Unified approach for exactly solvable potentials in quantum mechanics using shift operators
We present a unified approach for solving and classifying exactly solvable potentials. Our unified approach encompasses many well-known exactly solvable potentials. Moreover, the new approach can be used to search systematically for a new class of solvable potentials.
Repeat-until-success quantum computing using stationary and flying qubits
We introduce an architecture for robust and scalable quantum computation using both stationary qubits (e.g., single photon sources made out of trapped atoms, molecules, ions, quantum dots, or defect centers in solids) and flying qubits (e.g., photons). Our scheme solves some of the most pressing problems in existing nonhybrid proposals, which include the difficulty of scaling conventional stationary qubit approaches, and the lack of practical means for storing single photons in linear optics setups. We combine elements of two previous proposals for distributed quantum computing, namely the efficient photon-loss tolerant build up of cluster states by Barrett and Kok [Phys. Rev. A 71, 060310(R) (2005)] with the idea of repeat-until-success (RUS) quantum computing by Lim et al. [Phys. Rev. Lett. 95, 030505 (2005)]. This idea can be used to perform eventually deterministic two qubit logic gates on spatially separated stationary qubits via photon pair measurements. Under nonideal conditions, where photon loss is a possibility, the resulting gates can still be used to build graph states for one-way quantum computing. In this paper, we describe the RUS method, present possible experimental realizations, and analyze the generation of graph states.
Statistical reconstruction of qutrits
We discuss a procedure of measurement followed by the reproduction of the quantum state of a three-level optical system—a frequency—and spatially degenerate two-photon field. The method of statistical estimation of the quantum state based on solving the likelihood equation and analyzing the statistical properties of the obtained estimates is developed. Using the root approach of estimating quantum states, the initial two-photon state vector is reproduced from the measured fourth moments in the field. The developed approach applied to quantum-state reconstruction is based on the amplitudes of mutually complementary processes. The classical algorithm of statistical estimation based on the Fisher information matrix is generalized to the case of quantum systems obeying Bohr’s complementarity principle. It has been experimentally proved that biphoton-qutrit states can be reconstructed with the fidelity of 0.995–0.999 and higher.
Continuous multipartite entangled state in Wigner representation and violation of the Zukowski-Brukner inequality
We construct an explicit Wigner function for the N-mode squeezed state. Based on a previous observation that the Wigner function describes correlations in the joint measurement of the phase-space displaced parity operator, we investigate the nonlocality of the multipartite entangled state by the violation of the Żukowski-Brukner N-qubit Bell inequality. We find that quantum predictions for such a squeezed state violate these inequalities by an amount that grows with the number N.
Electronic entanglement purification scheme enhanced by charge detections
We present an entanglement purification scheme for the mixed entangled states of electrons with the aid of charge detections. Our scheme adopts the electronic polarizing beam splitters rather than the controlled-NOT (CNOT) operations, but the total successful probability of our scheme can reach the quantity as large as that of the CNOT-operation-based protocol and twice as large as that of linear-optics-based protocol for the purification of photonic entangled states. Thus our scheme can achieve a high successful prabability without the usage of CNOT operations.
Entanglement and discord in spin glass
We study the entanglement and discord in spin glass. By using the Edwards-Anderson XX model, we consider the Hamiltonian for 3 and 4 particles for nearest neighbor and next nearest neighbor interactions and to solve for the entanglement through concurrence. With a fixed mean and changing variances for the coupling J, the concurrence and discord are numerically plotted against the temperature. For J = 1, the critical temperature is found to be 2.106. The entanglement was found to increase beyond the critical temperature as the variance increases. The spin-spin correlation for 3 particles is plotted as a function of temperature T.
Quantum cryptography: Security criteria reexamined
We find that the generally accepted security criteria are flawed for a whole class of protocols for quantum cryptography. This is so because a standard assumption of the security analysis, namely that the so-called square-root measurement is optimal for eavesdropping purposes, is not true in general. There are rather large parameter regimes in which the optimal measurement extracts substantially more information than the square-root measurement.
Geometric and holonomic quantum computation
Geometric and holonomic quantum computation utilizes intrinsic geometric properties of quantum-mechanical state spaces to realize quantum logic gates. Since both geometric phases and quantum holonomies are global quantities depending only on the evolution paths of quantum systems, quantum gates based on them possess built-in resilience to certain kinds of errors. This review provides an introduction to the topic as well as gives an overview of the theoretical and experimental progress for constructing geometric and holonomic quantum gates and how to combine them with other error-resistant techniques.
Synchronization of a self-sustained cold atom oscillator
Nonlinear oscillations and synchronisation phenomena are ubiquitous in nature. We study the synchronization of self oscillating magneto-optically trapped cold atoms to a weak external driving. The oscillations arise from a dynamical instability due the competition between the screened magneto-optical trapping force and the inter-atomic repulsion due to multiple scattering of light. A weak modulation of the trapping force allows the oscillations of the cloud to synchronize to the driving. The synchronization frequency range increases with the forcing amplitude. The corresponding Arnold tongue is experimentally measured and compared to theoretical predictions. Phase-locking between the oscillator and drive is also observed.
Efficient on-chip training of optical neural networks using genetic algorithm
Recent advances in silicon photonic chips have made huge progress in optical computing owing to their flexibility in the reconfiguration of various tasks. Its deployment of neural networks serves as an alternative for mitigating the rapidly increased demand for computing resources in electronic platforms. However, it remains a formidable challenge to train the online programmable optical neural networks efficiently, being restricted by the difficulty in obtaining gradient information on a physical device when executing a gradient descent algorithm. Here, we experimentally demonstrate an efficient, physics-agnostic, and closed-loop protocol for training optical neural networks on chip. A gradient-free algorithm, that is, the genetic algorithm, is adopted. The protocol is on-chip implementable, physical agnostic (no need to rely on characterization and offline modeling), and gradient-free. The protocol works for various types of chip structures and is especially helpful to those that cannot be analytically decomposed and characterized. We confirm its viability using several practical tasks, including the crossbar switch and the Iris classification. Finally, by comparing our physics-agonistic and gradient-free method to the off-chip and gradient-based training methods, we demonstrate the robustness of our system to perturbations such as imperfect phase implementation and photodetection noise. Optical processors with gradient-free genetic algorithms have broad application potentials in pattern recognition, reinforcement learning, quantum computing, and realistic applications (such as facial recognition, natural language processing, and autonomous vehicles).