Vol.17 No.15&16, December 1, 2017

Research Articles:

Better protocol for XOR game using communication protocol and nonlocal boxes (pp1261-1276)
          Ryuhei Mori
Buhrman showed that an efficient communication protocol implies a reliable XOR game protocol. This idea rederives Linial and Shraibman's lower bound of randomized and quantum communication complexities, which was derived by using factorization norms, with worse constant factor in much more intuitive way. In this work, we improve and generalize Buhrman's idea, and obtain a class of lower bounds for randomized communication complexity including an exact Linial and Shraibman's lower bound as a special case. In the proof, we explicitly construct a protocol for XOR game from a randomized communication protocol by using a concept of nonlocal boxes and Paw\l owski et~al.'s elegant protocol, which was used for showing the violation of information causality in superquantum theories.

Quantum communication with continuum single-photon, two-photon and coherent states (pp1277-1291)
          F. Franklin S. Rios, A. Geovan de A.H. Guerra, and R.Viana Ramos
In this work, we analyze the behavior of continuum single-photon, two-photon and coherent states in some quantum communication schemes. In particular, we consider the single-photon in a Mach-Zenhder interferometer, the Hong-Ou-Mandel interference, the quantum bit commitment protocol and a new protocol for secure transmission of sampled analog signals. Furthermore, it is shown an equation for estimating the spectral distribution of the single-photon produced by a heralded single-photon source using four-wave mixing in an optical fiber.

Generalized coherent states, reproducing kernels, and quantum support vector machines (pp1292-1306)
          Rupak Chatterjee and Ting Yu
The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that these algorithms when executed on a classical computer do not scale well with the size of the feature space both in terms of data points and dimensionality. One of the most significant limitations of classical algorithms using non-linear kernels is that the kernel function has to be evaluated for all pairs of input feature vectors which themselves may be of substantially high dimension. This can lead to computationally excessive times during training and during the prediction process for a new data point. Here, we propose using both canonical and generalized coherent states to calculate specific nonlinear kernel functions. The key link will be the reproducing kernel Hilbert space (RKHS) property for SVMs that naturally arise from canonical and generalized coherent states. Specifically, we discuss the evaluation of radial kernels through a positive operator valued measure (POVM) on a quantum optical system based on canonical coherent states. A similar procedure may also lead to calculations of kernels not usually used in classical algorithms such as those arising from generalized coherent states. 

Weight reduction for quantum codes (pp1307-1334)
          Mathew B. Hastings
We present an algorithm that takes a CSS stabilizer code as input, and outputs another CSS stabilizer code such that the stabilizer generators all have weights $O(1)$ and such that $O(1)$ generators act on any given qubit.  The number of logical qubits is unchanged by the procedure, while we give bounds on the increase in number of physical qubits and in the effect on distance and other code parameters, such as soundness (as a locally testable code) and ``cosoundness" (defined later).  Applications are discussed, including to codes from high-dimensional manifolds which have logarithmic weight stabilizers.  Assuming a conjecture in geometry\cite{hdm}, this allows the construction of CSS stabilizer codes with generator weight $O(1)$ and almost linear distance.  Another application of the construction is to increasing the distance to $X$ or $Z$ errors, whichever is smaller, so that the two distances are equal.

Online scheduled execution of quantum circuits protected by surface codes (pp1335-1348)
          Alexandru Paler, Austin G. Fowler, and Robert Wille
Quantum circuits are the preferred formalism for expressing quantum information processing tasks. Quantum circuit design automation methods mostly use a waterfall approach and consider that high level circuit descriptions are hardware agnostic. This assumption has lead to a static circuit perspective: the number of quantum bits and quantum gates is determined before circuit execution and everything is considered reliable with zero probability of failure. Many different schemes for achieving reliable fault-tolerant quantum computation exist, with different schemes suitable for different architectures. A number of large experimental groups are developing architectures well suited to being protected by surface quantum error correcting codes. Such circuits could include unreliable logical elements, such as state distillation, whose failure can be determined only after their actual execution. Therefore, practical logical circuits, as envisaged by many groups, are likely to have a dynamic structure. This requires an online scheduling of their execution: one knows for sure what needs to be executed only after previous elements have finished executing. This work shows that scheduling shares similarities with place and route methods. The work also introduces the first online schedulers of quantum circuits protected by surface codes. The work also highlights scheduling efficiency by comparing the new methods with state of the art static scheduling of surface code protected fault-tolerant circuits.

Quaternionic quantum walks of Szegedy type and zeta functions of graphs (pp1349-1371)
          Norio Konno, Kaname Matsue, Hideo Mitsuhashi and Iwao Sato
We define a quaternionic extension of the Szegedy walk on a graph and study its right spectral properties. The condition for the transition matrix of the quaternionic Szegedy walk on a graph to be quaternionic unitary is given. In order to derive the spectral mapping theorem for the quaternionic Szegedy walk, we derive a quaternionic extension of the determinant expression of the second weighted zeta function of a graph. Our main results determine explicitly all the right eigenvalues of the quaternionic Szegedy walk by using complex right eigenvalues of the corresponding doubly weighted matrix. We also show the way to obtain eigenvectors corresponding to right eigenvalues derived from those of doubly weighted matrix.

Noise in one-dimensional measurement-based quantum computing (pp1372-1397)
          Nairi Usher and Dan E. Browne
Measurement-Based Quantum Computing (MBQC) is an alternative to the quantum circuit model, whereby the computation proceeds via measurements on an entangled resource state. Noise processes are a major experimental challenge to the construction of a quantum computer. Here, we investigate how noise processes affecting physical states affect the performed computation by considering MBQC on a one-dimensional cluster state. This allows us to break down the computation in a sequence of building blocks and map physical errors to logical errors. Next, we extend the Matrix Product State construction to mixed states (which is known as Matrix Product Operators) and once again map the effect of physical noise to logical noise acting within the correlation space.  This approach allows us to  consider more general errors than the conventional Pauli errors, and could be used in order to simulate noisy quantum computation.

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