Quantum computing of quantum chaos and imperfection effects

We study numerically the imperfection effects in the quantum computing of the kicked rotator model in the regime of quantum chaos. It is shown that there are two types of physical characteristics: for one of them the quantum computation errors grow exponentially with the number of qubits in the computer, while for the other the growth is polynomial. A certain similarity between classical and quantum computing errors is also discussed.     

Measurement base change for localization encoded dual rail photonic quantum computing

We study behavior of number states in systems of coupled modes. Using an auxiliary mode and linear transformations, we propose a simple method for measuring on orthogonal bases other than 0 and 1 in the case of dual rail photonic computing which may act as a simple filter too. Using two auxiliary modes it is shown that an equivalent polarizing beam splitter can be realized for dual rail encoding. Simple structures based on coupled waveguides are presented for these purposes.     

Controlling two-dimensional electron localization via phase-controlled absorption and gain in the three-coupled quantum wells

We investigate two-dimensional (2D) electron localization via phase-controlled absorption and gain of a weak probe field in an asymmetric semiconductor three-coupled quantum well (TCQW) with a closed loop under the action of two orthogonal standing-wave fields. It is found that we can achieve high-precision and high-resolution 2D electron localization via properly varying the parameters of the system. The influences of direct one-photon transition and indirect three-photon transition on the precision of probe absorption–gain spectra are also discussed in details. Thus, the proposed scheme shows the underlying probability for the formation of the 2D electron localization in a solid.     

Unstable periodic orbits and noise in chaos computing

Different methods to utilize the rich library of patterns and behaviors of a chaotic system have been proposed for doing computation or communication. Since a chaotic system is intrinsically unstable and its nearby orbits diverge exponentially from each other, special attention needs to be paid to the robustness against noise of chaos-based approaches to computation. In this paper unstable periodic orbits, which form the skeleton of any chaotic system, are employed to build a model for the chaotic system to measure the sensitivity of each orbit to noise, and to select the orbits whose symbolic representations are relatively robust against the existence of noise. Furthermore, since unstable periodic orbits are extractable from time series, periodic orbit-based models can be extracted from time series too. Chaos computing can be and has been implemented on different platforms, including biological systems. In biology noise is always present; as a result having a clear model for the effects of noise on any given biological implementation has profound importance. Also, since in biology it is hard to obtain exact dynamical equations of the system under study, the time series techniques we introduce here are of critical importance.     

Fat fractals in quantum chaos

Semiclassical quantum wavefunctions in a nonintegrable exchange-coupled three-spin system are studied by using Fock representations. Their projected binary phase patterns show a fat fractal area-scaling property, whose exponent distinguishes the difference between the quantum analogs of classical regular orbits and of chaos.     

Squeezed states and quantum chaos

We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of a quantum rotator excited by a periodic sequence of kicks. This model is the main model of quantum chaos and allows for a transition from regular behavior to chaotic in the classical limit. By doing a numerical experiment we study the generation of squeezed states in quasiclassical conditions and in a time interval when quantum-classical correspondence is well-defined. We find that the degree of squeezing depends on the degree of local instability in the system and increases with the Chirikov classical stochasticity parameter. We also discuss the dependence of the degree of squeezing on the initial width of the packet, the problem of stability and observability of squeezed states in the transition to quantum chaos, and the dynamics of disintegration of wave packets in quantum chaos. Zh. éksp. Teor. Fiz. 113, 111–127 (January 1998)     

Quantum instantons and quantum chaos

We suggest a closed form expression for the path integral of quantum transition amplitudes to construct a quantum action. Based on this we propose rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.     

Disappearance of quantum chaos in coupled chaotic quantum dots

Statistical properties of the single electron levels confined in the semiconductor (InAs/GaAs, Si/SiO₂) double quantum dots (DQDs) are considered. We demonstrate that in the electronically coupled chaotic quantum dots the chaos with its level repulsion disappears and the nearest neighbor level statistics becomes Poissonian. This result is discussed in the light of the recently predicted “huge conductance peak” by R.S. Whitney et al. [Phys. Rev. Lett. 102 (2009) 186802] in the mirror symmetric DQDs.     

Type II quantum chaos

A classification of quantum systems into three categories, type I, II and III, is proposed. The classification is based on the degree of sensitivity upon initial conditions, and the appearance of chaos. The quantum dynamics of type I systems is quasi periodic displaying no exponential sensitivity. They arise, e.g., as the quantized versions of classical chaotic systems. Type II systems are obtained when classical and quantum degrees of freedom are coupled. Such systems arise naturally in a dynamic extension of the first step of the Born-Oppenheimer approximation, and are of particular importance to molecular and solid state physics. Type II systems can show exponential sensitivity in the quantum subsystem. Type III systems are fully quantized systems which show exponential sensitivity in the quantum dynamics. No example of a type III system is currently established. This paper presents a detailed discussion of a type II quantum chaotic system which models a coupled electronic-vibronic system. It is argued that type II systems are of importance for any field systems (not necessarily quantum) that couple to classical degrees of freedom.     

Conservative quantum computing

The Wigner-Araki-Yanase theorem shows that conservation laws limit the accuracy of measurement. Here, we generalize the argument to show that conservation laws limit the accuracy of quantum logic operations. A rigorous lower bound is obtained of the error probability of any physical realization of the controlled-NOT gate under the constraint that the computational basis is represented by a component of spin, and that physical implementations obey the angular momentum conservation law. The lower bound is shown to be inversely proportional to the number of ancilla qubits or the strength of the external control field.     

Transient chaos in quantum and classical mechanics

Bogolubov's classical example of statistical relaxation in a many-dimensional linear oscillator is discussed. The relation of the discovered relaxation mechanism to quantum dynamics as well as to some new problems in classical mechanics is considered.     

Holographic quantum computing

We propose to use a single mesoscopic ensemble of trapped polar molecules for quantum computing. A "holographic quantum register" with hundreds of qubits is encoded in collective excitations with definite spatial phase variations. Each phase pattern is uniquely addressed by optical Raman processes with classical optical fields, while one- and two-qubit gates and qubit readout are accomplished by transferring the qubit states to a stripline microwave cavity field and a Cooper pair box where controllable two-level unitary dynamics and detection is governed by classical microwave fields.     

Classical and quantum chaos in atom optics

The interaction of an atom with an electro-magnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electro-magnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits dynamical localization and quantum recurrences.