Enhancing quantum annealing performance by a degenerate two-level system

Quantum annealing is an innovative idea and method for avoiding the increase of the calculation cost of the combinatorial optimization problem. Since the combinatorial optimization problems are ubiquitous, quantum annealing machine with high efficiency and scalability will give an immeasurable impact on many fields. However, the conventional quantum annealing machine may not have a high success probability for finding the solution because the energy gap closes exponentially as a function of the system size. To propose an idea for finding high success probability is one of the most important issues. Here we show that a degenerate two-level system provides the higher success probability than the conventional spin-1/2 model in a weak longitudinal magnetic field region. The physics behind this is that the quantum annealing in this model can be reduced into that in the spin-1/2 model, where the effective longitudinal magnetic field may open the energy gap, which suppresses the Landau–Zener tunneling providing leakage of the ground state. We also present the success probability of the Λ-type system, which may show the higher success probability than the conventional spin-1/2 model.

Multi-prover proof of retrievability

There has been considerable recent interest in “cloud storage” wherein a user asks a server to store a large file. One issue is whether the user can verify that the server is actually storing the file, and typically a challenge-response protocol is employed to convince the user that the file is indeed being stored correctly. The security of these schemes is phrased in terms of an extractor which will recover the file given any “proving algorithm” that has a sufficiently high success probability. This forms the basis of proof-of-retrievability (PoR) systems. In this paper, we study multiple server PoR systems. We formalize security definitions for two possible scenarios: (i) A threshold of servers succeeds with high enough probability (worst case), and (ii) the average of the success probability of all the servers is above a threshold (average case). We also motivate the study of confidentiality of the outsourced message. We give MPoR schemes which are secure under both these security definitions and provide reasonable confidentiality guarantees even when there is no restriction on the computational power of the servers. We also show how classical statistical techniques previously used by us can be extended to evaluate whether the responses of the provers are accurate enough to permit successful extraction. We also look at one specific instantiation of our construction when instantiated with the unconditionally secure version of the Shacham–Waters scheme. This scheme gives reasonable security and privacy guarantee. We show that, in the multi-server setting with computationally unbounded provers, one can overcome the limitation that the verifier needs to store as much secret information as the provers.

A quantum algorithm to approximate the linear structures of Boolean functions

A quantum algorithm to determine approximations of linear structures of Boolean functions is presented and analysed. Similar results have already been published (see Simon's algorithm) but only for some promise versions of the problem, and it has been shown that no exponential quantum speedup can be obtained for the general (no promise) version of the problem. In this paper, no additional promise assumptions are made. The approach presented is based on the method used in the Bernstein–Vazirani algorithm to identify linear Boolean functions and on ideas from Simon's period finding algorithm. A proper combination of these two approaches results here to a polynomial-time approximation to the linear structures set. Specifically, we show how the accuracy of the approximation with high probability changes according to the running time of the algorithm. Moreover, we show that the time required for the linear structure determine problem with high success probability is related to so called relative differential uniformity δf of a Boolean function f. Smaller differential uniformity is, shorter time is needed.

Financing successful small business projects

Purpose – The current credit rationing strongly influences the viability of SMEs innovation projects. In this context, the practice of screening borrowers by project success probability has become a paramount consideration for both lenders and firms. The aim of this paper is to test the screening role of loan contracts that consider collateral-interest margins simultaneously. Design/methodology/approach – This paper presents an empirical analysis that uses a unique data set composed of 323 bank loans granted by 28 banks to SMEs backed by a Spanish Mutual Guarantee Institution. Findings – The results show that appropriate combinations of collateral and interest rates can distinguish between borrowers with different project success probability: low success probability borrowers finance its projects without collateral and with high interest rates, whereas high success probability borrowers accept loans with real estate collateral and low interest rates. Practical implications – This screening mechanism reduces credit rationing, thus increasing good projects' access to credit. Originality/value – This study provides the first empirical evidence on the effectiveness of collateral-interest pairs as a self-selection mechanism.

PROBABILISTIC MULTIPARTY-CONTROLLED REMOTE PREPARATION OF AN ARBITRARY m-QUDIT STATE VIA POSITIVE OPERATOR-VALUED MEASUREMENT

We present a scheme for multiparty-controlled remote preparation of an arbitrary m-qudit (d-dimensional quantum system) state via positive operator-valued measurement (POVM) by using nonmaximally entangled states as the quantum channel, not resorting to auxiliary qubits. The sender performs an optimal POVM measurement on her m particles with measurement operators that depend on the original state, the controllers perform generalized X-basis measurement X d and the receiver can prepare the original state if he cooperates with all the controllers and the sender. The scheme has the advantage of having high success probability for remote preparing an arbitrary m-qudit state and more convenient than others in a practical application. Moreover, it discusses the relationship between the probability that the receiver obtains the originally state and the coefficients of the entangled states.

Deciding unitary equivalence between matrix polynomials and sets of bipartite quantum states

In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree $m$ matrix polynomials are unitarily equivalent; i.e. $UA_iV^\dagger=B_i$ for $0\leq i\leq m$ where $U$ and $V$ are unitary and $(A_i, B_i)$ are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices $U$ and $V$.

EFFICIENT SCHEME FOR PREPARING POLARIZATION-ENTANGLED PHOTONIC CLUSTER STATES BASED ON CROSS-KERR NONLINEARITY

A scheme is proposed for generating a polarization four-photon cluster, which is believed to be suitable to achieve the one-way quantum computing via single-qubit projective measurements, with the help of only cross-Kerr nonlinearity and current linear optical systems. Compared with the existing schemes, the distinct advantage of the present scheme is that cluster states can be achieved with high success probability close to unity. Our scheme is experimentally demanding but efficient. Based on the present scheme, the cluster state of 3N + 1 photons can be obtained with the help of linear optical elements.

A NEW FAULT-TOLERANT BROADCAST ROUTING ALGORITHM ON MESH NETWORKS

Mesh networks are a kind of very important network topologies in massively multicomputer parallel systems. One-to-all or broadcast communication is one of the most important routing patterns and can be applied in many important applications. With the continuous increment in network size, routing in large size mesh networks with faults is unavoidable. In this paper, we propose a new fault-tolerant, local-information-based, and distributed broadcast routing algorithm based on the concept of k-submesh in all-port mesh networks. We suppose that each node has independent failure probability, under the assumption, we analyze the fault tolerance of our algorithm. We show that our routing algorithm is highly fault tolerant and has a high success probability to broadcast messages. For example, we formally prove that if the node failure probability is bounded by 0.12%, our broadcast routing algorithm works successfully with probability at least 99%. Simulation results show that our algorithm is efficient and effective in practice and theory, and the time steps of our algorithm is very close to the optimum.