Universal quantum gates based on a pair of orthogonal cyclic states: Application to NMR systems

NMR dynamics of quantum discord for spin-carrying gas molecules in a closed nanopore

A local orthogonal transformation that transforms any centrosymmetric (CS) matrix of fourth order to the X form is found. A picewise-analytic-numerical formula Q=min{Q_π/2,Q_θ,Q_0}, where Q_π/2 and Q_0 are analytical expressions and the branch Q_θ is found by numerical searching the optimal measurement angle θ\in(0,π/2), is proposed to calculate the quantum discord Q of general X state. The developed approaches are applied to a quantitative description of recently predicted flickerings (periodic birth and death) of the quantum-information pair correlation between nuclear 1/2 spin of atoms or m…

Computational speed-up in a single qudit NMR quantum information processor

Quantum algorithms are known for presenting more efficient solutions to certain computational tasks than any corresponding classical algorithm. It has been thought that the origin of the power of quantum computation has its roots in non-classical correlations such as entanglement or quantum discord. However, it has been recently shown that even a single pure qudit is sufficient to design an oracle-based algorithm which solves a black-box problem faster than any classical approach to the same problem. In particular, the algorithm that we consider determines whether eight permutation functions d…

Experimental Demonstration of Non-Destructive Discrimination of Arbitrary Set of Orthogonal Quantum States Using 5-qubit IBM Quantum Computer on Cloud

A protocol for non-destructive descrimination of arbitrary set of orthogonal quantum states was proposed by V. S. Manu et al., using an algorithm based on quantum phase estimation. IBM Corporation has released a superconductivity based 5-qubit (5-qubit transmon bowtie chip 3 and IBM 5-qubit real processor) quantum computer named Quantum Experience and placed it on cloud. In this paper we take advantage of the online availability of those real quantum processors(ibmqx2 amd ibmqx4) and carry out the above protocol that has experimentally demonstrated earlier using NMR quantum processor. Here, we…

Quantum state tomography of large nuclear spins in a semiconductor quantum well: Optimal robustness against errors as quantified by condition numbers

We discuss methods of quantum state tomography for solid-state systems with a large nuclear spin $I=3/2$ in nanometer-scale semiconductors devices based on a quantum well. Due to quadrupolar interactions, the Zeeman levels of these nuclear-spin devices become nonequidistant, forming a controllable four-level quantum system (known as quartit or ququart). The occupation of these levels can be selectively and coherently manipulated by multiphoton transitions using the techniques of nuclear magnetic resonance (NMR) [Yusa et al., Nature (London) 434, 101 (2005)]. These methods are based on an uncon…

Geometric phase with nonunitary evolution in presence of a quantum critical bath

Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications, the quantum geometric phase was generalized to open systems. The definition takes a kinematical approach, with an initial state that is evolved cyclically but coupled to an environment --- leading to a correction of the geometric phase with respect to the uncoupled case. We obtain this correction by measuring the nonunitary evolution of the reduced density …

列重为2且围长为12的量子准循环低密度奇偶校验码的显式构造

Explicit Construction of Quantum Quasi-Cyclic Low-Density Parity-Check Codes with Column Weight 2 and Girth 12

本文提出一种列重为2且围长为12的量子QC-LDPC码显式构造方法，利用代数技术消除短环并保持正交性，且可扩展至非二进制和空间耦合LDPC码，无需随机搜索即可设计高性能量子纠错码。

Quasi-Cyclic Constructions of Quantum Codes

We give sufficient conditions for self-orthogonality with respect to symplectic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index two. We provide lower bounds for the symplectic weight and the minimum distance of the involved codes. Supported in the previous results, we show algebraic constructions of good quantum codes and determine their parameters.

基于非互易 Mach-Zehnder 干涉仪的轨道角动量模式可扩展循环变换

Scalable cyclic transformation of orbital angular momentum modes based on a nonreciprocal Mach-Zehnder interferometer

本研究利用非互易 Mach-Zehnder 干涉仪实验实现了六种轨道角动量模式的高效循环变换，平均效率超 96%，为可扩展高维量子计算的单光子量子 Pauli-X 门奠定了基础。

Geometric Aspects of Composite Pulses

Unitary operations acting on a quantum system must be robust against systematic errors in control parameters for reliable quantum computing. Composite pulse technique in nuclear magnetic resonance (NMR) realises such a robust operation by employing a sequence of possibly poor quality pulses. In this article, we demonstrate that two kinds of composite pulses, one compensates for a pulse length error in a one-qubit system and the other compensates for a J-coupling error in a twoqubit system, have vanishing dynamical phase and thereby can be seen as geometric quantum gates, which implement unitar…

Implementation of universal quantum gates based on nonadiabatic geometric phases

We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this set of gates is designed for Josephson junctions and for NMR systems. Interestingly, we find that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions. A remarkable feature of the present nonadiabatic geometric gates is that there is no intrinsic limitation on the operation time, unlike adiabatic ge…

通过正交测量实现群协变 POVM

Implementation of group-covariant POVMs by orthogonal measurements

本文基于对称群的表示理论，提出利用矩阵分解方法实现由秩一算子构成的群协变 POVM 的量子电路，并给出了由 Weyl-Heisenberg 群生成的高效量子电路示例，实现了粒子位置与晶体动量的近似同时测量。

素数维数下的循环三正交码

Cyclic triorthogonal codes in prime dimension

本文研究素数维数下的循环三正交码，利用谱支撑和集条件进行穷举搜索，并证明三偶性与经典三正交性等价，找到优于现有码的短码及无限码族。