Physical Optimization of Quantum Error Correction Circuits

Quantum error correcting codes have been developed to protect a quantum computer from decoherence due to a noisy environment. In this paper, we present two methods for optimizing the physical implementation of such error correction schemes. First, we discuss an optimal quantum circuit implementation of the smallest error-correcting code (the three bit code). Quantum circuits are physically implemented by serial pulses, i.e. by switching on and off external parameters in the Hamiltonian one after another. In contrast to this, we introduce a new parallel switching method that allows faster gate operation by switching all external parameters simultaneously. These two methods are applied to electron spins in coupled quantum dots subject to a Heisenberg coupling H=J(t) S_1*S_2 which can generate the universal quantum gate `square-root-of-swap'. Using parallel pulses, the encoding for three-bit quantum error correction in a Heisenberg system can be accelerated by a factor of about two. We point out that parallel switching has potential applications for arbitrary quantum computer architectures.Comment: 13 pages, 6 figure

Towards deterministic optical quantum computation with coherently driven atomic ensembles

Scalable and efficient quantum computation with photonic qubits requires (i) deterministic sources of single-photons, (ii) giant nonlinearities capable of entangling pairs of photons, and (iii) reliable single-photon detectors. In addition, an optical quantum computer would need a robust reversible photon storage devise. Here we discuss several related techniques, based on the coherent manipulation of atomic ensembles in the regime of electromagnetically induced transparency, that are capable of implementing all of the above prerequisites for deterministic optical quantum computation with single photons.Comment: 11 pages, 7 figure

Complete quantum teleportation with a Kerr nonlinearity

We present a scheme for the quantum teleportation of the polarization state of a photon employing a cross-Kerr medium. The experimental feasibility of the scheme is discussed and we show that, using the recently demonstrated ultraslow light propagation in cold atomic media, our proposal can be realized with presently available technology.Comment: 4 pages, revtex, 1 eps figur

Quantum Computation with Quantum Dots

We propose a new implementation of a universal set of one- and two-qubit gates for quantum computation using the spin states of coupled single-electron quantum dots. Desired operations are effected by the gating of the tunneling barrier between neighboring dots. Several measures of the gate quality are computed within a newly derived spin master equation incorporating decoherence caused by a prototypical magnetic environment. Dot-array experiments which would provide an initial demonstration of the desired non-equilibrium spin dynamics are proposed.Comment: 12 pages, Latex, 2 ps figures. v2: 20 pages (very minor corrections, substantial expansion), submitted to Phys. Rev.

Quantum strategies

We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely related to the traditional Matching Pennies game. While not every two-person zero-sum finite game has an equilibrium in the set of pure strategies, von Neumann showed that there is always an equilibrium at which each player follows a mixed strategy. A mixed strategy deviating from the equilibrium strategy cannot increase a player's expected payoff. We show, however, that in our example a player who implements a quantum strategy can increase his expected payoff, and explain the relation to efficient quantum algorithms. We prove that in general a quantum strategy is always at least as good as a classical one, and furthermore that when both players use quantum strategies there need not be any equilibrium, but if both are allowed mixed quantum strategies there must be.Comment: 8 pages, plain TeX, 1 figur

Coupled quantum dots as quantum gates

We consider a new quantum gate mechanism based on electron spins in coupled semiconductor quantum dots. Such gates provide a general source of spin entanglement and can be used for quantum computers. We determine the exchange coupling J in the effective Heisenberg model as a function of magnetic (B) and electric fields, and of the inter-dot distance (a) within the Heitler-London approximation of molecular physics. This result is refined by using sp-hybridization, and by the Hund-Mulliken molecular-orbit approach which leads to an extended Hubbard description for the two-dot system that shows a remarkable dependence on B and a due to the long-range Coulomb interaction. We find that the exchange J changes sign at a finite field (leading to a pronounced jump in the magnetization) and then decays exponentially. The magnetization and the spin susceptibilities of the coupled dots are calculated. We show that the dephasing due to nuclear spins in GaAs can be strongly suppressed by dynamical nuclear spin polarization and/or by magnetic fields.Comment: 10 pages, 4 figures. v2: minor corrections, appendix added. to be published in Phys.Rev.

Calcium mimics the chemotactic effect of conditioned media and is an effective inducer of bone regeneration

Background: after bone resorption, ions and degraded organic components are co-released into the extracellular space. Ions and growth factors, although different in their biological nature, induce a common and coordinated chemotactic effect. Conditioned media has been used successfully in bone regeneration by promoting endogenous cell recruitment. Likewise, calcium alone act as a paracrine chemotactic signal, inducing the host's undifferentiated progenitor cell infiltration into the implanted biomaterials. The aim of the present study was to compare the chemotactic effect of calcium and conditioned media in primary calvarial cells. Methods: the chemotactic cell response was evaluated in vitro using an agarose spot and a wound healing assay. In addition, we used a calvarial bone explant model ex-vivo. The healing potential was also tested through an in vivo model, a critical-size calvarial bone defect in mice. For the in vivo experiment, cell-free calcium-containing or conditioned media-containing scaffolds were implanted, and MSC's seeded scaffolds were used as positive control. After seven weeks post-implantation, samples were retrieved, and bone regeneration was evaluated by μCT and histological analysis. Osteogenic gene expression was evaluated by qPCR. Results: we found that chemotactic cell migration in response to either calcium or conditioned media was equivalent in vitro and ex vivo. Accordingly, μCT analysis showed that bone regeneration induced by the MSC's seeded scaffolds was similar to that obtained with cell-free calcium or conditioned media-containing scaffolds. Pre-treatment with SB202190, a highly selective p38 inhibitor, abrogated the chemotactic effect induced by conditioned media. In contrast, p38 activity was not essential for the calcium-induced chemotaxis. Moreover, BAPTA-AM treatment, a cytosolic calcium chelator, decreased the chemotactic effect and the expression of key osteogenic genes induced by calcium or conditioned media. Conclusion: we show that calcium ions alone not only mimic the conditioned media chemotactic effect, but also induce an osteogenic effect similar to that produced by transplanted MSC's in vivo. Furthermore, the chemotactic effect induced by conditioned media is calcium and p38 dependent. The rise in cytosolic calcium might integrate the different signaling pathways triggered by conditioned media and extracellular Ca2+. This calcium-driven in situ bone regeneration is a promising and convenient alternative to promote endogenous cell recruitment into the injured bone site. This pre-clinical cell-free and growth factor-free approach might avoid the disadvantages of the ex vivo cell manipulation

Generating entangled superpositions of macroscopically distinguishable states within a parametric oscillator

We suggest a variant of the recently proposed experiment for the generation of a new kind of Schroedinger-cat states, using two coupled parametric down-converter nonlinear crystals [F. De Martini, Phys. Rev. Lett. 81, 2842 (1998)]. We study the parametric oscillator case and find that an entangled Schroedinger-cat type state of two cavities, whose mirrors are placed along the output beams of the nonlinear crystals, can be realized under suitable conditions.Comment: RevTeX 17 pages, 9 eps files for 7 figures. Submitted to Physical Review