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We review our work on the interplay between non-resonant gates and solid state environment in various solid state quantum computer architectures and the resulting gate errors. Particular, we show that adiabatic condition can be satisfied in…

We present experimental and theoretical results for the fluctuation properties in the incomplete spectra of quantum systems with symplectic symmetry and a chaotic dynamics in the classical limit. To obtain theoretical predictions, we extend…

We explore quantum chaos diagnostics of variational circuit states at random parameters and study their correlation with the circuit expressibility and the optimization of control parameters. By measuring the operator spreading coefficient…

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…

This work theoretically investigates the transition from topology to chaos in a periodically driven system consisting of a quantum top coupled to a spin-1/2 particle. The system is driven by two alternating interaction kicks per period. For…

Digital quantum simulation is a promising application of quantum computers, where quantum dynamics is simulated by using quantum gate operations. Many techniques for decomposing a time-evolution operator of quantum dynamics into simulatable…

Level fluctuations in quantum system have been used to characterize quantum chaos using random matrix models. Recently time series methods were used to relate level fluctuations to the classical dynamics in the regular and chaotic limit. In…

By using numerical simulations, we investigate the dynamics of a quantum system of interacting bosons. We find an increase of properly defined mixing properties when the number of particles increases at constant density or the interaction…

A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one…

Quantum chaos is central to understanding quantum dynamics and is crucial for generating random quantum states, a key resource for quantum information tasks. In this work, we introduce a new class of quantum many-body dynamics, termed…

The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…

Quantum computing holds potential for accelerating the simulation of fluid dynamics. However, hardware noise in the noisy intermediate-scale quantum era significantly distorts simulation accuracy. Although error magnitudes are frequently…

The Quantum Computer Condition (QCC) provides a rigorous and completely general framework for carrying out analyses of questions pertaining to fault-tolerance in quantum computers. In this paper we apply the QCC to the problem of…

Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in…

Quantum fluctuations are inherent in open quantum systems and they affect not only the statistical properties of the initial state but also the time evolution of the system. Using a generic minimal model, we show that quantum noise…

How classical chaos emerges from the underlying quantum world is a fundamental problem in physics. The origin of this question is in the correspondence principle. Classical chaos arises due to non-linear dynamics, whereas quantum mechanics,…

We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of quantum kicked rotator. This main model of quantum chaos, which allows for a transition from regular to to chaotic behavior in the…

Quasi-integrable Hamiltonian systems are of great interest in many research fields of physics and mathematics. In these systems, the phase space has regular and chaotic trajectories. These trajectories depend in part on the magnitude of…

This review article will present some recent results and methods in the study of 1-particle quantum or wave scattering systems, in the semiclassical/high frequency limit, in cases where the corresponding classical/ray dynamics is chaotic.…

It was recently shown (quant-ph/9909074) that parasitic random interactions between the qubits in a quantum computer can induce quantum chaos and put into question the operability of a quantum computer. In this work I investigate whether…