Set Of Input States Research Articles

Generative and discriminative training of Boltzmann machine through quantum annealing

A hybrid quantum-classical method for learning Boltzmann machines (BM) for a generative and discriminative task is presented. BM are undirected graphs with a network of visible and hidden nodes where the former is used as the reading site. In contrast, the latter is used to manipulate visible states’ probability. In Generative BM, the samples of visible data imitate the probability distribution of a given data set. In contrast, the visible sites of discriminative BM are treated as Input/Output (I/O) reading sites where the conditional probability of output state is optimized for a given set of input states. The cost function for learning BM is defined as a weighted sum of Kullback-Leibler (KL) divergence and Negative conditional Log-likelihood (NCLL), adjusted using a hyper-parameter. Here, the KL Divergence is the cost for generative learning, and NCLL is the cost for discriminative learning. A Stochastic Newton-Raphson optimization scheme is presented. The gradients and the Hessians are approximated using direct samples of BM obtained through quantum annealing. Quantum annealers are hardware representing the physics of the Ising model that operates on low but finite temperatures. This temperature affects the probability distribution of the BM; however, its value is unknown. Previous efforts have focused on estimating this unknown temperature through regression of theoretical Boltzmann energies of sampled states with the probability of states sampled by the actual hardware. These approaches assume that the control parameter change does not affect the system temperature; however, this is usually untrue. Instead of using energies, the probability distribution of samples is employed to estimate the optimal parameter set, ensuring that the optimal set can be obtained from a single set of samples. The KL divergence and NCLL are optimized for the system temperature, and the result is used to rescale the control parameter set. The performance of this approach, as tested against the theoretically expected distributions, shows promising results for Boltzmann training on quantum annealers.

Implementing efficient selective quantum process tomography of superconducting quantum gates on IBM quantum experience

The experimental implementation of selective quantum process tomography (SQPT) involves computing individual elements of the process matrix with the help of a special set of states called quantum 2-design states. However, the number of experimental settings required to prepare input states from quantum 2-design states to selectively and precisely compute a desired element of the process matrix is still high, and hence constructing the corresponding unitary operations in the lab is a daunting task. In order to reduce the experimental complexity, we mathematically reformulated the standard SQPT problem, which we term the modified SQPT (MSQPT) method. We designed the generalized quantum circuit to prepare the required set of input states and formulated an efficient measurement strategy aimed at minimizing the experimental cost of SQPT. We experimentally demonstrated the MSQPT protocol on the IBM QX2 cloud quantum processor and selectively characterized various two- and three-qubit quantum gates.

Optimal quantum channels

A method to optimize the cost of a quantum channel is developed. The goal is to determine the cheapest channel that produces prescribed output states for a given set of input states. This is essentially a quantum version of optimal transport. To attach a clear conceptual meaning to the cost, channels are viewed in terms of what we call elementary transitions, which are analogous to point-to-point transitions between classical systems. The role of entanglement in optimization of cost is emphasized. We also show how our approach can be applied to theoretically search for channels performing a prescribed set of tasks on the states of a system, while otherwise disturbing the state as little as possible.

Quantum Process Fidelity Bounds from Sets of Input States.

We investigate the problem of bounding the quantum process fidelity given bounds on the fidelities between target states and the action of a process on a set of pure input states. We formulate the problem as a semidefinite program and prove convexity of the minimum process fidelity as a function of the errors on the output states. We characterize the conditions required to uniquely determine a process in the case of no errors, and derive a lower bound on its fidelity in the limit of small errors for any set of input states satisfying these conditions. We then consider sets of input states whose one-dimensional projectors form a symmetric positive operator-valued measure (POVM). We prove that for such sets the minimum fidelity is bounded by a linear function of the average output state error. A symmetric POVM with minimal number of elements contains d + 1 states, where d is the Hilbert space dimension. Our bounds applied to such states provide an efficient method for estimating the process fidelity without the use of full process tomography.

Quantum Communication Using Coherent Rejection Sampling.

Compression of a message up to the information it carries is key to many tasks involved in classical and quantum information theory. Schumacher [B. Schumacher, Phys. Rev. A 51, 2738 (1995)PLRAAN1050-294710.1103/PhysRevA.51.2738] provided one of the first quantum compression schemes and several more general schemes have been developed ever since [M. Horodecki, J. Oppenheim, and A. Winter, Commun. Math. Phys. 269, 107 (2007); CMPHAY0010-361610.1007/s00220-006-0118-xI. Devetak and J.Yard, Phys. Rev. Lett. 100, 230501 (2008); PRLTAO0031-900710.1103/PhysRevLett.100.230501A. Abeyesinghe, I. Devetak, P. Hayden, and A. Winter, Proc.R. Soc. A 465, 2537 (2009)PRLAAZ1364-502110.1098/rspa.2009.0202]. However, the one-shot characterization of these quantum tasks is still under development, and often lacks a direct connection with analogous classical tasks. Here we show a new technique for the compression of quantum messages with the aid of entanglement. We devise a new tool that we call the convex split lemma, which is a coherent quantum analogue of the widely used rejection sampling procedure in classical communication protocols. As a consequence, we exhibit new explicit protocols with tight communication cost for quantum state merging, quantum state splitting, and quantum state redistribution (up to a certain optimization in the latter case). We also present a port-based teleportation scheme which uses a fewer number of ports in the presence of information about input.

Amplification uncertainty relation for probabilistic amplifiers

Traditionally, quantum amplification limit refers to the property of inevitable noise addition on canonical variables when the field amplitude of an unknown state is linearly transformed through a quantum channel. Recent theoretical studies have determined amplification limits for cases of probabilistic quantum channels or general quantum operations by specifying a set of input states or a state ensemble. However, it remains open how much excess noise on canonical variables is unavoidable and whether there exists a fundamental trade-off relation between the canonical pair in a general amplification process. In this paper we present an uncertainty-product form of amplification limits for general quantum operations by assuming an input ensemble of Gaussian distributed coherent states. It can be derived as a straightforward consequence of canonical uncertainty relations and retrieves basic properties of the traditional amplification limit. In addition, our amplification limit turns out to give a physical limitation on probabilistic reduction of an Einstein-Podolsky-Rosen uncertainty. In this regard, we find a condition that probabilistic amplifiers can be regarded as local filtering operations to distill entanglement. This condition establishes a clear benchmark to verify an advantage of non-Gaussian operations beyond Gaussian operations with a feasible input set of coherent states and standard homodyne measurements.

Subspace quantum process tomography via nuclear magnetic resonance

Experimental investigation of subspace quantum process tomography in three-spin system was implemented via nuclear magnetic resonance. A quantum process was characterized by measuring a complete set of input states and corresponding outputs. The method using ancillary qubit remarkably reduces the number of the initial input states. And the pulse sequences used in this paper have fewer J-coupling evolutions. The experiment time was shortened and quantum decoherence of the system was weakened efficiently.

Toward Autonomic Computing

Cognitive approach through the neural network “NN” paradigm is a critical discipline that will help bring about autonomic computing “AC.” NN-related research, some involving new ways to apply control theory and control laws, can provide insight into how to run complex systems that optimize to their environments. NN is one kind of AC system that can embody human cog-nitive powers and that can adapt, learn, and take over certain functions previously performed by humans. In recent years, artificial neural networks have received a great deal of attention for their ability to perform nonlinear mappings. In trajectory control of robotic devices, neural networks provide a fast method of autonomously learning the relation between a set of output states and a set of input states. In this article, we apply the cognitive approach to solve position controller problems using an inverse geometrical model. In order to control a robot manipulator in the accomplishment of a task, trajectory planning is required in advance or in real time. The desired trajectory is usually described in Cartesian coordinates and needs to be converted to joint space for the purpose of analyzing and controlling the system behavior. In this article, we use a memory neural network (MNN) to solve the optimization problem concerning the inverse of the direct geometrical model of the redundant manipulator when subject to constraints. Our approach offers substantially better accuracy, avoids the computation of the inverse or pseudo-inverse Jacobian matrix, and does not produce problems such as singularity, redundancy, and considerably increased computational complexity.

Dividing a light beam into two beams of orthogonal polarizations by reflection and refraction at a dielectric surface

Reflection and refraction of monochromatic light by an air-dielectric interface at an incidence angle below the Brewster angle can generate split beams of equal power and orthogonal polarizations under certain achievable conditions. Generation of photon streams of orthogonal polarizations, previously thought to be possible mainly by double refraction in anisotropic crystals, is achieved for an infinite set of input states that leads to a correspondingly infinite set of pairs of orthogonal output states. A bare substrate of PbTe is particularly suitable for this beam splitting function in the IR. However, use of a high-refractive-index quarter-wave layer on a low-refractive-index substrate extends the operating range of this interesting device to a much wider spectral range including the visible.

Broadband teleportation

Quantum teleportation of an unknown broadband electromagnetic field is investigated. The continuous-variable teleportation protocol by Braunstein and Kimble [Phys. Rev. Lett. {\bf 80}, 869 (1998)] for teleporting the quantum state of a single mode of the electromagnetic field is generalized for the case of a multimode field with finite bandwith. We discuss criteria for continuous-variable teleportation with various sets of input states and apply them to the teleportation of broadband fields. We first consider as a set of input fields (from which an independent state preparer draws the inputs to be teleported) arbitrary pure Gaussian states with unknown coherent amplitude (squeezed or coherent states). This set of input states, further restricted to an alphabet of coherent states, was used in the experiment by Furusawa {\it et al.} [Science {\bf 282}, 706 (1998)]. It requires unit-gain teleportation for optimizing the teleportation fidelity. In our broadband scheme, the excess noise added through unit-gain teleportation due to the finite degree of the squeezed-state entanglement is just twice the (entanglement) source's squeezing spectrum for its ``quiet quadrature.'' The teleportation of one half of an entangled state (two-mode squeezed vacuum state), i.e., ``entanglement swapping,'' and its verification are optimized under a certain nonunit gain condition. We will also give a broadband description of this continuous-variable entanglement swapping based on the single-mode scheme by van Loock and Braunstein [Phys. Rev. A {\bf 61}, 10302 (2000)]

A fuzzy controller for construction activities

Abstract Construction activities are highly uncertain systems. They do not lend themselves to the application of traditional control theory because of their highly subjective nature. A fuzzy-based self-learning control strategy is utilized in this paper. The system comprises a rule-base, a self-learning unit and a conflict resolution unit. A new three dimensional implication function was developed and integrated in the system to model the individual rules. A condition assessment procedure is also integrated in the system in order to evaluate the output levels given a set of input states. The condition assessment procedure acts as a transfer function in traditional control theory.