Author(s): J. J. W. H. Sørensen, M. Dalgaard, A. H. Kiilerich, K. Mølmer, and J. F. Sherson

We introduce an efficient iterative method to prepare a target state in Hilbert spaces with high dimensionality using a combination of unitary evolution, measurements, and quantum Zeno dynamics. The latter confines the evolution within Zeno subspaces of decreasing size. This gives an exponential spe...

[Phys. Rev. A 98, 062317] Published Fri Dec 14, 2018

Author(s): Ulysse Chabaud, Eleni Diamanti, Damian Markham, Elham Kashefi, and Antoine Joux

We present a scheme for a universal device which can be programed by quantum states to approximate a chosen projective measurement to a given precision. Our scheme can be viewed as an extension of the swap test to the instance where one state is supplied many times. As such, it has many potential ap...

[Phys. Rev. A 98, 062318] Published Fri Dec 14, 2018

Optical signatures of the effective nonlinear couplings among electromagnetic fields in the quantum vacuum can be conveniently described in terms of stimulated photon emission processes induced by strong classical, space-time dependent electromagnetic fields. Recent studies have adopted this approach to study collisions of Gaussian laser pulses in paraxial approximation. The present study extends these investigations beyond the paraxial approximation by using an efficient numerical solver for the classical input fields. This new numerical code allows for a consistent theoretical description of optical signatures of QED vacuum nonlinearities in generic electromagnetic fields governed by Maxwell's equations in the vacuum, such as manifestly non-paraxial laser pulses. Our code is based on a locally constant field approximation of the Heisenberg-Euler effective Lagrangian. As this approximation is applicable for essentially all optical high-intensity laser experiments, our code is capable of calculating signal photon emission amplitudes in completely generic input field configurations, limited only by numerical cost.

We model a particle entering a complicated system from free space using an infinite chain of simple harmonic oscillators coupled to a finite, $n$-site cluster. For a particle wavepacket with small wavenumber, an expression for the time delay in terms of the coupling strengths of the cluster is found. When the coupling strengths are varied, a minimum and maximum time delay can be found for $n=1$. When $n=2$, we can obtain seemingly arbitrarily large time delays. In both cases, the time delays share similarities with the time delays for the scattering from an analogous quantum well target. We conclude that this could mean that large time delays are caused by interference within the wavefunction in the target's region of space.

Despite almost a century worth of study, it is still unclear how general relativity (GR) and quantum theory (QT) should be unified into a consistent theory. The conventional approach is to retain the foundational principles of QT, such as the superposition principle, and modify GR. This is referred to as 'quantizing gravity', resulting in a theory of 'quantum gravity'. The opposite approach is 'gravitizing QT' where we attempt to keep the principles of GR, such as the equivalence principle, and consider how this leads to modifications of QT. What we are most lacking in understanding which route to take, if either, is experimental guidance. Here we consider using a Bose-Einstein condensate (BEC) to search for clues. In particular, we study how a single BEC in a superposition of two locations could test a gravitizing QT proposal where wavefunction collapse emerges from a unified theory as an objective process, resolving the measurement problem of QT. Such a modification to QT due to general relativistic principles is testable at the Planck mass scale, which is much closer to experiments than the Planck length scale where quantum, general relativistic effects are traditionally anticipated in quantum gravity theories. Furthermore, experimental tests of this proposal should be simpler to perform than recently suggested experiments that would test the quantizing gravity approach in the Newtonian gravity limit by searching for entanglement between two massive systems that are both in a superposition of two locations.

Quantum batteries are quantum mechanical systems with many degrees of freedom which can be used to store energy and that display fast charging. The physics behind fast charging is still unclear. Is this just due to the collective behavior of the underlying interacting many-body system or does it have its roots in the quantum mechanical nature of the system itself? In this work we address these questions by studying three examples of quantum-mechanical many-body batteries with rigorous classical analogs. We find that the answer is model dependent and, even within the same model, depends on the value of the coupling constant that controls the interaction between the charger and the battery itself.

We study the dynamics of a Bose-Einstein condensate trapped circumferentially on a ring, and which is governed by an interacting gauge theory. We show that the associated density-dependent gauge potential and concomitant current nonlinearity permits a ground state in the form of a rotating chiral bright soliton. This chiral soliton is constrained to move in one direction by virtue of the current nonlinearity, and represents a time crystal in the same vein as Wilczek's original proposal.

We consider a spatially periodic (cosine) potential as a model for a crystalline solid that interacts with a harmonically oscillating external electric field. This problem is periodic both in space and time and can be solved analytically using the Kramers-Henneberger co-moving frame. By analyzing the stability of the closely related Mathieu-type differential equation, the electronic band structure can be obtained. We demonstrate that by changing the field intensity, the width of the zero-field band gaps can be drastically modified, including the special case when the external field causes the band gaps to disappear

We study relative entropy in QFT, comparing the vacuum state to a special family of purifications determined by an input state and constructed using relative modular flow. We use this to prove a conjecture by Wall that relates the shape derivative of relative entropy to a variational expression over the averaged null energy of possible purifications. This variational expression can be used to easily prove the quantum null energy condition. We formulate Wall's conjecture as a theorem pertaining to operator algebras satisfying the properties of a half-sided modular inclusion, with the additional assumption that the input state has finite averaged null energy. We also give a new derivation of the strong superadditivity property of relative entropy in this context. We speculate about possible connections to the recent methods used to strengthen monotonicity of relative entropy with recovery maps.

I've applied multiple-scale perturbation theory to a generalized complex PT-symmetric Mathieu equation in order to find the stability boundaries between bounded and unbounded solutions. The analysis suggests that the non-Hermitian parameter present in the equation can be used to control the shape and curvature of these boundaries. Although this was suggested earlier by several authors, analytic formulas for the boundary curves were not given. This paper is a first attempt to fill this gap in the theory

We experimentally characterize photon leakage from 112Gbps data channels in both non-trench and trench-assistant 7-core fibers, demonstrating telecom compatibility for QKD co-existing with high-speed data transmission when a proper core/wavelength allocation is carried out.

In his constructive and well-informed commentary, Andrei Khrennikov acknowledges a privileged status of classical probability theory with respect to statistical analysis. He also sees advantages offered by the Contextuality-by-Default theory, notably, that it `demystifies quantum mechanics by highlighting the role of contextuality,' and that it can detect and measure contextuality in inconsistently connected systems. He argues, however, that classical probability theory may have difficulties in describing empirical phenomena if they are described entirely in terms of observable events. We disagree: contexts in which random variables are recorded are as observable as the variables' values. Khrennikov also argues that the Contextuality-by-Default theory suffers the problem of non-uniqueness of couplings. We disagree that this is a problem: couplings are all possible ways of imposing counterfactual joint distributions on random variables that de facto are not jointly distributed. The uniqueness of modeling experiments by means of quantum formalisms brought up by Khrennikov is achieved for the price of additional, substantive assumptions. This is consistent with our view of quantum theory as a special-purpose generator of classical probabilities. Khrennikov raises the issue of `mental signaling,' by which he means inconsistent connectedness in behavioral systems. Our position is that it is as inherent to behavioral systems as their stochasticity.

Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of optimization, material science, chemistry, and biology. Thus, the realization of large-scale, reliable quantum-computers will likely have a significant impact on the world. For this reason, the focus of this dissertation is on the development of quantum-computing applications and robust, scalable quantum-architectures. I begin by presenting an overview of the language of quantum computation. I then, in joint work with Ojas Parekh, analyze the performance of the quantum approximate optimization algorithm (QAOA) on a graph problem called Max Cut. Next, I present a new stabilizer simulation algorithm that gives improved runtime performance for topological stabilizer codes. After that, in joint work with Andrew Landahl, I present a new set of procedures for performing logical operations called "color-code lattice-surgery." Finally, I describe a software package I developed for studying, developing, and evaluating quantum error-correcting codes under realistic noise.

Although quantum key distribution is regarded as promising secure communication, security of Y00 protocol proposed by Yuen in 2000 for the affinity to conventional optical communication is not well-understood yet; its security has been evaluated only by the eavesdropper's error probabilities of detecting individual signals or masking size, the number of hidden signal levels under quantum and classical noise. Our study is the first challenge of evaluating the guessing probabilities on shared secret keys for pseudorandom number generators in a simplified Y00 communication system based on quantum multiple hypotheses testing theory. The result is that even unlimitedly long known-plaintext attack only lets the eavesdropper guess the shared secret keys of limited lengths with a probability strictly < 1. This study will give some insights for detailed future works on this quantum communication protocol.

How a many-body quantum system thermalizes --or fails to do so-- under its own interaction is a fundamental yet elusive concept. Here we demonstrate nuclear magnetic resonance observation of the emergence of prethermalization by measuring out-of-time ordered correlations. We exploit Hamiltonian engineering techniques to tune the strength of spin-spin interactions and of a transverse magnetic field in a spin chain system, as well as to invert the Hamiltonian sign to reveal out-of-time ordered correlations. At large fields, we observe an emergent conserved quantity due to prethermalization, which can be revealed by an early saturation of correlations. Our experiment not only demonstrates a new protocol to measure out-of-time ordered correlations, but also provides new insights in the study of quantum thermodynamics.

We investigate analytically and numerically the steady-state entanglement and coherence of two coupled qubits each interacting with a local boson or fermion reservoir, based on the Bloch-Redfield master equation beyond the secular approximation. We find that there is non-vanishing steady-state coherence in the nonequilibrium scenario, which grows monotonically with the nonequilibrium condition quantified by the temperature difference or chemical potential difference of the two baths. The steady-state entanglement in general is a non-monotonic function of the nonequilibrium condition as well as the bath parameters in the equilibrium setting. We also find that weak inter-qubit coupling and high base temperature or chemical potential of the baths can strongly suppress the steady-state entanglement and coherence, regardless of the strength of the nonequilibrium condition. On the other hand, the energy detuning of the two qubits, when used in a compensatory way with the nonequilibrium condition, can lead to significant enhancement of the steady-state entanglement in some parameter regimes. In addition, the qubits typically have a stronger steady-state entanglement when coupled to fermion baths exchanging particle with the system than boson baths exchanging energy with the system under similar conditions. We also discussed the possible experimental realization of measuring the steady state entanglement and coherence for coupled qubits systems in nonequilibrium environments. These results offer some general guidelines for optimizing the steady-state entanglement and coherence in the coupled qubit system and may find potential applications in quantum information technology.

We investigate simultaneous estimation of multi-parameter quantum estimation with time-dependent Hamiltonians. We analytically obtain the maximal quantum Fisher information matrix for two-parameter in time-dependent three-level systems. The optimal coherent control scheme is proposed to increase the estimation precisions. In a example of a spin-1 particle in a uniformly rotating magnetic field, the optimal coherent Hamiltonians for different parameters can be chosen to be completely same. However, in general, the optimal coherent Hamiltonians for different parameters are incompatibility. In this situation, we suggest a variance method to obtain the optimal coherent Hamiltonian for estimating multiple parameters simultaneously, and obtain the optimal simultaneous estimation precision of two-parameter in a three-level Landau-Zener Hamiltonian.

We explore an open driven three-level $V$-system coupled to an environment with dynamics governed by the Lindblad master equation. We perform a transformation into superoperator space, which brings the Lindblad equation into a Schr\"{o}dinger-like form, thus allowing us to obtain an exact analytical solution for the density matrix of the $V$-system in a closed form. We demonstrate a regime for continuous lasing without inversion for an open $V$-system driven by a continuous wave laser. We show a mechanism for achieving superluminal, negative, and vanishing light pulse group velocities and provide physical parameters for realizing these regimes experimentally.

The fidelity susceptibility measures sensitivity of eigenstates to a change of an external parameter. It has been fruitfully used to pin down quantum phase transitions when applied to ground states (with extensions to thermal states). Here we propose to use the fidelity susceptibility as a useful dimensionless measure for complex quantum systems. We find analytically the fidelity susceptibility distributions for Gaussian orthogonal and unitary universality classes for arbitrary system size. The results are verified by a comparison with numerical data.

In this thesis, I present several results on quantum statistical inference in the following two directions. Firstly, I demonstrate that quantum algorithms can be applied to enhance the computing and training of Gaussian processes (GPs), a powerful model widely used in classical statistical inference and supervised machine learning. A crucial component of the quantum GP algorithm is solving linear systems with quantum computers, for which I present a novel algorithm that achieves a provable advantage over previously known methods. I will also explicitly address the task of encoding the classical data into a quantum state for machine learning applications. I then apply the quantum enhanced GPs to Bayesian deep learning and present an experimental demonstration on contemporary hardware and simulators. Secondly, I look into the notion of quantum causality and apply it to inferring spatial and temporal quantum correlations, and present an analytical toolkit for causal inference in quantum data. I will also make the connection between causality and quantum communications, and present a general bound for the quantum capacity of noisy communication channels.