Two Qubit Quantum Computing in a Projected Subspace

A formulation for performing quantum computing in a projected subspace is presented, based on the subdynamical kinetic equation (SKE) for an open quantum system. The eigenvectors of the kinetic equation are shown to remain invariant before and after interaction with the environment. However, the eigenvalues in the projected subspace exhibit a type of phase shift to the evolutionary states. This phase shift does not destroy the decoherence-free (DF) property of the subspace because the associated fidelity is 1. This permits a universal formalism to be presented - the eigenprojectors of the free part of the Hamiltonian for the system and bath may be used to construct a DF projected subspace based on the SKE. To eliminate possible phase or unitary errors induced by the change in the eigenvalues, a cancellation technique is proposed, using the adjustment of the coupling time, and applied to a two qubit computing system. A general criteria for constructing a DF projected subspace from the SKE is discussed. Finally, a proposal for using triangulation to realize a decoherence-free subsystem based on SKE is presented. The concrete formulation for a two-qubit model is given exactly. Our approach is novel and general, and appears applicable to any type of decoherence. Key Words: Quantum Computing, Decoherence, Subspace, Open System PACS number: 03.67.Lx,33.25.+k,.76.60.-kComment: 24 pages. accepted by Phys. Rev.

Quantum Bayesian methods and subsequent measurements

After a derivation of the quantum Bayes theorem, and a discussion of the reconstruction of the unknown state of identical spin systems by repeated measurements, the main part of this paper treats the problem of determining the unknown phase difference of two coherent sources by photon measurements. While the approach of this paper is based on computing correlations of actual measurements (photon detections), it is possible to derive indirectly a probability distribution for the phase difference. In this approach, the quantum phase is not an observable, but a parameter of an unknown quantum state. Photon measurements determine a probability distribution for the phase difference. The approach used in this paper takes into account both photon statistics and the finite efficiency of the detectors.Comment: Expanded and corrected version. 13 pages, 1 figur

Four-level and two-qubit systems, sub-algebras, and unitary integration

Four-level systems in quantum optics, and for representing two qubits in quantum computing, are difficult to solve for general time-dependent Hamiltonians. A systematic procedure is presented which combines analytical handling of the algebraic operator aspects with simple solutions of classical, first-order differential equations. In particular, by exploiting $su(2) \oplus su(2)$ and $su(2) \oplus su(2) \oplus u(1)$ sub-algebras of the full SU(4) dynamical group of the system, the non-trivial part of the final calculation is reduced to a single Riccati (first order, quadratically nonlinear) equation, itself simply solved. Examples are provided of two-qubit problems from the recent literature, including implementation of two-qubit gates with Josephson junctions.Comment: 1 gzip file with 1 tex and 9 eps figure files. Unpack with command: gunzip RSU05.tar.g