Experimental realization of a highly structured search algorithm

The highly structured search algorithm proposed by Hogg[Phys.Rev.Lett. 80,2473(1998)] is implemented experimentally for the 1-SAT problem in a single search step by using nuclear magnetic resonance technique with two-qubit sample. It is the first demonstration of the Hogg's algorithm, and can be readily extended to solving 1-SAT problem for more qubits in one step if the appropriate samples possessing more qubits are experimentally feasible.Comment: RevTex, 11 pages + 3 pages of figure

Solving payoff sets of perfect public equilibria: an example

We study an example of infinitely repeated games in which symmetric duopolistic firms produce experience goods. After consuming the products, short-run consumers only observe imperfect public information about product quality. We characterize perfect public equilibrium payoff set E(δ) of firms for each fixed discount factor δ∈[0,1) when each firm has two action choices, signals follow binomial distributions and the game has a product structure. The set E(δ) turns out a single point or symmetric pentagon for fixed δ. And δ∈[0, 1) can be divided into countable infinite subintervals in which E(δ) remains constant. The strategies to implement payoffs in boundaries of E(δ) are constructed in a recursive way, in which infinite repetition of Nash Equilibrium of stage game could be viewed as an absorbing state in a Markov Process where state transitions are controlled through public signals and optimal punishments in each period

Solving payoff sets of perfect public equilibria: an example

We study an example of infinitely repeated games in which symmetric duopolistic firms produce experience goods. After consuming the products, short-run consumers only observe imperfect public information about product quality. We characterize perfect public equilibrium payoff set E(δ) of firms for each fixed discount factor δ∈[0,1) when each firm has two action choices, signals follow binomial distributions and the game has a product structure. The set E(δ) turns out a single point or symmetric pentagon for fixed δ. And δ∈[0, 1) can be divided into countable infinite subintervals in which E(δ) remains constant. The strategies to implement payoffs in boundaries of E(δ) are constructed in a recursive way, in which infinite repetition of Nash Equilibrium of stage game could be viewed as an absorbing state in a Markov Process where state transitions are controlled through public signals and optimal punishments in each period

Use of non-adiabatic geometric phase for quantum computing by nuclear magnetic resonance

Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled logic gates by controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of errors. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1>, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using these geometric phase gates we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system

Method based on fast fourier transform for calculating conical refraction of beams with noncircular symmetry

Conical refraction of optical beams with circular symmetry is often analyzed using Belsky-Khapalyuk-Berry (BKB) theory; however, for beams with noncircular symmetry, it is difficult to obtain analytical expressions for far-field diffraction patterns. We propose a method, based on fast Fourier transform (FFT), for calculating conical refraction of beams with noncircular symmetry and verify it experimentally using a quasi-plane wave passing through a square aperture and focusing lens. Excellent agreement between theoretical and experimental results has been achieved

Transition-based directed graph construction for emotion-cause pair extraction

Emotion-cause pair extraction aims to extract all potential pairs of emotions and corresponding causes from unannotated emotion text. Most existing methods are pipelined framework, which identifies emotions and extracts causes separately, leading to a drawback of error propagation. Towards this issue, we propose a transition-based model to transform the task into a procedure of parsing-like directed graph construction. The proposed model incrementally generates the directed graph with labeled edges based on a sequence of actions, from which we can recognize emotions with the corresponding causes simultaneously, thereby optimizing separate subtasks jointly and maximizing mutual benefits of tasks interdependently. Experimental results show that our approach achieves the best performance, outperforming the state-of-the-art methods by 6.71% (p<0.01) in F1 measure

Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor

Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. In some cases, such as the adiabatic versions of Grover's search algorithm and Deutsch-Jozsa algorithm, applying the global adiabatic evolution yields a complexity similar to their classical algorithms. However, using the local adiabatic evolution, the algorithms given by J. Roland and N. J. Cerf for Grover's search [ Phys. Rev. A. {\bf 65} 042308(2002)] and by Saurya Das, Randy Kobes and Gabor Kunstatter for the Deutsch-Jozsa algorithm [Phys. Rev. A. {\bf 65}, 062301 (2002)], yield a complexity of order $\sqrt{N}$ (where N=2$^{\rm n}$ and n is the number of qubits). In this paper we report the experimental implementation of these local adiabatic evolution algorithms on a two qubit quantum information processor, by Nuclear Magnetic Resonance.Comment: Title changed, Adiabatic Grover's search algorithm added, error analysis modifie

DISPEL: Domain Generalization via Domain-Specific Liberating

Domain generalization aims to learn a generalization model that can perform well on unseen test domains by only training on limited source domains. However, existing domain generalization approaches often bring in prediction-irrelevant noise or require the collection of domain labels. To address these challenges, we consider the domain generalization problem from a different perspective by categorizing underlying feature groups into domain-shared and domain-specific features. Nevertheless, the domain-specific features are difficult to be identified and distinguished from the input data. In this work, we propose DomaIn-SPEcific Liberating (DISPEL), a post-processing fine-grained masking approach that can filter out undefined and indistinguishable domain-specific features in the embedding space. Specifically, DISPEL utilizes a mask generator that produces a unique mask for each input data to filter domain-specific features. The DISPEL framework is highly flexible to be applied to any fine-tuned models. We derive a generalization error bound to guarantee the generalization performance by optimizing a designed objective loss. The experimental results on five benchmarks demonstrate DISPEL outperforms existing methods and can further generalize various algorithms

Implementing universal multi-qubit quantum logic gates in three and four-spin systems at room temperature

In this paper, we present the experimental realization of multi-qubit gates $$ in macroscopic ensemble of three-qubit and four-qubit molecules. Instead of depending heavily on the two-bit universal gate, which served as the basic quantum operation in quantum computing, we use pulses of well-defined frequency and length that simultaneously apply to all qubits in a quantum register. It appears that this method is experimentally convenient when this procedure is extended to more qubits on some quantum computation, and it can also be used in other physical systems.Comment: 5 Pages, 2 Figure

Minimum average-case queries of q + 1 -ary search game with small sets

Given a search space S={1,2,...,n}, an unknown element x*∈S and fixed integers ℓ≥1 and q≥1, a q+1-ary ℓ-restricted query is of the following form: which one of the set {A 0,A 1,...,A q} is the x* in?, where (A 0,A 1,...,A q) is a partition of S and | Ai|≤ℓ for i=1,2,...,q. The problem of finding x* from S with q+1-ary size-restricted queries is called as a q+1-ary search game with small sets. In this paper, we consider sequential algorithms for the above problem, and establish the minimum number of average-case sequential queries when x* satisfies the uniform distribution on S. © 2011 Elsevier B.V. All rights reserved