Parametrizing Quantum States and Channels

This work describes one parametrization of quantum states and channels and several of its possible applications. This parametrization works in any dimension and there is an explicit algorithm which produces it. Included in the list of applications are a simple characterization of pure states, an explicit formula for one additive entropic quantity which does not require knowledge of eigenvalues, and an algorithm which finds one Kraus operator representation for a quantum operation without recourse to eigenvalue and eigenvector calculations. PACS: 03.67a, 03.67-Hk, 03.67-Lx     

Quantum Information Processing in Cavity-QED

We give a brief overview of cavity-QED and its roles in quantum information science. In particular, we discuss setups in optical cavity-QED, where either atoms serve as stationary qubits, or photons serve as flying qubits. PACS: 42.50.Pq, 03.67.Lx, 03.67.Hk, 32.80.Pj     

Ion Trap Quantum Computing with Ca+ Ions

The scheme of an ion trap quantum computer is described and the implementation of quantum gate operations with trapped Ca⁺ ions is discussed. Quantum information processing with Ca⁺ ions is exemplified with several recent experiments investigating entanglement of ions. PACS: 03.67.Lx, 03.67.Mn, 32.80.Pj     

Spin-Based Quantum Dot Quantum Computing in Silicon

The spins of localized electrons in silicon are strong candidates for quantum information processing because of their extremely long coherence times and the integrability of Si within the present microelectronics infrastructure. This paper reviews a strategy for fabricating single electron spin qubits in gated quantum dots in Si/SiGe heterostructures. We discuss the pros and cons of using silicon, present recent advances, and outline challenges. PACS: 03.67.Pp, 03.67.Lx, 85.35.Be, 73.21.La     

Noiseless Subsystems and the Structure of the Commutant in Quantum Error Correction

The effect of noise on a quantum system can be described by a set of operators obtained from the interaction Hamiltonian. Recently it has been shown that generalized quantum error correcting codes can be derived by studying the algebra of this set of operators. This led to the discovery of noiseless subsystems. They are described by a set of operators obtained from the commutant of the noise generators. In this paper we derive a general method to compute the structure of this commutant in the case of unital noise. PACS: 03.67.–a, 03.67.Pp     

On a Parametrization of Purifications of a Qubit

This work provides, constructively, explicit one–one parametrizations of all purifications of a mixed state in dimension 2 and all joint purifications, if any, of two mixed states in the same dimension. The former is parametrized by SO(3, R), while the latter is parametrized by SO(2, R), except when the state being purified is already pure. These parametrizations are derived without any passage to the spectral decompositions of the state(s) being purified. Using this, we show how to calculate certain measures of quantum information. The appendix considers an alternative one–one parametrization of mixed states in C² C², which provides a different explicit construction of joint purifications. PACS: 03.67-a; 03.67-Hk; 03.67-Lx     

适应物体形状的虚拟手抓取

目的 虚拟手抓取是虚拟交互中的核心技术之一,直接影响沉浸感。已有的虚拟手抓取规则基于接触点法矢夹角和接触点与体心连线的夹角,但在部分形状上不能正确抓取。为此提出一种适应物体形状的抓取规则。方法 针对长方体、球、圆柱这些构成物体的基本几何体,利用形状特征和手指抓握的接触关系制定抓取规则：1）长方体的规则是至少有3个不共线的接触点,并且一对接触点法矢夹角超过90°;2）球的规则要对接触点和球心的空间关系进行计算;3）圆柱的规则根据接触点是否在曲面上,使用长方体规则,或是仿照球的规则判断。对于需要使用多个几何体描述外形的复杂物体,先按照这3种基本几何体分解、单独计算,然后筛选出其中不稳定状态的几何体,把整体的接触点位置、法矢信息集中在这些不稳定状态几何体上,用单一几何体的抓取规则计算整体的抓取。同时加入力矩平衡可能性的计算,抓取规则和力矩平衡二者都满足才判定抓取成功,进一步减少了错误判断的发生。结果 使用unity3d构建虚拟场景,并用neuron的数据手套采集人体、手指数据,进行虚拟交互的仿真。该方法可以正确处理类似水杯这样的多几何体组合物体的抓取判断。结论 本文提出了基于物体形状的抓取规则,和用简单基本形状分解复杂物体的计算方法,准确计算抓取,符合直观感受。     

Estimation of Quantum Channels with Finite Resources

We examine the problem of determining the parameters that describe a quantum channel. It is assumed that the users of the channel have at best only partial knowledge of it and make use of a finite amount of resources to estimate it. We discuss simple protocols for the estimation of the parameters of several classes of channels that are studied in the current literature. A quantitative measures of the quality of the estimation schemes can be given on the basis of the standard deviation or of the fidelity. Protocols that employ entangled particles are also discussed. The use of entangled particles as a nonclassical resource enhances the estimation quality of some classes of quantum channel. Further, the methods presented here can be extended to higher dimensional quantum systems. PACS: 03.67.Hk     

Quantum Codes for Simplifying Design and Suppressing Decoherence in Superconducting Phase-Qubits

We introduce simple qubit-encodings and logic gates which eliminate the need for certain difficult single-qubit operations in superconducting phase-qubits, while preserving universality. The simplest encoding uses two physical qubits per logical qubit. Two architectures for its implementation are proposed: one employing N physical qubits out of which N/2 are ancillas fixed in the |1 state, the other employing N/2+1 physical qubits, one of which is a bus qubit connected to all others. Details of a minimal set of universal encoded logic operations are given, together with recoupling schemes, that require nanosecond pulses. A generalization to codes with higher ratio of number of logical qubits per physical qubits is presented. Compatible decoherence and noise suppression strategies are also discussed. PACS: 03.67.Lx; 85.25.Hv; 03.67.-a; 89.70.+c     

Towards Scalable Linear-Optical Quantum Computers

Scalable quantum computation with linear optics was considered to be impossible due to the lack of efficient two-qubit logic gates, despite the ease of implementation of one-qubit gates. Two-qubit gates necessarily need a non-linear interaction between the two photons, and the efficiency of this non-linear interaction is typically very small in bulk materials. However, it has recently been shown that this barrier can be circumvented with effective non-linearities produced by projective measurements, and with this work linear-optical quantum computing becomes a new avenue towards scalable quantum computation. We review several issues concerning the principles and requirements of this scheme. PACS: 03.67.Lx, 03.67.Pp, 42.50.Dv, 42.65.Lm     

Progress in Quantum Algorithms

We discuss the progress (or lack of it) that has been made in discovering algorithms for computation on a quantum computer. Some possible reasons are given for the paucity of quantum algorithms so far discovered, and a short survey is given of the state of the field. PACS: 03.67.Lx     

Approximate Quantum Error Correction

The errors that arise in a quantum channel can be corrected perfectly if and only if the channel does not decrease the coherent information of the input state. We show that, if the loss of coherent information is small, then approximate quantum error correction is possible. PACS: 03.67.H, 03.65.U     

Data Compression Limit for an Information Source of Interacting Qubits

A system of interacting qubits can be viewed as a non-i.i.d quantum information source. A possible model of such a source is provided by a quantum spin system, in which spin-1/2 particles located at sites of a lattice interact with each other. We establish the limit for the compression of information from such a source and show that asymptotically it is given by the von Neumann entropy rate. Our result can be viewed as a quantum ana-logue of Shannon's noiseless coding theorem for a class of non-i.i.d. quantum informa-tion sources. From the probabilistic point of view it is an analog of the Shannon-McMillan-Breiman theorem considered as a cornerstone of modern Information Theory. PACS: 03.67-a; 03.67.Lx     

An Example of the Difference Between Quantum and Classical Random Walks

In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analog. In this graph, propagation between a particular pair of nodes is exponentially faster in the quantum case. PACS: 03.67.Hk     

Natural Majorization of the Quantum Fourier Transformation in Phase-Estimation Algorithms

We prove that majorization relations hold step by step in the Quantum Fourier Transformation (QFT) for phase-estimation algorithms. Our result relies on the fact that states which are mixed by Hadamard operators at any stage of the computation only differ by a phase. This property is a consequence of the structure of the initial state and of the QFT, based on controlled-phase operators and a single action of a Hadamard gate per qubit. The detail of our proof shows that Hadamard gates sort the probability distribution associated to the quantum state, whereas controlled-phase operators carry all the entanglement but are immaterial to majorization. We also prove that majorization in phase-estimation algorithms follows in a most natural way from unitary evolution, unlike its counterpart in Grover's algorithm. PACS: 03.67.-a, 03.67.Lx     

Scaling and Renormalization in Fault-Tolerant Quantum Computers

This work is concerned with phrasing the concepts of fault-tolerant quantum computation within the framework of disordered systems, Bernoulli site percolation in particular. We show how the so-called threshold theorems on the possibility of fault-tolerant quantum computation with constant error rate can be cast as a renormalization (coarse-graining) of the site percolation process describing the occurrence of errors during computation. We also use percolation techniques to derive a trade-off between the complexity overhead of the fault-tolerant circuit and the threshold error rate. PACS: 03.67.Pp; 03.67.Lx     

Geometric Approach to Digital Quantum Information

We present geometric methods for uniformly discretizing the continuous N-qubit Hilbert space H_N. When considered as the vertices of a geometrical figure, the resulting states form the equivalent of a Platonic solid. The discretization technique inherently describes a class of /2 rotations that connect neighboring states in the set, i.e., that leave the geometrical figures invariant. These rotations are shown to generate the Clifford group, a general group of discrete transformations on N qubits. Discretizing H_N allows us to define its digital quantum information content, and we show that this information content grows as N². While we believe the discrete sets are interesting because they allow extra-classical behavior—such as quantum entanglement and quantum parallelism—to be explored while circumventing the continuity of Hilbert space, we also show how they may be a useful tool for problems in traditional quantum computation. We describe in detail the discrete sets for one and two qubits.PACS: 03.67.Lx; 03.67.pp; 03.67.-a; 03.67.Mn.PACS: 03.67.Lx; 03.67.pp; 03.67.-a; 03.67.Mn.     

Quantum Computing with Trapped Ion Hyperfine Qubits

We discuss the basic aspects of quantum information processing with trapped ions, including the principles of ion trapping, preparation and detection of hyperfine qubits, single-qubit operations and multi-qubit entanglement protocols. Recent experimental advances and future research directions are outlined. PACS: 03.67.Lx, 32.80.Pj, 32.80.Qk, 42.50.Vk     

Spin Squeezing Criterion with Local Unitary Invariance

We propose a spin squeezing criterion for arbitrary multi-qubit states that is invariant under local unitary operations. We find that, for arbitrary pure two-qubit states, spin squeezing is equivalent to entanglement, and multi-qubit states are entangled if this new spin squeezing parameter is less than unity. PACS: 03.67.-a; 03.65.Ud     

Experimental Concatenation of Quantum Error Correction with Decoupling

We experimentally explore the reduction of decoherence via concatenating quantum error correction (QEC) with decoupling in liquid-state NMR quantum information processing. Decoupling provides an efficient means of suppressing decoherence from noise sources with long correlation times, and then QEC can be used more profitably for the remaining noise sources. PACS: 03.67.Lx, 03.65.Bz