpei Goto, Kazuki Koshino

We develop an efficient numerical approach for simulating the high-power dispersive readout in circuit quantum electrodynamics. In the numerical simulations of the high-power readout, a large-amplitude coherent state induced in a cavity is an obstacle because many Fock states are required to describe such a state. We remove the large-amplitude coherent state from the numerical simulations by simulating the dynamics in a frame where the amplitude of the coherent state is almost absent. Using the developed method, we numerically simulate the high-power dispersive readout of the two-level system and the transmon. Our proposed method succeeds in producing reasonable behaviors of the high-power dispersive readout which can be deduced from the photon-number dependence of the cavity frequency: The high-power dispersive readout works in the two-level-system case while it does not work in the transmon case.

‎Louis Marchildon

Pierluigi Contucci, Cristian Giardinà

In this chapter we present some results on numerical simulation in three-dimensional spin glasses. In fact, there are problems for which the analytical approach is out of reach. In such cases numerical simulations are a source of hints and suggestions. Their robustness is based on the fact that the asymptotic properties of the model for large volumes are identified. After describing the standard algorithm used (parallel tempering) we address the following problems: overlap equivalence among site and link overlaps, ultrametricity or hierarchical organization of the equilibrium states, decay of correlations, pure state identification, energy interfaces, and stiffness exponents related to the lower critical dimension. Introduction Numerical simulations have played a crucial role in the development of spin glass theory, especially in those cases in which exact results are unavailable due to formidable mathematical difficulties. Some of the first systematic works were by Bray and Moore (1984), Ogielski and Morgenstern (1985), and Bhatt and Young (1988). For a recent review, see Marinari et al . (1997) and the references therein. It is also interesting to check Newman and Stein (1996) and Marinari et al . (2000) for examples of the difficulties of reconciling theory with numerical simulations in finite-dimensional spin glasses. The general outcome of these (and other) numerical studies is that many features of themean-field theory are seen in the ever larger finite-volume systems accessible to numerical simulations. However, no definite conclusions can be reached by means of the sole use of computers.