Fault-Tolerant Quantum Dynamical Decoupling

Dynamical decoupling pulse sequences have been used to extend coherence times in quantum systems ever since the discovery of the spin-echo effect. Here we introduce a method of recursively concatenated dynamical decoupling pulses, designed to overcome both decoherence and operational errors. This is important for coherent control of quantum systems such as quantum computers. For bounded-strength, non-Markovian environments, such as for the spin-bath that arises in electron- and nuclear-spin based solid-state quantum computer proposals, we show that it is strictly advantageous to use concatenated, as opposed to standard periodic dynamical decoupling pulse sequences. Namely, the concatenated scheme is both fault-tolerant and super-polynomially more efficient, at equal cost. We derive a condition on the pulse noise level below which concatenated is guaranteed to reduce decoherence.Comment: 5 pages, 4 color eps figures. v3: Minor changes. To appear in Phys. Rev. Let

Efficient Coherent Control by Optimized Sequences of Pulses of Finite Duration

Reliable long-time storage of arbitrary quantum states is a key element for quantum information processing. In order to dynamically decouple a spin or quantum bit from a dephasing environment, we introduce an optimized sequence of $N$ control pulses of finite durations \tau\pp and finite amplitudes. The properties of this sequence of length $T$ stem from a mathematically rigorous derivation. Corrections occur only in order $T^{N+1}$ and \tau\pp^3 without mixed terms such as T^N\tau\pp or T^N\tau\pp^2. Based on existing experiments, a concrete setup for the verification of the properties of the advocated realistic sequence is proposed.Comment: 8 pages, 1 figur

Encoded Recoupling and Decoupling: An Alternative to Quantum Error Correcting Codes, Applied to Trapped Ion Quantum Computation

A recently developed theory for eliminating decoherence and design constraints in quantum computers, ``encoded recoupling and decoupling'', is shown to be fully compatible with a promising proposal for an architecture enabling scalable ion-trap quantum computation [D. Kielpinski et al., Nature 417, 709 (2002)]. Logical qubits are encoded into pairs of ions. Logic gates are implemented using the Sorensen-Molmer (SM) scheme applied to pairs of ions at a time. The encoding offers continuous protection against collective dephasing. Decoupling pulses, that are also implemented using the SM scheme directly to the encoded qubits, are capable of further reducing various other sources of qubit decoherence, such as due to differential dephasing and due to decohered vibrational modes. The feasibility of using the relatively slow SM pulses in a decoupling scheme quenching the latter source of decoherence follows from the observed 1/f spectrum of the vibrational bath.Comment: 12 pages, no figure

Quantum Computing in the Presence of Detected Spontaneous Emission

A new method for quantum computation in the presence of detected spontaneous emission is proposed. The method combines strong and fast (dynamical decoupling) pulses and a quantum error correcting code that encodes $n$ logical qubits into only $n+1$ physical qubits. Universal fault-tolerant quantum computation is shown to be possible in this scheme using Hamiltonians relevant to a range of promising proposals for the physical implementation of quantum computers.Comment: 7 pages, no figures. This version corrects an error in the description of spontaneous emission in the quantum jumps picture. As a consequence the error correcting code and some aspects of the preparation, computation, and recovery operations have been modified. The main conclusions of the published paper remain intact. An erratum will be published shortly in Phys. Rev. A, detailing all the corrections required in the published paper. The present version includes all these corrections in the body of the pape

Bang-bang control of fullerene qubits using ultra-fast phase gates

Quantum mechanics permits an entity, such as an atom, to exist in a superposition of multiple states simultaneously. Quantum information processing (QIP) harnesses this profound phenomenon to manipulate information in radically new ways. A fundamental challenge in all QIP technologies is the corruption of superposition in a quantum bit (qubit) through interaction with its environment. Quantum bang-bang control provides a solution by repeatedly applying `kicks' to a qubit, thus disrupting an environmental interaction. However, the speed and precision required for the kick operations has presented an obstacle to experimental realization. Here we demonstrate a phase gate of unprecedented speed on a nuclear spin qubit in a fullerene molecule (N@C60), and use it to bang-bang decouple the qubit from a strong environmental interaction. We can thus trap the qubit in closed cycles on the Bloch sphere, or lock it in a given state for an arbitrary period. Our procedure uses operations on a second qubit, an electron spin, in order to generate an arbitrary phase on the nuclear qubit. We anticipate the approach will be vital for QIP technologies, especially at the molecular scale where other strategies, such as electrode switching, are unfeasible

Near-IR Atlas of S0-Sa galaxies (NIRS0S)

An atlas of Ks-band images of 206 early-type galaxies is presented, including 160 S0-S0/a galaxies, 12 ellipticals, and 33 Sa galaxies. A majority of the Atlas galaxies belong to a magnitude-limited (mB<12.5 mag) sample of 185 NIRS0S (Near-IR S0 galaxy Survey) galaxies. To assure that mis-classified S0s are not omitted, 25 ellipticals from RC3 classified as S0s in the Carnegie Atlas were included in the sample. The images are 2-3 mag deeper than 2MASS images. Both visual and photometric classifications are made. Special attention is paid to the classification of lenses, coded in a systematic manner. A new lens-type, called a 'barlens', is introduced. Also, boxy/peanut/x-shaped structures are identified in many barred galaxies, even-though the galaxies are not seen in edge-on view, indicating that vertical thickening is not enough to explain them. Multiple lenses appear in 25% of the Atlas galaxies, which is a challenge to the hierarchical evolutionary picture of galaxies. Such models need to explain how the lenses were formed and survived in multiple merger events that galaxies may have suffered during their lifetimes. Following the early suggestion by van den Bergh, candidates of S0c galaxies are shown, which galaxies are expected to be former Sc-type spirals stripped out of gas.Comment: 67 pages (include 16 figures and 6 tables). Accepted to MNRAS 2011 June 1

Quantitative Treatment of Decoherence

We outline different approaches to define and quantify decoherence. We argue that a measure based on a properly defined norm of deviation of the density matrix is appropriate for quantifying decoherence in quantum registers. For a semiconductor double quantum dot qubit, evaluation of this measure is reviewed. For a general class of decoherence processes, including those occurring in semiconductor qubits, we argue that this measure is additive: It scales linearly with the number of qubits.Comment: Revised version, 26 pages, in LaTeX, 3 EPS figure

Advantages of Randomization in Coherent Quantum Dynamical Control

Control scenarios have been identified where the use of randomized design may substantially improve the performance of dynamical decoupling methods [L. F. Santos and L. Viola, Phys. Rev. Lett. {\bf 97}, 150501 (2006)]. Here, by focusing on the suppression of internal unwanted interactions in closed quantum systems, we review and further elaborate on the advantages of randomization at long evolution times. By way of illustration, special emphasis is devoted to isolated Heisenberg-coupled chains of spin-1/2 particles. In particular, for nearest-neighbor interactions, two types of decoupling cycles are contrasted: inefficient averaging, whereby the number of control actions increases exponentially with the system size, and efficient averaging associated to a fixed-size control group. The latter allows for analytical and numerical studies of efficient decoupling schemes created by exploiting and merging together randomization and deterministic strategies, such as symmetrization, concatenation, and cyclic permutations. Notably, sequences capable to remove interactions up to third order are explicitly constructed. The consequences of faulty controls are also analyzed.Comment: 27 pages, 7 figure