We propose a strategy for engineering multi-qubit quantum gates. As a first step, it employs an eigengate to map states in the computational basis to eigenstates of a suitable many-body Hamiltonian. The second step employs resonant driving to enforce a transition between a single pair of eigenstates, leaving all others unchanged. The procedure is completed by mapping back to the computational basis. We demonstrate the strategy for the case of a linear array with an even number N of qubits, with specific XX+YY couplings between nearest neighbors. For this so-called Krawtchouk chain, a 2-body driving term leads to the iSWAP$_N$ gate, which we numerically test for N = 4 and 6.

We present a symmetry-based approach for shape coexistence in nuclei, founded on the concept of partial dynamical symmetry (PDS). The latter corresponds to a situation when only selected states (or bands of states) of the coexisting configurations preserve the symmetry while other states are mixed. We construct explicitly critical-point Hamiltonians with two or three PDSs of the type U(5), SU(3), ${\overline{\rm SU(3)}}$ and SO(6), appropriate to double or triple coexistence of spherical, prolate, oblate and $\gamma$-soft deformed shapes, respectively. In each case, we analyze the topology of the energy surface with multiple minima and corresponding normal modes. Characteristic features and symmetry attributes of the quantum spectra and wave functions are discussed. Analytic expressions for quadrupole moments and $E2$ rates involving the remaining solvable states are derived and isomeric states are identified by means of selection rules.

A Lorentz invariant framework is developed to interpret exotic cross-correlations in the signals of two separate interferometers, associated with the emergence of space-time and inertial frames from a Planck scale quantum system. The framework extends our earlier models of exotic autospectra based on invariant causal structure. Space-time relationships between world lines are modeled as antisymmetric cross-correlations on past and future light cones between sequences in proper time with Planck bandwidth, arising from nonlocal entanglement information in geometrical states. These exotic correlations of a flat space-time are normalized to have the same holographic information content as black holes. Simple models of interferometer response are shown to produce a unique signature: a broad band imaginary cross spectrum, with a frequency structure determined by the layout of the apparatus. The framework will be useful for interpreting data in the bent reconfiguration of the Fermilab Holometer, and for conceptual design of future experiments.

Chakraborty and Leonardo have shown that a spatial search by quantum walk is optimal for almost all graphs. However, we observed that on some graphs, certain states cannot be searched optimally. We present a method for constructing an optimal graph that searches an arbitrary state and provides the optimal condition. We also analyze the monotonicity of the search performance and conclude that the search performance can be improved by adding edges.

Classical simulation of quantum computation has often been viewed as the method to determine where the horizon of quantum supremacy is located---that is, where quantum computation can no longer be simulated by classical methods. As of now, the 50 qubit threshold for quantum supremacy has been determined largely by the state vector simulation method's exponential space demands placing an upper bound on simulation memory capabilities. To investigate this claim, we present and test an implementation of a known path integral simulation algorithm running in linear space; the method is based on recursively traversing the underlying computation tree for quantum algorithms and summing over possible amplitudes. We find that the implementation is able to simulate the hidden subgroup method (HSP) standard method---a notable class of circuits including Shor's algorithm amongst others---in a reasonable amount of time using extremely low memory, as well as other circuits with similar parameters. The performance results of this algorithm suggest that it can serve as a feasible alternative to state vector simulation and that with respect to the HSP standard method, quantum supremacy may be more accurately measured using the recursive path-summing method on large numbers of qubits, compared to the state vector method.

Hong-Ou-Mandel (HOM) effect was long believed to be a two-photon interference phenomenon. It describes the fact that two indistinguishable photons mixed at a beam splitter will bunch together to one of the two output modes. Considering the two single-photon emitters such as trapped ions, we explore a hidden scenario of the HOM effect, where entanglement can be generated between the two ions when a single photon is detected by one of the detectors. A second photon emitted by the entangled photon sources will be subsequently detected by the same detector. However, we can also control the fate of the second photon by manipulating the entangled state. Instead of two-photon interference, phase of the entangled state is responsible for photon's path in our proposal. Toward a feasible experimental realization, we conduct a quantum jump simulation on the system to show its robustness against experimental errors.

In this paper, we utilize coupled mode theory (CMT) to model the coupling between surface plasmon-polaritons (SPPs) between multiple graphene sheets. By using the Stimulated Raman Adiabatic Passage (STIRAP) Quantum Control Technique, we propose a novel directional coupler based on SPPs evolution in three layers of graphene sheets in some curved configuration. Our calculated results show that the SPP can be transferred efficiently from the input graphene sheet to the output graphene sheet, and the coupling is also robust that it is not sensitive to the length of the device.

The efficient representation of quantum many-body states with classical resources is a key challenge in quantum many-body theory. In this work we analytically construct classical networks for the description of the quantum dynamics in transverse-field Ising models that can be solved efficiently using Monte Carlo techniques. Our perturbative construction encodes time-evolved quantum states of spin-1/2 systems in a network of classical spins with local couplings and can be directly generalized to other spin systems and higher spins. Using this construction we compute the transient dynamics in one, two, and three dimensions including local observables, entanglement production, and Loschmidt amplitudes using Monte Carlo algorithms and demonstrate the accuracy of this approach by comparisons to exact results. We include a mapping to equivalent artificial neural networks, which were recently introduced to provide a universal structure for classical network wave functions.

Author(s): Yannis Kominis, Vassilios Kovanis, and Tassos Bountis

The fundamental active photonic dimer consisting of two coupled quantum well lasers is investigated in the context of the rate-equation model. Spectral transition properties and exceptional points are shown to occur under general conditions, not restricted by parity-time symmetry as in coupled-mode ...

[Phys. Rev. A 96, 053837] Published Fri Nov 17, 2017

Author(s): David Ehrenstein

Experiments mimicking a common oil drilling technique, in which fluid is forced into an oil-filled, porous medium, have uncovered four different flow patterns.

[Physics 10, 125] Published Fri Nov 17, 2017

Categories: Physics

We investigate quantum backtracking algorithms of a type previously introduced by Montanaro (arXiv:1509.02374). These algorithms explore trees of unknown structure, and in certain cases exponentially outperform classical procedures (such as DPLL). Some of the previous work focused on obtaining a quantum advantage for trees in which a unique marked vertex is promised to exist. We remove this restriction and re-characterise the problem in terms of the effective resistance of the search space. To this end, we present a generalisation of one of Montanaro's algorithms to trees containing $k \geq 1$ marked vertices, where $k$ is not necessarily known \textit{a priori}.

Our approach involves using amplitude estimation to determine a near-optimal weighting of a diffusion operator, which can then be applied to prepare a superposition state that has support only on marked vertices and ancestors thereof. By repeatedly sampling this state and updating the input vertex, a marked vertex is reached in a logarithmic number of steps. The algorithm thereby achieves the conjectured bound of $\widetilde{\mathcal{O}}(\sqrt{TR_{\mathrm{max}}})$ for finding a single marked vertex and $\widetilde{\mathcal{O}}\left(k\sqrt{T R_{\mathrm{max}}}\right)$ for finding all $k$ marked vertices, where $T$ is an upper bound on the tree size and $R_{\mathrm{max}}$ is the maximum effective resistance encountered by the algorithm. This constitutes a speedup over Montanaro's original procedure in both the case of finding one and finding multiple marked vertices in an arbitrary tree. If there are no marked vertices, the effective resistance becomes infinite, and we recover the scaling of Montanaro's existence algorithm.

We present and demonstrate a general 3-step method for extracting the quantum efficiency of dispersive qubit readout in circuit QED. We use active depletion of post-measurement photons and optimal integration weight functions on two quadratures to maximize the signal-to-noise ratio of non-steady-state homodyne measurement. We derive analytically and demonstrate experimentally that the method robustly extracts the quantum efficiency for arbitrary readout conditions in the linear regime. We use the proven method to optimally bias a Josephon traveling-wave parametric amplifier and to quantify the different noise contributions in the readout amplification chain.

In this work, we establish an exact relation which connects the heat exchange between two systems initialized in their thermodynamic equilibrium states at different temperatures and the R\'{e}nyi divergences between the initial thermodynamic equilibrium state and the final non-equilibrium state of the total system. The relation tells us that the various moments of the heat statistics are determined by the Renyi divergences between the initial equilibrium state and the final non-equilibrium state of the global system. In particular the average heat exchange is quantified by the relative entropy between the initial equilibrium state and the final non-equilibrium state of the global system. The relation is applicable to both finite classical systems and finite quantum systems.

We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of discretized Laplacian operators to allow for improved scaling in truncation errors and improved scaling for state preparation relative to general purpose linear differential equation algorithms. We also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell's equations.

Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. Here, we discuss quantum simulation of strongly correlated fermionic systems. We focus specifically on 2D and linear geometry with nearest neighbor qubit-qubit couplings, typical for superconducting transmon qubit arrays. We improve an existing algorithm to prepare an arbitrary Slater determinant by exploiting a unitary symmetry. We also present a quantum algorithm to prepare an arbitrary fermionic Gaussian state with $O(N^2)$ gates and $O(N)$ circuit depth. Both algorithms are optimal in the sense that the numbers of parameters in the quantum circuits are equal to those to describe the quantum states. Furthermore, we propose an algorithm to implement the 2-dimensional (2D) fermionic Fourier transformation on a 2D qubit array with only $O(N^{1.5})$ gates and $O(\sqrt N)$ circuit depth, which is the minimum depth required for quantum information to travel across the qubit array. We also present methods to simulate each time step in the evolution of the 2D Fermi-Hubbard model---again on a 2D qubit array---with $O(N)$ gates and $O(\sqrt N)$ circuit depth. Finally, we discuss how these algorithms can be used to determine the ground state properties and phase diagrams of strongly correlated quantum systems using the Hubbard model as an example.

We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their $\mathcal{P}$-, $\mathcal{T}$-, and $\mathcal{P}\mathcal{T}$-symmetries. In particular, we review various relevant concepts such as Jost solutions, transfer and scattering matrices, reciprocity principle, unidirectional reflection and invisibility, and spectral singularities. We discuss in some detail the mathematical conditions that imply or forbid reciprocal transmission, reciprocal reflection, and the presence of spectral singularities and their time-reversal. We also derive generalized unitarity relations for time-reversal-invariant and $\mathcal{P}\mathcal{T}$-symmetric scattering systems, and explore the consequences of breaking them. The results reported here apply to the scattering systems defined by a real or complex local potential as well as those determined by energy-dependent potentials, nonlocal potentials, and general point interactions.

Investigating a particle, a charged particle in an electromagnetic field and a particle with spin-orbit interaction confined to a space curve in square and circular cases, respectively, we first find that their effective Hamiltonian can be defined in terms of the ground states of their confined dimensions. And we obtain interesting results: the torsion-induced geometric potential appears in the square case, while in the circular case it vanishes; the geometrically induced gauge potential and Zeeman coupling appear in the circular case; and the geometric gauge potential, curvature and torsion simultaneously emerge in the spin-orbit interaction in the circular case. In the example, a helix nanowire, the previous results are all demonstrated. These results provide a way to generate an artificial gauge field and to manipulate spin transport by designing the geometry of curved nanodevice.

Photon detectors are an elementary tool to measure electromagnetic waves at the quantum limit and are heavily demanded in the emerging quantum technologies such as communication, sensing, and computing. Of particular interest is a quantum non-demolition (QND) type detector, which projects the quantum state of a photonic mode onto the photon-number basis without affecting the temporal or spatial properties. This is in stark contrast to conventional photon detectors which absorb a photon to trigger a `click' and thus inevitably destroy the photon. The long-sought QND detection of a flying photon was recently demonstrated in the optical domain using a single atom in a cavity. However, the counterpart for microwaves has been elusive despite the recent progress in microwave quantum optics using superconducting circuits. Here, we implement a deterministic entangling gate between a superconducting qubit and a propagating microwave pulse mode reflected by a cavity containing the qubit. Using the entanglement and the high-fidelity qubit readout, we demonstrate a QND detection of a single photon with the quantum efficiency of 0.84, the photon survival probability of 0.87, and the dark-count probability of 0.0147. Our scheme can be a building block for quantum networks connecting distant qubit modules as well as a microwave photon counting device for multiple-photon signals.

Employing counterdiabatic shortcut to adiabaticity (STA), we design shorter and robust achromatic two- and three- waveguide couplers. We assume that the phase mismatch between the waveguides has a sign flip at maximum coupling, while the coupling between the waveguides has a smooth spatial shape. We show that the presented coupler operates as a complete achromatic optical switch for two coupled waveguides and as an equal superposition beam splitter for three coupled waveguides. An important feature of our devices is that they do not require larger coupling strength as compared to previous designs, which make them easier to realize in an experimental setting. Additionally, we show that the presented waveguide couplers operate at a shorter device length and are robust against variations in the coupling strength and the phase mismatch.

We consider a very general class of theories, process theories, which capture the underlying structure common to most theories of physics as we understand them today (be they established, toy or speculative theories). Amongst these theories, we will be focusing on those which are `causal', in the sense that they are intrinsically compatible with the causal structure of space-time -- as required by relativity. We demonstrate that there is a sharp contrast between these theories and the corresponding time-reversed theories, where time is taken to flow backwards from the future to the past. While the former typically feature a rich gamut of allowed states, the latter only allow for a single state: eternal noise. We illustrate this result by considering of the time-reverse of quantum theory. We also derive a strengthening of the result in PRL 108, 200403 on signalling in time-reversed theories.