Multi-qubit compensation sequences

The Hamiltonian control of n qubits requires precision control of both the strength and timing of interactions. Compensation pulses relax the precision requirements by reducing unknown but systematic errors. Using composite pulse techniques designed for single qubits, we show that systematic errors for n qubit systems can be corrected to arbitrary accuracy given either two non-commuting control Hamiltonians with identical systematic errors or one error-free control Hamiltonian. We also examine composite pulses in the context of quantum computers controlled by two-qubit interactions. For quantum computers based on the XY interaction, single-qubit composite pulse sequences naturally correct systematic errors. For quantum computers based on the Heisenberg or exchange interaction, the composite pulse sequences reduce the logical single-qubit gate errors but increase the errors for logical two-qubit gates.Comment: 9 pages, 5 figures; corrected reference formattin

A Quantum Random Walk Search Algorithm

Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel properties to gain an algorithmic speed-up over classical algorithms. In this paper, we present a quantum search algorithm based on the quantum random walk architecture that provides such a speed-up. It will be shown that this algorithm performs an oracle search on a database of $N$ items with $O(\sqrt{N})$ calls to the oracle, yielding a speed-up similar to other quantum search algorithms. It appears that the quantum random walk formulation has considerable flexibility, presenting interesting opportunities for development of other, possibly novel quantum algorithms.Comment: 13 pages, 3 figure

Encoded Universality for Generalized Anisotropic Exchange Hamiltonians

We derive an encoded universality representation for a generalized anisotropic exchange Hamiltonian that contains cross-product terms in addition to the usual two-particle exchange terms. The recently developed algebraic approach is used to show that the minimal universality-generating encodings of one logical qubit are based on three physical qubits. We show how to generate both single- and two-qubit operations on the logical qubits, using suitably timed conjugating operations derived from analysis of the commutator algebra. The timing of the operations is seen to be crucial in allowing simplification of the gate sequences for the generalized Hamiltonian to forms similar to that derived previously for the symmetric (XY) anisotropic exchange Hamiltonian. The total number of operations needed for a controlled-Z gate up to local transformations is five. A scalable architecture is proposed.Comment: 11 pages, 4 figure

Cyanide-Bridged Polynuclear Compounds of Molybdenum(III) and Rhenium(II)

Since the discovery of [Mn₁₂O₁₂(CH₃COO)₁₆(H₂O)₄], research in the area of molecular magnetism has been directed at designing single molecule magnets (SMMs) whose slow paramagnetic relaxation occurs with long relaxation times and at relatively high temperatures. Both polynuclear and mononuclear compounds have been studied with respect to the fundamental characteristics required to make SMMs viable options for device applications including memory storage, spintronics, and quantum computing. In recent years much progress has been made with respect to mononuclear magnets but approaches that incorporate knowledge of strong anisotropy in exchange coupled systems are still underexplored. Specifically, anisotropic exchange represents an important option for improving the properties of polynuclear SMMs. Despite growing interest in the topic, lack of numerous examples of such systems have hampered progress in this area. This dissertation describes studies of new molecules and synthetic techniques to systematically study conditions that lead to Ising-type anisotropic exchange in heavier transition element molecules. By drawing on previous work with the cyanometallate moieties [Moᶦᶦᶦ(CN)₇]⁴⁻ and [(triphos)Reᶦᶦ(CN)₃]⁻ , new precursors and synthetic strategies were developed to aid research in the area of anisotropic exchange interactions. Mo-Ln chains with the formula {K[Ln(tmphen)₂(H₂O)₂Moᶦᶦᶦ(CN)₇]} were characterized structurally and magnetically and revealed that more work could lead to interesting Mo-Ln nanomagnets. A cyanometallate wheel with the formula [Moᶦᶦᶦ(CN)₇]₆[Ni(L)]₁₂∙24H₂O demonstrated that incorporating [Moᶦᶦᶦ(CN)₇]⁴⁻ into known architectures can improve magnetic properties. A new, heteroleptic Moᶦᶦᶦ cyanometallate was isolated that will facilitate synthesis of new molecules. Three new compounds that incorporate Reᶦᶦ and Vᶦᶦ demonstrate the requirements for observing anisotropic exchange with [(triphos)Reᶦᶦ(CN)₃]⁻ . Future work with these strategies will be helpful for investigating the importance of anisotropic exchange as an alternative for the design of single molecule magnets with higher barriers for both the d and f-block elements

Perdeuterated cyanobiphenyl liquid crystals for infrared applications

Perdeuterated 4'-pentyl-4-cyanobiphenyl (D5CB) was synthesized and its physical properties evaluated and compared to those of 5CB. D5CB retains physical properties similar to those of 5CB, such as phase transition temperatures, dielectric constants, and refractive indices. An outstanding feature of D5CB is that it exhibits a much cleaner and reduced infrared absorption. Perdeuteration, therefore, extends the usable range of liquid crystals to the mid infrared by significantly reducing the absorption in the near infrared, which is essential for telecom applications

Entanglement measures and approximate quantum error correction

It is shown that, if the loss of entanglement along a quantum channel is sufficiently small, then approximate quantum error correction is possible, thereby generalizing what happens for coherent information. Explicit bounds are obtained for the entanglement of formation and the distillable entanglement, and their validity naturally extends to other bipartite entanglement measures in between. Robustness of derived criteria is analyzed and their tightness compared. Finally, as a byproduct, we prove a bound quantifying how large the gap between entanglement of formation and distillable entanglement can be for any given finite dimensional bipartite system, thus providing a sufficient condition for distillability in terms of entanglement of formation.Comment: 7 pages, two-columned revtex4, no figures. v1: Deeply revised and extended version: different entanglement measures are separately considered, references are added, and some remarks are stressed. v2: Added a sufficient condition for distillability in terms of entanglement of formation; published versio