Dima Mozyrsky

Indirect Interaction of Solid-State Qubits via Two-Dimensional Electron Gas

We propose a mechanism of long-range coherent coupling between nuclear spin qubits in semiconductor-heterojunction quantum information processing devices. The coupling is via localized donor electrons which interact with the two-dimensional electron gas. An effective interaction Hamiltonian is derived and the coupling strength is evaluated. We also discuss mechanisms of decoherence and consider gate control of the interaction between qubits. The resulting quantum computing scheme retains all the control and measurement aspects of earlier approaches, but allows qubit spacing at distances of the order of 100 nm, attainable with the present-day semiconductor device technologies.

Quantum computing with spin qubits in semiconductor structures

Abstract We survey recent work on designing and evaluating quantum computing implementations based on nuclear or bound-electron spins in semiconductor heterostructures at low temperatures and in high magnetic fields. General overview is followed by a summary of results of our theoretical calculations of decoherence time scales and spin–spin interactions. The latter were carried out for systems for which the two-dimensional electron gas provides the dominant carrier for spin dynamics via exchange of spin-excitons in the integer quantum Hall regime.

DIFFUSIONAL GROWTH OF COLLOIDS

We consider incorporation of particle detachment in the Smoluchowski model of colloidal growth. Two approaches are considered, utilizing phenomenological rate equation and exact large-time results. Our main conclusion is that the value of the large-time diffusing particle concentration at the aggregate surface is the only parameter needed to describe the added effect of detachment. Explicit expression is given for the particle intake rate.

Nuclear-spin qubit dephasing time in the integer quantum Hall effect regime

We report a theoretical estimate of the nuclear-spin dephasing time T2 owing to the spin interaction with the two-dimensional electron gas, when the latter is in the integer quantum Hall state, in a two-dimensional heterojunction or quantum well at low temperature, and in large applied magnetic field. We argue that the leading mechanism of dephasing is due to the impurity potentials that influence the dynamics of the spin via virtual magnetic spin-exciton scattering. Implications of our results for implementation of nuclear spins as quantum bits ~qubits! for quantum computing are discussed.

Design of Gates for Quantum Computation: The Three-Spin XOR Gate in Terms of Two-Spin Interactions

Considerations of feasibility of quantum computing lead to the study of multispin quantum gates in which the input and output two-state systems (spins) are not identical. We provide a general discussion of this approach and then propose an explicit two-spin interaction Hamiltonian which accomplishes the quantum XOR gate function for a system of three spins: two input and one output.We propose to design multispin quantum gates in which the input and output two-state systems (spins) are not necessarily identical. We describe the motivations for such studies and then derive an explicit general two-spin interaction Hamiltonian which accomplishes the quantum XOR gate function for a system of three spins: two input and one output.

A Hamiltonian for quantum copying

We derive an explicit Hamiltonian for copying the basis up and down states of a quantum two-state system - a qubit - onto n “copy” qubits (n ≥ 1) initially all prepared in the down state. In terms of spin components, for spin-12 particle spin states, the resulting Hamiltonian involves n- and (n + 1)-spin interactions. The case n = 1 also corresponds to a quantum-computing controlled-NOT gate.

DESIGN OF GATES FOR QUANTUM COMPUTATION : THE NOT GATE

We offer an alternative to the conventional network formulation of quantum computing. We advance the analog approach to quantum logic gate/circuit construction. As an illustration, we consider the spatially extended NOT gate as the first step in the development of this approach. We derive an explicit form of the interaction Hamiltonian corresponding to this gate and analyze its properties. We also discuss general extensions to the case of certain time-dependent interactions which may be useful for practical realization of quantum logic gates.

Quantum Signal Splitting that Avoids Initialization of the Targets

The classical signal splitting and copying are not possible in quantum mechanics. Specifically, one cannot copy the basis up and down states of the input (I) two-state system (qubit, spin) into the copy (C) and duplicate-copy (D) two-state systems if the latter systems are initially in an arbitrary state. We consider instead a quantum evolution in which the basis states of I at time t are duplicated in at least two of the systems I, C, D, at time t+Δt. In essence, the restriction on the initial target states is exchanged for uncertainty as to which two of the three qubits retain copies of the initial source state.

Exactly Solvable Model of a Two-Level Quantum System Interacting with Spin Environment

An exactly solvable model of a two-level quantum system interacting with spin environment is considered. The interaction is assumed to be such that the state of the environment is conserved. Dynamics of the reduced density matrix of the two-level system is calculated for arbitrary coupling strength. The stationary state of the spin is obtained explicitly in the t→∞ limit.

Decoherence and measurement in open quantum systems

We review results of a recently developed model of a microscopic quantum system interacting with the macroscopic world components which are modeled by collections of bosonic modes. The interaction is via a general operator (Lambda) of the system, coupled to the creation and annihilation operators of the environment modes. We assume that in the process of a nearly instantaneous quantum measurement, the function of the environment involves two distinct parts: the pointer and the bath. Interaction of the system with the bath leads to decoherence such that the system and the pointer both evolve into a statistical mixture state described by the density matrix such that the system is in one of the eigenstates of (Lambda) with the correct quantum mechanical probability, whereas the expectation values of pointer operators retain amplified information on that eigenstate. We argue that this process represents the initial step of a quantum measurement.