QIC Abstracts

 Vol.16 No.7&8, May 1, 2016

Research Articles:

Quantum deep learning (pp0541-0587)
          
Nathan Wiebe, Ashish Kapoor and Krysta M. Svore
In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on conventional, classical computers. We show that quantum computing not only reduces the time required to train a deep restricted Boltzmann machine, but also provides a richer and more comprehensive framework for deep learning than classical computing and leads to significant improvements in the optimization of the underlying objective function. Our quantum methods also permit efficient training of multiā€“layer and fully connected models.

Quantum advice enhances social optimality in three-party conflicting interest games (pp0588-0596)
          
Haozhen Situ, Cai Zhang, and Fang Yu
Quantum pseudo-telepathy games are good examples of explaining the strangeness of quantum mechanics and demonstrating the advantage of quantum resources over classical resources. Most of the quantum pseudo-telepathy games are common interest games, nevertheless conflicting interest games are more widely used to model real world situations. Recently Pappa \emph{et al.} (Phys. Rev. Lett. 114, 020401, 2015) proposed the first two-party conflicting interest game where quantum advice enhances social optimality. In the present paper we give two new three-party conflicting interest games and show that quantum advice can enhance social optimality in a three-party setting. The first game we propose is based on the famous GHZ game which is a common interest game. The second game we propose is related to the Svetlichny inequality which demonstrates quantum mechanics cannot be explained by the local hidden variable model in a three-party setting.

Quantum feedback control for qubit-qutrit entanglement (pp0597-0614)
          
Tiantian Ma, Jun Jing, Yi Guo, and Ting Yu
We study a hybrid quantum open system consisting of two interacting subsystems formed by one two-level atom (qubit) and one three-level atom (qutrit). The quantum open system is coupled to an external environment (cavity) via the qubit-cavity interaction. It is found that the feedback control on different parts of the system (qubit or qutrit) gives dramatically different asymptotical behaviors of the open system dynamics. We show that the local feedback control mechanism acting on the qutrit subsystem is superior than that on the qubit in the sense of improving the entanglement. Particularly, the qutrit-control scheme may result in an entangled steady state, depending on the initial state.

The learnability of unknown quantum measurements (pp0615-0656)
          
Hao-Chung Cheng, Min-Hsiu Hsieh, and Ping-Cheng Yeh
In this work, we provide an elegant framework to analyze learning matrices in the Schatten class by taking advantage of a recently developed methodology---matrix concentration inequalities. We establish the fat-shattering dimension, Rademacher/Gaussian complexity, and entropy number of learning bounded operators and trace class operators. By characterizing the tasks of learning quantum states and two-outcome quantum measurements into learning matrices in the Schatten-$1$ and $\infty$ classes, our proposed approach directly solves the sample complexity problems of learning quantum states and quantum measurements. Our main result in the paper is that, for learning an unknown quantum measurement, the upper bound, given by the fat-shattering dimension, is linearly proportional to the dimension of the underlying Hilbert space. Learning an unknown quantum state becomes a dual problem to ours, and as a byproduct, we can recover Aaronson's famous result solely using a classical machine learning technique. In addition, other famous complexity measures like covering numbers and Rademacher/Gaussian complexities are derived explicitly under the same framework. We are able to connect measures of sample complexity with various areas in quantum information science, e.g. quantum state/measurement tomography, quantum state discrimination and quantum random access codes, which may be of independent interest. Lastly, with the assistance of general Bloch-sphere representation, we show that learning quantum measurements/states can be mathematically formulated as a neural network. Consequently, classical ML algorithms can be applied to efficiently accomplish the two quantum learning tasks.

General fixed points of quasi-local frustration-free quantum semigroups: from invariance to stabilization (pp0657-0699)
          
Peter D. Johnson, Francesco Ticozzi, and Lorenza Viola
We investigate under which conditions a mixed state on a finite-dimensional multipartite quantum system may be the unique, globally stable fixed point of frustration-free semigroup dynamics subject to specified quasi-locality constraints. Our central result is a linear-algebraic necessary and sufficient condition for a generic (full-rank) target state to be frustration-free quasi-locally stabilizable, along with an explicit procedure for constructing Markovian dynamics that achieve stabilization. If the target state is not full-rank, we establish sufficiency under an additional condition, which is naturally motivated by consistency with pure-state stabilization results yet provably not necessary in general.  Several applications are discussed, of relevance to both dissipative quantum engineering and information processing, and non-equilibrium quantum statistical mechanics. In particular, we show that a large class of graph product states (including arbitrary thermal graph states) as well as Gibbs states of commuting Hamiltonians are frustration-free stabilizable relative to natural quasi-locality constraints. Likewise, we provide explicit examples of non-commuting Gibbs states and non-trivially entangled mixed states that are stabilizable despite the lack of an underlying commuting structure, albeit scalability to arbitrary system size remains in this case an open question.

An n-bit general implementation of Shor's quantum period-finding algorithm for quantum information and computation (pp0700-0718)
          
J.T. Davies, Christopher J. Rickerd, Mike A. Grimes, and Durduo Guney
The goal of this paper is to outline a general-purpose scalable implementation of Shor's period-finding algorithm using fundamental quantum gates, and to act as a blueprint for linear optical implementations of Shor's algorithm for both general and specific values of $N$. This offers a broader view of a problem often overlooked in favour of compiled versions of the algorithm.

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