Applications of coherent classical communication and the Schur transform to quantum information theory

Quantum mechanics has led not only to new physical theories, but also a new understanding of information and computation. Quantum information began by yielding new methods for achieving classical tasks such as factoring and key distribution but also suggests a completely new set of quantum problems, such as sending quantum information over quantum channels or efficiently performing particular basis changes on a quantum computer. This thesis contributes two new, purely quantum, tools to quantum information theory--coherent classical communication in the first half and an efficient quantum circuit for the Schur transform in the second half.Comment: 176 pages. Chapters 1 and 4 are a slightly older version of quant-ph/0512015. Chapter 2 is quant-ph/0205057 plus unpublished extensions (slightly outdated by quant-ph/0511219) and chapter 3 is quant-ph/0307091, quant-ph/0412126 and change. Chapters 5-8 are based on quant-ph/0407082, but go much furthe

Symmetric coupling of four spin-1/2 systems

We address the non-binary coupling of identical angular momenta based upon the representation theory for the symmetric group. A correspondence is pointed out between the complete set of commuting operators and the reference-frame-free subsystems. We provide a detailed analysis of the coupling of three and four spin-1/2 systems and discuss a symmetric coupling of four spin-1/2 systems.Comment: 20 pages, no figure

Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms

The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient (size poly(n,d,log(1/\epsilon)) for accuracy \epsilon) quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. These circuits are based on efficient circuits for the Clebsch-Gordan transformation. We also present an efficient circuit for a limited version of the Schur transform in which one needs only to project onto different Schur subspaces. This second circuit is based on a generalization of phase estimation to any nonabelian finite group for which there exists a fast quantum Fourier transform.Comment: 4 pages, 3 figure

A practical scheme for quantum computation with any two-qubit entangling gate

Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not (CNOT), are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. Here we present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this important result for systems of arbitrary finite dimension has been provided by J. L. and R. Brylinski [arXiv:quant-ph/0108062, 2001]; however, their proof relies upon a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical [C. M. Dawson and A. Gilchrist, online implementation of the procedure described herein (2002), http://www.physics.uq.edu.au/gqc/].Comment: 3 pages, online implementation of procedure described can be found at http://www.physics.uq.edu.au/gqc

Event Stream Processing with Multiple Threads

Current runtime verification tools seldom make use of multi-threading to speed up the evaluation of a property on a large event trace. In this paper, we present an extension to the BeepBeep 3 event stream engine that allows the use of multiple threads during the evaluation of a query. Various parallelization strategies are presented and described on simple examples. The implementation of these strategies is then evaluated empirically on a sample of problems. Compared to the previous, single-threaded version of the BeepBeep engine, the allocation of just a few threads to specific portions of a query provides dramatic improvement in terms of running time

The tammar wallaby major histocompatibility complex shows evidence of past genomic instability

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.Abstract Background The major histocompatibility complex (MHC) is a group of genes with a variety of roles in the innate and adaptive immune responses. MHC genes form a genetically linked cluster in eutherian mammals, an organization that is thought to confer functional and evolutionary advantages to the immune system. The tammar wallaby (Macropus eugenii), an Australian marsupial, provides a unique model for understanding MHC gene evolution, as many of its antigen presenting genes are not linked to the MHC, but are scattered around the genome. Results Here we describe the 'core' tammar wallaby MHC region on chromosome 2q by ordering and sequencing 33 BAC clones, covering over 4.5 MB and containing 129 genes. When compared to the MHC region of the South American opossum, eutherian mammals and non-mammals, the wallaby MHC has a novel gene organization. The wallaby has undergone an expansion of MHC class II genes, which are separated into two clusters by the class III genes. The antigen processing genes have undergone duplication, resulting in two copies of TAP1 and three copies of TAP2. Notably, Kangaroo Endogenous Retroviral Elements are present within the region and may have contributed to the genomic instability. Conclusions The wallaby MHC has been extensively remodeled since the American and Australian marsupials last shared a common ancestor. The instability is characterized by the movement of antigen presenting genes away from the core MHC, most likely via the presence and activity of retroviral elements. We propose that the movement of class II genes away from the ancestral class II region has allowed this gene family to expand and diversify in the wallaby. The duplication of TAP genes in the wallaby MHC makes this species a unique model organism for studying the relationship between MHC gene organization and function.Peer Reviewe

Quantum Bootstrap Aggregation

We set out a strategy for quantizing attribute bootstrap aggregation to enable variance-resilient quantum machine learning. To do so, we utilise the linear decomposability of decision boundary parameters in the Rebentrost et al. Support Vector Machine to guarantee that stochastic measurement of the output quantum state will give rise to an ensemble decision without destroying the superposition over projective feature subsets induced within the chosen SVM implementation. We achieve a linear performance advantage, O(d), in addition to the existing O(log(n)) advantages of quantization as applied to Support Vector Machines. The approach extends to any form of quantum learning giving rise to linear decision boundaries

Chemical Tuning of Positive and Negative Magnetoresistances, and Superconductivity in 1222-type Ruthenocuprates

High critical-temperature superconductivity and large (colossal) magnetoresistances are two important electronic conducting phenomena found in transition metal oxides. High-Tc materials have applications such as superconducting magnets for MRI and NMR, and magnetoresistive materials may find use in magnetic sensors and spintronic devices. Here we report chemical doping studies of RuSr2(R2-xCex)Cu2O10-d ruthenocuprates which show that a single oxide system can be tuned between superconductivity at high hole dopings and varied magnetoresistive properties at low doping levels. A robust variation of negative magnetoresistance with hole concentration is found in the RuSr2R1.8-xY0.2CexCu2O10-d series, while RuSr2R1.1Ce0.9Cu2O10-d materials show an unprecedented crossover from negative to positive magnetoresistance with rare earth (R) ion radius

Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing

Being able to quantify the level of coherent control in a proposed device implementing a quantum information processor (QIP) is an important task for both comparing different devices and assessing a device's prospects with regards to achieving fault-tolerant quantum control. We implement in a liquid-state nuclear magnetic resonance QIP the randomized benchmarking protocol presented by Knill et al (PRA 77: 012307 (2008)). We report an error per randomized $\frac{\pi}{2}$ pulse of $1.3 \pm 0.1 \times 10^{-4}$ with a single qubit QIP and show an experimentally relevant error model where the randomized benchmarking gives a signature fidelity decay which is not possible to interpret as a single error per gate. We explore and experimentally investigate multi-qubit extensions of this protocol and report an average error rate for one and two qubit gates of $4.7 \pm 0.3 \times 10^{-3}$ for a three qubit QIP. We estimate that these error rates are still not decoherence limited and thus can be improved with modifications to the control hardware and software.Comment: 10 pages, 6 figures, submitted versio

Efficient and feasible state tomography of quantum many-body systems

We present a novel method to perform quantum state tomography for many-particle systems which are particularly suitable for estimating states in lattice systems such as of ultra-cold atoms in optical lattices. We show that the need for measuring a tomographically complete set of observables can be overcome by letting the state evolve under some suitably chosen random circuits followed by the measurement of a single observable. We generalize known results about the approximation of unitary 2-designs, i.e., certain classes of random unitary matrices, by random quantum circuits and connect our findings to the theory of quantum compressed sensing. We show that for ultra-cold atoms in optical lattices established techniques like optical super-lattices, laser speckles, and time-of-flight measurements are sufficient to perform fully certified, assumption-free tomography. Combining our approach with tensor network methods - in particular the theory of matrix-product states - we identify situations where the effort of reconstruction is even constant in the number of lattice sites, allowing in principle to perform tomography on large-scale systems readily available in present experiments.Comment: 10 pages, 3 figures, minor corrections, discussion added, emphasizing that no single-site addressing is needed at any stage of the scheme when implemented in optical lattice system