We present an \textit{ab initio} auxiliary field quantum Monte Carlo method for studying the electronic structure of molecules, solids, and model Hamiltonians at finite temperature. The algorithm marries the \textit{ab initio} phaseless auxiliary field quantum Monte Carlo algorithm known to produce high accuracy ground state energies of molecules and solids with its finite temperature variant, long used by condensed matter physicists for studying model Hamiltonian phase diagrams, to yield a phaseless, \textit{ab initio} finite temperature method. We demonstrate that the method produces internal energies within chemical accuracy of exact diagonalization results across a wide range of temperatures for H$_{2}$O (STO-3G), C$_{2}$ (STO-6G), the one-dimensional hydrogen chain (STO-6G), and the multi-orbital Hubbard model. Our method effectively controls the phase problem through importance sampling, \textit{often even without invoking the phaseless approximation}, down to temperatures at which the systems studied approach their ground states and may therefore be viewed as exact over wide temperature ranges. This technique embodies a versatile tool for studying the finite temperature phase diagrams of a plethora of systems whose properties cannot be captured by a Hubbard U term alone. Our results moreover illustrate that the severity of the phase problem for model Hamiltonians far exceeds that for many molecules at all of the temperatures studied.

The application of quantum estimation theory to the problem of imaging two incoherent point sources has recently led to new insights and better measurements for incoherent imaging and spectroscopy. To establish a more general quantum limit beyond the case of two sources, here I evaluate a measurement-independent quantum bound on the Fisher information for estimating the moments of any subdiffraction object. The bound matches the performance of a spatial-mode-demultiplexing (SPADE) measurement scheme in terms of its scaling with the object size, indicating that SPADE is close to quantum-optimal. Coincidentally, the result is also applicable to the estimation of diffusion parameters with a quantum probe subject to random displacements.

Fermionic systems differ from bosonic ones in several ways, in particular that the time-reversal operator $T$ is odd, $T^2=-1$. For $PT$-symmetric bosonic systems, the no-signaling principle and the quantum brachistochrone problem have been studied to some degree, both of them controversially. In this paper, we apply the basic methods proposed for bosonic systems to {\it fermionic} two- and four-dimensional $PT$-symmetric Hamiltonians, and obtain several surprising results: We find - in contrast to the bosonic case - that the no-signaling principle is upheld for two-dimensional fermionic Hamiltonians, however, the $PT$ symmetry is broken. In addition, we find that the time required for the evolution from a given initial state, the spin-up, to a given final state, the spin-down, is a constant, independent of the parameters of the Hamiltonian, under the eigenvalue constraint. That is, it cannot - as in the bosonic case - be optimized. We do, however, also find a dimensional dependence: four-dimensional $PT$-symmetric fermionic Hamiltonians considered here again uphold the no-signaling principle, but it is not essential that the $PT$ symmetry be broken. The symmetry is, however, broken if the measure of entanglement is conserved. In the four-dimensional systems, the evolution time between orthogonal states is dependent on the parameters of the Hamiltonian, with the conclusion that it again can be optimized, and approach zero under certain circumstances. However, if we require the conservation of entanglement, the transformation time between these two states becomes the same constant as found in the two-dimensional case, which coincides with the minimum time for such a transformation to take place in the Hermitian case.

Physical annealing systems provide heuristic approaches to solving NP-hard Ising optimization problems. Here, we study the performance of two types of annealing machines--a commercially available quantum annealer built by D-Wave Systems, and measurement-feedback coherent Ising machines (CIMs) based on optical parametric oscillator networks--on two classes of problems, the Sherrington-Kirkpatrick (SK) model and MAX-CUT. The D-Wave quantum annealer outperforms the CIMs on MAX-CUT on regular graphs of degree 3. On denser problems, however, we observe an exponential penalty for the quantum annealer ($\exp(-\alpha_\textrm{DW} N^2)$) relative to CIMs ($\exp(-\alpha_\textrm{CIM} N)$) for fixed anneal times, on both the SK model and on 50%-edge-density MAX-CUT, where the coefficients $\alpha_\textrm{CIM}$ and $\alpha_\textrm{DW}$ are problem-class-dependent. On instances with over $50$ vertices, a several-orders-of-magnitude time-to-solution difference exists between CIMs and the D-Wave annealer. An optimal-annealing-time analysis is also consistent with a significant projected performance difference. The difference in performance between the sparsely connected D-Wave machine and the measurement-feedback facilitated all-to-all connectivity of the CIMs provides strong experimental support for efforts to increase the connectivity of quantum annealers.

We present a class of hybrid classical systems using quantum co-processors and point out that unlike purely quantum computers, such hybrids can be both universal and Turing complete; we introduce such quantum-classical hybrids as "quassical." We discuss the benefits of quassical architectures from a theoretical point of view: for some classes of problems they achieve computational supremacy. From a practical point of view, quassical architectures can also reduce the overhead burden imposed by most error correction schemes and minimize the challenges of interconnecting qubits in a usefully large connection graph. All quantum computing systems are cyber-physical machines and thus quassical to at least a trivial degree but only the more profoundly quassical hybrids can exhibit an optimum problem-solving capability for the amount of quantum resources deployed. Most significantly, quassical architectures advance our thinking past that of seeing quantum machines as simply quantum embodiments of classical ones and can enliven whole new fields of analytical thinking that takes us beyond quantum information science per se into a deeper understanding of the duality between quantum information and fundamental thermodynamics, possibly suggesting unexpectedly useful new technologies.

We show how one can prepare and detect entanglement and Einstein-Podolsky-Rosen (EPR) steering between two distinguishable groups (modes) of atoms in a Bose-Einstein condensate (BEC) atom interferometer. Our paper extends previous work that developed criteria for two-mode entanglement and EPR steering based on the reduced variances of two spins defined in a plane. Observation of planar spin squeezing will imply entanglement, and sufficient planar spin squeezing implies EPR steering, between the two groups of atoms. By using a two-mode dynamical model to describe BEC interferometry experiments, we show that the two-mode entanglement and EPR steering criteria are predicted to be satisfied for realistic parameters. The reported observation of spin squeezing in these parameter regimes suggests it is very likely that the criteria can be used to infer an EPR steering between mesoscopic groups of atoms, provided the total atom number can be determined to sub-Poissonian uncertainty. The criteria also apply to a photonic Mach-Zehnder interferometer. Finally, we give a method based on the amount of planar spin squeezing to determine a lower bound on the number of particles that are genuinely comprise the two-mode EPR steerable state - the so-called two-mode EPR steering depth.

Author(s): Giacomo Guarnieri, Michal Kolář, and Radim Filip

We identify sufficient conditions on the structure of the interaction Hamiltonian between a two-level quantum system and a thermal bath that, without any external drive or coherent measurement, guarantee the generation of steady-state coherences (SSC). The SSC obtained this way, remarkably, turn out...

[Phys. Rev. Lett. 121, 070401] Published Wed Aug 15, 2018

Author(s): Naoto Shiraishi, Ken Funo, and Keiji Saito

We consider the speed limit for classical stochastic Markov processes with and without the local detailed balance condition. We find that, for both cases, a trade-off inequality exists between the speed of the state transformation and the entropy production. The dynamical activity is related to a ti...

[Phys. Rev. Lett. 121, 070601] Published Wed Aug 15, 2018

Author(s): Qian Jiang, Qingmei Hu, Bingsuo Zou, and Yongyou Zhang

We design a single microwave photon switch through a one-dimensional waveguide coupled with a side Jaynes-Cummings system, namely, a single-mode cavity with an embedded Rydberg atom Rb87. Since the energy spectra of the Rb87 atom depend on the electrostatic field, the Rb87 atom can couple with the c...

[Phys. Rev. A 98, 023830] Published Wed Aug 15, 2018

Author(s): Priyanka Lochab, P. Senthilkumaran, and Kedar Khare

We report experiments on propagation of scalar and vector optical beams through random phase screens mimicking turbulence and show that the intensity profile of the beam containing a C-point polarization singularity shows maximally robust behavior. This observation is explained in terms of the polar...

[Phys. Rev. A 98, 023831] Published Wed Aug 15, 2018

In the last years several estimation strategies have been formulated to determine the value of an unknown parameter in the most precise way, taking into account the presence of noise. These strategies typically rely on the use of quantum entanglement between the sensing probes and they have been shown to be optimal in the asymptotic limit in the number of probes, as long as one performs measurements on shorter and shorter time scales. Here, we present a different approach to frequency estimation, which exploits quantum coherence in the state of each sensing particle in the long time limit and is obtained by properly engineering the environment. By means of a commonly used master equation, we show that our strategy can overcome the precision achievable with entanglement-based strategies for a finite number of probes. We discuss a possible implementation of the scheme in a realistic setup that uses trapped ions as quantum sensors.

We show that the Brussels operational-realistic approach to quantum physics and quantum cognition offers a fundamental strategy for modeling the meaning associated with collections of documental entities. To do so, we take the World Wide Web as a paradigmatic example and emphasize the importance of distinguishing the Web, made of printed documents, from a more abstract meaning entity, which we call the Quantum Web, or QWeb, where the former is considered to be the collection of traces that can be left by the latter, in specific measurements, similarly to how a non-spatial quantum entity, like an electron, can leave localized traces of impact on a detection screen. The double-slit experiment is extensively used to illustrate the rationale of the modeling, which is guided by how physicists constructed quantum theory to describe the behavior of the microscopic entities. We also emphasize that the superposition principle and the associated interference effects are not sufficient to model all experimental probabilistic data, like those obtained by counting the relative number of documents containing certain words and co-occurrences of words. For this, additional effects, like context effects, must also be taken into consideration.

Quantum systems are typically subject to various environmental noise sources. Treating these environmental disturbances with a system-bath approach beyond weak coupling one must refer to numerical methods as, for example, the numerically exact quasi-adiabatic path integral approach. This approach, however, cannot treat baths which couple to the system via operators, which do not commute. We extend the quasi-adiabatic path integral approach by determining the time discrete influence functional for such non-commuting fluctuations and by modifying the propagation scheme accordingly. We test the extended quasi-adiabatic path integral approach by determining the time evolution of a quantum two-level system coupled to two independent bath via non-commuting operators. We show that convergent results can be obtained and agreement with analytical weak coupling results is achieved in the respective limits.

Quantum resources, such as coherence, discord, and entanglement, play as a key role for demonstrating advantage in many computation and communication tasks. In order to find the nature behind these resources, tremendous efforts have been made to explore the connections between them. In this work, we extend the single party coherence resource framework to the distributed scenario and relate it to basis-dependent discord. We show the operational meaning of basis-dependent discord in quantum key distribution. By formulating a framework of basis-dependent discord, we connect these quantum resources, coherence, discord, and entanglement, quantitatively, which leads to a unification of measures of different quantum resources.

We emphasize the role of the precise correlations loophole in attempting to connect the CHSH type inequalities with the EPR-argument. The possibility to test theories with hidden variables experimentally by using such inequalities is questioned. The role of the original Bell inequality is highlighted. The interpretation of the CHSH inequality in the spirit of Bohr, as a new test of incompatibility, is presented. The positions of Bohr, Einstein, Podolsky, Rosen, Bell, Clauser, Horne, Shimony, Holt, De Broglie, Hertz, and Boltzmann on interrelation of theory and experiment are enlightened.

We investigate quantum phase transitions in $XY$ spin models using Dzyaloshinsky-Moriya (DM) interactions. We identify the quantum critical points via quantum Fisher information and quantum coherence, finding that higher DM couplings suppress quantum phase transitions. However, quantum coherence (characterized by the $l_1$-norm and relative entropy) decreases as the DM coupling increases. Herein, we present both analytical and numerical results.

We study a single two-level system coupled resonantly to an oscillator mode or a large spin. By adiabatically turning on a linear driving term on the oscillator or the spin, the eigenstates of the system change character and its ground state evolves into squeezed states of the oscillator or the spin. The robust generation of such states is of interest in many experimental systems with applications for sensing and quantum information processing.

Magnetometry utilizing a spin qubit in a solid state possesses high sensitivity. In particular, a magnetic sensor with a high spatial resolution can be achieved with the electron-spin states of a nitrogen vacancy (NV) center in diamond. In this study, we demonstrated that NV quantum sensing based on multiple-pulse decoupling sequences can sensitively measure not only the amplitude but also the phase shift of an alternating-current (AC) magnetic field. In the AC magnetometry based on decoupling sequences, the maximum phase accumulation of the NV spin due to an AC field can be generally obtained when the $\pi$-pulse period in the sequences matches the half time period of the field and the relative phase difference between the sequences and the field is zero. By contrast, the NV quantum sensor acquires no phase accumulation if the relative phase difference is $\pi/2$. Thus, this phase-accumulation condition does not have any advantage for the magnetometry. However, we revealed that the non-phase-accumulation condition is available for detecting a very small phase shift of an AC field from its initial phase. This finding is expected to provide a guide for realizing sensitive measurement of a complex AC magnetic field in micrometer and nanometer scales.

This paper is a pedagogical yet critical introduction to the quantum description of unstable systems, mostly at the level of a graduate quantum mechanics course. Quantum decays appear in many different fields of physics, and their description beyond the exponential approximation is the source of technical and conceptual challenges. In this article, we present both general methods that can be adapted to a large class of problems, and specific elementary models to describe phenomena like photo-emission, beta emission and tunneling-induced decays. We pay particular attention to the emergence of exponential decay; we analyze the approximations that justify it, and we present criteria for its breakdown. We also present a detailed model for non-exponential decays due to resonance, and an elementary model describing decays in terms of particle-detection probabilities. We argue that the traditional methods for treating decays face significant problems outside the regime of exponential decay, and that the exploration of novel regimes of current interest requires new tools.

Recently the Casimir self-entropy of an electromagnetic $\delta$-function shell was considered by two different groups, with apparently discordant conclusions, although both had concluded that a region of negative entropy existed for sufficiently weak coupling. We had found that the entropy contained an infrared divergence, which we argued should be discarded on physical grounds. On the contrary, Bordag and Kirsten recently found a completely finite self-entropy, although they, in fact, have to remove an infrared divergence. Apart from this, the high- and low-temperature results for finite coupling agree precisely for the transverse electric mode, but there are significant discrepancies in the transverse magnetic mode. We resolve those discrepancies here. In particular, it is shown that coupling-independent terms do not occur in a consistent calculation, they being an artefact of the real frequency, unregulated treatment. The results of our previous analysis, especially, the existence of a negative entropy region for sufficiently weak coupling, are therefore confirmed. Finally, we offer some analogous remarks concerning the Casimir entropy of a thin electromagnetic sheet, where the total entropy is always positive.