Realizing time crystals in discrete quantum few-body systems

The exotic phenomenon of time translation symmetry breaking under periodic driving - the time crystal - has been shown to occur in many-body systems even in clean setups where disorder is absent. In this work, we propose the realization of time-crystals in few-body systems, both in the context of trapped cold atoms with strong interactions and of a circuit of superconducting qubits. We show how these two models can be treated in a fairly similar way by adopting an effective spin chain description, to which we apply a simple driving protocol. We focus on the response of the magnetization in the presence of imperfect pulses and interactions, and show how the results can be interpreted, in the cold atomic case, in the context of experiments with trapped bosons and fermions. Furthermore, we provide a set of realistic parameters for the implementation of the superconducting circuit.Comment: 6 pages, 4 figure

Multiqubit State Learning with Entangling Quantum Generative Adversarial Networks

The increasing success of classical generative adversarial networks (GANs) has inspired several quantum versions of GANs. Fully quantum mechanical applications of such quantum GANs have been limited to one- and two-qubit systems. In this paper, we investigate the entangling quantum GAN (EQ-GAN) for multiqubit learning. We show that the EQ-GAN can learn a circuit more efficiently compared to a swap test. We also consider the EQ-GAN for learning VQE-approximated eigenstates, and find that it generates excellent overlap matrix elements when learning VQE states of small molecules. However, this does not directly translate to a good estimate of the energy due to a lack of phase estimation. Finally, we consider random state learning with the EQ-GAN for up to six qubits, using different two-qubit gates, and show that it is capable of learning completely random quantum states, something which could be useful in quantum state loading.Comment: 6 pages, 4 figures, 1 table + Supporting materia

Simple implementation of high fidelity controlled-iiSWAP gates and quantum circuit exponentiation of non-Hermitian gates

The $i$swap gate is an entangling swapping gate where the qubits obtain a phase of $i$ if the state of the qubits is swapped. Here we present a simple implementation of the controlled-$i$swap gate. The gate can be implemented with several controls and works by applying a single flux pulse. The gate time is independent of the number of controls, and we find high fidelities for any number of controls. We discuss an implementation of the gates using superconducting circuits and present a realistic implementation proposal, where we have taken decoherence noise and fabrication errors on the superconducting chip in to account, by Monte Carlo simulating possible errors. The general idea presented in this paper is, however, not limited to such implementations. An exponentiation of quantum gates is desired in some quantum information schemes and we therefore also present a quantum circuit for probabilistic exponentiating the $i$swap gate and other non-Hermitian gates.Comment: 16 Pages, 10 figures, 4 tables. Version accepted for publication in PR

Time-varying Learning and Content Analytics via Sparse Factor Analysis

We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) analyzes learner concept knowledge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc, or the forgetting effect), and (iii) estimates the content organization and intrinsic difficulty of the assessment questions. These quantities are estimated solely from binary-valued (correct/incorrect) graded learner response data and a summary of the specific actions each learner performs (e.g., answering a question or studying a learning resource) at each time instance. Experimental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner's concept knowledge evolution over time, as well as analyzing the quality and content organization of learning resources, the question-concept associations, and the question intrinsic difficulties. Moreover, we show that SPARFA-Trace achieves comparable or better performance in predicting unobserved learner responses than existing collaborative filtering and knowledge tracing approaches for personalized education

Statistical mechanics of a nonlinear discrete system

Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of $T=\infty$, we identify a phase transition, through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breather-like localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.Comment: 4 pages, 3 figure

High-pressure x-ray diffraction of icosahedral Zr-Al-Ni-Cu-Ag quasicrystals

The effect of pressure on the structural stability of icosahedral Zr-Al-Ni-Cu-Ag quasicrystals forming from a Zr65Al7.5Ni10Cu7.5Ag10 metallic glass with a supercooled liquid region of 44 K has been investigated by in situ high-pressure angle-dispersive x-ray powder diffraction at ambient temperature using synchrotron radiation. The icosahedral quasicrystal structure is retained up to the highest hydrostatic pressure used (approximately 28 GPa) and is reversible after decompression. The bulk modulus at zero pressure and its pressure derivative of the icosahedral Zr-Al-Ni-Cu-Ag quasicrystal are 99.10+/-1.26 GPa and 4.25+/-0.16, respectively. The compression behavior of different Bragg peaks is isotropic and the full width at half maximum of each peak remains almost unchanged during compression, indicating no anisotropic elasticity and no defects in the icosahedral Zr-Al-Ni-Cu-Ag quasicrystals induced by pressure