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Only a few classes of quantum algorithms are known which provide a speed-up over classical algorithms. However, these and any new quantum algorithms provide important motivation for the development of quantum computers. In this article new quantum algorithms are given which are based on quantum state tomography. These include an algorithm for the calculation of several quantum mechanical expectation values and an algorithm for the determination of polynomial factors. These quantum algorithms are important in their own right. However, it is remarkable that these quantum algorithms are immune to a large class of errors. We describe these algorithms and provide conditions for immunity. [ABSTRACT FROM AUTHOR]

We solve exactly the dynamics of N strongly driven two-level atoms equally coupled on resonance to a dissipative cavity mode. Analytical results are derived on decoherence, entanglement, purity, atomic correlations and cavity field mean photon number. Decoherence-free subspaces are predicted for the whole system and the N-qubit subsystem. Multi-partite entangled states and cavity cat-like states can be conditionally generated. The decay of quantum coherence and purity can be monitored by joint measurements on atomic populations. Atoms prepared in states invariant under permutation of any two components evolve within the subspace spanned by the completely symmetric Dicke states. Applications to N = 3, 4 are discussed. [ABSTRACT FROM AUTHOR]

A dynamic problem for a system coupled to a reservoir possessing a dense discrete spectrum of states has been analytically solved under two simplifying assumptions proposed by Zwanzig [15], according to which the reservoir spectrum is equidistant and all the system-reservoir coupling matrix elements are identical (i.e., independent of reservoir states). It is demonstrated that a multicomponent Loschmidt echo arises in each recurrence cycles, the number of components being equal to the cycle number. At a certain critical cycle number, the components of neighboring cycles exhibit mixing. As a result, the dynamics of the system transforms from a regular to stochastic-like dynamics, in which an arbitrarily small coarse graining (inherent in any real system) of the results of measurements or uncertainty in the initial conditions leads to (i) the loss of one-to-one correspondence between the discrete spectrum of eigenvalues and the state of the system and (ii) the loss of invariance with respect to the time reversal. Interrelation between the mixing of cycles with the entanglement of trajectories, on the one hand, and the overlap of resonances in classical systems with mixing, on the other hand, is discussed. The properties of the proposed model are consistent with a variety of the kinetic regimes of vibrational relaxation (from exponential decay to irregular, weakly damping oscillations) observed in various objects. Common features are average distances between neighboring levels on the order of 1–10 cm−1 and recurrence cycles on a time scale of 10–13–10−11 s, which is studied using femtosecond spectroscopy techniques. [ABSTRACT FROM AUTHOR]

Using the spin-boson model with coupling to Ohmic bath, an analytical approach is developed to study the dynamics of the current correlation function in dissipative two-state systems with the view of understanding the effects of environment and tunneling on the coherent oscillation and the long-time decay of the current correlation function in these systems. An analytic expression of current correlation function is obtained and the results agree very well with that of numerical simulations. [ABSTRACT FROM AUTHOR]

The geometric phase of a bi-particle model is discussed. One can drive the system to evolve by applying an external magnetic field, thereby controlling the geometric phase. The model has degenerate lowest-energy eigenvectors. The initial state is assumed to be the linear superposition or mixture of the eigenvectors. The relationship between the geometric phase and the structures of the initial state is considered, and the results are extended to a more general model. [ABSTRACT FROM AUTHOR]

A model of a single atom interacting with isotropic two modes pumped simultaneously within a perfect cavity is examined. The quantum fidelity is employed to measure the quality of transmitted information as a function of the input state. The behavior of the quantum fidelity is studied at off-resonances between the atom and fields for different preparations of initial states. [ABSTRACT FROM AUTHOR]

We show that the time evolution of the density operator of a qubit can always be described in terms of the Kraus representation. A general scheme on how to construct the Kraus operators for an open qubit system is proposed, which can be generalized to open higher dimensional quantum systems. [ABSTRACT FROM AUTHOR]

We study two quantum versions of the Eddington clock-synchronization protocol in the presence of decoherence. The first protocol uses maximally entangled states to achieve the Heisenberg limit for clock synchronization. The second protocol achieves the limit without using entanglement. We show the equivalence of the two protocols under any single-qubit decoherence model that does not itself provide synchronization information. [ABSTRACT FROM AUTHOR]

Geometric phases are an interesting resource for quantum computation in view of their robustness against decoherence effects. We study the effects of the environment on a class of one-qubit holonomic gates that have recently been shown to be characterized by “optimal” working times. We numerically analyze the behavior of these optimal points and focus on their robustness against noise. [ABSTRACT FROM AUTHOR]

Nonpositive Markov approximations are sometimes used to describe the dynamics of qubits in weak interaction with suitable environments; the appearance of negative probabilities is avoided by assuming that the transient regime eliminates from the possible initial conditions those qubit states which would otherwise be mapped out of the Bloch sphere by the subsequent Markovian time evolution. By means of a simple model, we discuss some physical inconsistencies of this approach in relation to entanglement; in particular, we show that slipped nonpositive reduced dynamics might create entanglement through a purely local action. [ABSTRACT FROM AUTHOR]

Adopting the framework of single electrons or Cooper pairs where the rate of particle transfer is controlled by an external frequency, we investigate the dynamics of the coupled system, considering the single-mode cavity field prepared in a generalized geometric state. Considering a density matrix approach, we obtain a full description of the dynamics of the coupled system for a weak quantized radiation field. Using the relevant processes involved in the detection of the charge state of the box and a realistic description of the gate pulse, we are able to analyze some aspects of the information entropy in a quantitative way. We aim to clarify results from previous work, alluding to a link between the entropy squeezing and entanglement. The numerical and analytical results obtained in this work elucidate information entropy effects. We also show that the occupation probability amplitudes possess regular structures with collapses and revivals in the Rabi oscillations. [ABSTRACT FROM AUTHOR]

The effect of the absolute robustness of the first principal Fourier-state component is developed upon rounding off the density matrix elements. A protocol for extracting the pure state using the Fourier transform and auxiliary qubits is proposed. [ABSTRACT FROM AUTHOR]

The non-Markovian wave function method (NMWF) using the stochastic unravelling of the master equation in the doubled Hilbert space is implemented for quantum Brownian motion. A comparison between the simulation and the analytical results shows that the method can be conveniently used to study the non-Markovian dynamics of the system. [ABSTRACT FROM AUTHOR]

The time evolution operator is obtained as a stochastic average of operators constructed from individual quantum trajectories. It is shown that simultaneously determining the time evolution of many initial states is more efficient than performing the task one by one using the conventional quantum state diffusion method. [ABSTRACT FROM AUTHOR]

This paper focuses on the possibility of simulating the open system dynamics of a paradigmatic model, namely the damped harmonic oscillator, with single trapped ions. The key idea consists in using a controllable physical system, i.e. a single trapped ion interacting with an engineered reservoir, to simulate the dynamics of other open systems usually difficult to study. The exact dynamics of the damped harmonic oscillator under very general conditions is firstly derived. Some peculiar characteristic of the system's dynamics are then presented. Finally a way to implement with trapped ion the specific quantum simulator of interest is discussed. [ABSTRACT FROM AUTHOR]

A new method to obtain an operatorial exact solution of a wide class of Markovian master equations is presented. Its key point is the existence of a constant of motion partitioning the Hilbert space into finite-dimensional subspaces. The consequent possibility of representing the reduced density operator as a block diagonal matrix is shown. Each 'block operator' evolves under the action of a non-unitary operator explicitly derived. Our mathematical approach is illustrated applying it to simple physical systems. [ABSTRACT FROM AUTHOR]

The 20th-century physics starts with Einstein and ends with Feynman. Einstein introduced the Lorentz-covariant world with E=mc 2. Feynman observed that fast-moving hadrons consist of partons which interact incoherently with external signals. If quarks and partons are the same entities observed in different Lorentz frames, the question then is why partons are incoherent while quarks are coherent. This is the most puzzling question Feynman left for us to solve. In this report, we discuss Wigner’s role in settling this question. Einstein’s E=mc 2, which takes the form $$E = \sqrt {m^2 + p^2 } $$ , unifies the energy-momentum relations for massive and massless particles, but it does not take into account internal space-time structure of relativistic particles. It is pointed out Wigner’s 1939 paper on the inhomogeneous Lorentz group defines particle spin and gauge degrees of freedom in the Lorentz-covariant world. Within the Wigner framework, it is shown possible to construct the internal space-time structure for hadrons in the quark model. It is then shown that the quark model and the parton model are two different manifestations of the same covariant entity. It is shown therefore that the lack of coherence in Feynman’s parton picture is an effect of the Lorentz covariance. [ABSTRACT FROM AUTHOR]

Using real time Feynman histories, a quasi-distribution of tunneling time Q(τ) is introduced. For the tunneling time of resident time type, an explicit expression for Q is shown for square barriers. Q becomes oscillatory as the barrier becomes opaque. Some well-known tunneling times fall within the range of τ where Q takes non-negligible values. The formal “average” and the “variance” of the tunneling time are found to be related to known tunneling times. It is thus demonstrated that the quasi-distribution extracts the temporal information about tunneling from real time Feynman histories. [ABSTRACT FROM AUTHOR]

We describe an embedding of a quantum mechanically described structure into a macroscopic flow. The open quantum system is partly driven by an adjacent macroscopic flow acting on the boundary of the bounded spatial domain designated to quantum mechanics. This leads to an essentially non-selfadjoint Schrödinger-type operator, the spectral properties of which will be investigated. [ABSTRACT FROM AUTHOR]

We present a one-dimensional tight-binding chain of two-level systems coupled only through common dissipative Markovian reservoirs. This quantum chain can demonstrate anomalous thermodynamic behavior contradicting Fourier law. Population dynamics of individual systems of the chain is polynomial with the order determined by the initial state of the chain. The chain can simulate classically hard problems, such as multi-dimensional random walks.

Identifying the microscopic origins of decoherence sources prevalent in Josephson junction (JJ) based circuits is central to their use as functional quantum devices. Focussing on so called ‘strongly coupled’ two-level defects, we construct a theoretical model using the atomic position of the oxygen which is spatially delocalized in the oxide forming the JJ barrier. Using this model, we investigate which atomic configurations give rise to two-level behaviour of the type seen in experiments. We compute experimentally observable parameters for phase qubits and examine defect response under the effects of applied electric field and strain.

The change of the von Neumann entropy of a set of harmonic oscillators initially in thermal equilibrium and interacting linearly with an externally driven quantum system is computed by adapting the Feynman–Vernon influence functional formalism. This quantum entropy production has the form of the expectation value of three functionals of the forward and backward paths describing the system history in the Feynman–Vernon theory. In the classical limit of Kramers–Langevin dynamics (Caldeira–Leggett model) these functionals combine to three terms, where the first is the entropy production functional of stochastic thermodynamics, the classical work done by the system on the environment in units of k _B T, and the second and the third other functionals which have no analogue in stochastic thermodynamics.

Understanding the role of correlations in quantum systems is both a fundamental challenge as well as of high practical relevance for the control of multi-particle quantum systems. Whereas a lot of research has been devoted to study the various types of correlations that can be present in the states of quantum systems, in this work we introduce a general and rigorous method to quantify the amount of correlations in the dynamics of quantum systems. Using a resource-theoretical approach, we introduce a suitable quantifier and characterize the properties of correlated dynamics. Furthermore, we benchmark our method by applying it to the paradigmatic case of two atoms weakly coupled to the electromagnetic radiation field, and illustrate its potential use to detect and assess spatial noise correlations in quantum computing architectures.

We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm distance. The classical algorithm is constructed by decomposing a quantum channel into a convex combination of generalized extreme channels by convex optimization of a set of nonlinear coupled algebraïc equations. The resultant circuit is a randomly chosen generalized extreme channel circuit whose run-time is logarithmic with respect to the error tolerance and quadratic with respect to Hilbert space dimension, which requires only a single ancillary qudit plus classical dits.

We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum-walk experiments realized with neutral atoms walking in an optical lattice. From the measured spatial distributions, we determine with good precision the amount of decoherence per step, which provides a quantitative indication of the quality of our quantum walks. In particular, we find that spin decoherence is the main mechanism responsible for the loss of coherence in our experiment. We also find that the sole observation of ballistic—instead of diffusive—expansion in position space is not a good indicator of the range of coherent delocalization. We provide further physical insight by distinguishing the effects of short- and long-time spin dephasing mechanisms. We introduce the concept of coherence length in the discrete-time quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasi-stationary dephasing does not modify the local properties of the quantum walk, but instead affects spatial coherences. For a visual representation of decoherence phenomena in phase space, we have developed a formalism based on a discrete analogue of the Wigner function. We show that the effects of spin and spatial decoherence differ dramatically in momentum space.

Using an efficient one and two qubit gate simulator operating on graphical processing units, we investigate ergodic properties of a quantum Ising spin $1/2$ model on a two-dimensional lattice, which is periodically driven by a δ -pulsed transverse magnetic field. We consider three different dynamical properties: (i) level density, (ii) level spacing distribution of the Floquet quasienergy spectrum, and (iii) time-averaged autocorrelation function of magnetization components. Varying the parameters of the model, we found transitions between ordered (non-ergodic) and quantum chaotic (ergodic) phases, but the transitions between flat and non-flat spectral density do not correspond to transitions between ergodic and non-ergodic local observables. Even more surprisingly, we found good agreement of level spacing distribution with the Wigner surmise of random matrix theory for almost all values of parameters except where the model is essentially non-interacting, even in regions where local observables are not ergodic or where spectral density is non-flat. These findings question the versatility of the interpretation of level spacing distribution in many-body systems and stress the importance of the concept of locality.

Transport properties play a crucial role in several fields of science, for example biology, chemistry, sociology, information science and physics. The behavior of many dynamical processes running over complex networks is known to be closely related to the geometry of the underlying topology, but this connection becomes even harder to understand when quantum effects come into play. Here, we exploit the Kossakowski–Lindblad formalism of quantum stochastic walks to investigate the capability of quickly and robustly transmitting energy (or information) between two distant points in very large complex structures, remarkably assisted by external noise and quantum features such as coherence. An optimal mixing of classical and quantum transport is, very surprisingly, quite universal for a large class of complex networks. This widespread behavior turns out to be also extremely robust with respect to geometry changes. These results might pave the way for designing optimal bio-inspired geometries of efficient transport nanostructures that can be used for solar energy and also quantum information and communication technologies.

The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here, this problem is addressed by investigating the uncertainty trade-off between measurement errors and disturbance for measurement interactions controlled by the state of a single qubit, where the measurement is described by a quantum coherent superposition of a fully projective measurement and the identity operation. It is shown that the measurement statistics obtained from a quantum controlled measurement of $\hat{A}$ followed by a projective measurement of $\hat{B}$ can be explained in terms of a simple combination of resolution and back-action errors acting on an intrinsic joint probability of the non-commuting observables defined by the input state of the system. These intrinsic joint probabilities are consistent with the complex-valued joint probabilities recently observed in weak measurements of quantum systems and provide direct evidence of non-commutativity in the form of imaginary correlations between the non-commuting operators. In quantum controlled measurements, these imaginary correlations can be converted into well-defined contributions to the real measurement statistics, allowing a direct experimental observation of the less intuitive aspects of quantum theory.

It was recently argued (Wiseman and Gambetta 2012 Phys. Rev. Lett. http://dx.doi.org/10.1103/PhysRevLett.108.220402 108 http://dx.doi.org/10.1103/PhysRevLett.108.220402 ) that the stochastic dynamics (jumps or diffusion) of an open quantum system are not inherent to the system, but rather depend on the existence and nature of a distant detector. The proposed experimental tests involved homodyne detection, giving rise to quantum diffusion, and required efficiencies $\eta $ of well over 50%. Here we prove that this requirement ( $\eta \gt 0.5$ ) is universal for diffusive-type detection, even if the system is coupled to multiple baths. However, this no-go theorem does not apply to quantum jumps, and we propose a test involving a qubit with jump-type detectors, with a threshold efficiency of only 37%. That is, quantum jumps are ‘more quantum’, and open the way to practical experimental tests. Our scheme involves a novel sort of adaptive monitoring scheme on a system coupled to two baths.

We propose a time-delayed feedback control scheme for open quantum systems that can dramatically reduce the time to reach steady state. No measurement is performed in the feedback loop, and we suggest a simple all-optical implementation for a cavity QED system. We demonstrate the potential of the scheme by applying it to a driven and dissipative Dicke model, as recently realized in a quantum gas experiment. The time to reach steady state can be reduced by two orders of magnitude for the parameters taken from the experiment, making previously inaccessible long time attractors reachable within typical experimental run times. The scheme also offers the possibility of slowing down the dynamics, as well as qualitatively changing the phase diagram of the system.

We present a non-Markovian quantum jump (NMQJ) approach for simulating coherent energy transfer dynamics in molecular systems in the presence of laser fields. By combining a coherent modified Redfield theory (CMRT) and a NMQJ method, this new approach inherits the broad-range validity from the CMRT and highly efficient propagation from the NMQJ. To implement NMQJ propagation of CMRT, we show that the CMRT master equation can be cast into a generalized Lindblad form. Moreover, we extend the NMQJ approach to treat time-dependent Hamiltonian, enabling the description of excitonic systems under coherent laser fields. As a benchmark of the validity of this new method, we show that the CMRT–NMQJ method accurately describes the energy transfer dynamics in a prototypical photosynthetic complex. Finally, we apply this new approach to simulate the quantum dynamics of a dimer system coherently excited to coupled single-excitation states under the influence of laser fields, which allows us to investigate the interplay between the photoexcitation process and ultrafast energy transfer dynamics in the system. We demonstrate that laser-field parameters significantly affect coherence dynamics of photoexcitations in excitonic systems, which indicates that the photoexcitation process must be explicitly considered in order to properly describe photon-induced dynamics in photosynthetic systems. This work should provide a valuable tool for efficient simulations of coherent control of energy flow in photosynthetic systems and artificial optoelectronic materials.

In this paper, we investigate the exact decoherence dynamics of a superconducting resonator coupled to an electromagnetic reservoir characterized by $1/f$ noise at finite temperature, where a full quantum description of the environment with $1/{{f}^{x}}$ noise (with $x\approx 1$ ) is presented. The exact master equation and the associated non-equilibrium Greenʼs functions are solved exactly for such an open system. We show a clear signal of non-Markovian dynamics induced purely by $1/f$ noise. Our analysis is also applicable to other nano/micro mechanical oscillators. Finally, we demonstrate the non-Markovian decoherence dynamics of photon number superposition states using Wigner distribution that could be measured in experiments.

In this paper, spin-orbit coupling induced photovoltaic effect of cold atoms has been studied in a three-trap system which is an two-dimensional extension of a two-trap system reported previously. It is proposed here that atom coherent length is one of the important influences to the resistance of this photovoltaic battery. Current properties of the system for different geometrical structures of the trapping potentials are discussed. Numerical results show extension in the number of traps could cause current increase directly. Quantum master equation at finite temperature is used to treat this open system. This work may give a theoretical basis for further development of the photovoltaic effect of neutral atoms., (© 2021 IOP Publishing Ltd.)

Abstract: We analyze the time evolution of mixed state in a dissipative channel, characteristic of a decay constant , by virtue of the elegant properties of entangled state representation . We find that the matrix element of the mixed state at time t in representation is proportional to that of the initial in the decayed entangled state representation, accompanying with a Gaussian damping factor . Thus we have a new insight about the nature of the dissipative process. [Copyright &y& Elsevier]

Efforts to achieve quantum computation, teleportation, and communication depend on minimizing decoherence, which is the destruction of a quantum interference pattern. Here, we examine effects arising from the universal zero-point (temperature T = 0) oscillations of the electromagnetic field on a free electron in a Schrödinger cat superposition state. A unique conclusion is that the spreading of an electron wavepacket and the rate of decay of decoherence depend on the bare mass m of the electron. However, only for m = 0 does decoherence occur and the fact that it occurs almost instantly is ruled out by electron interference experiments. For m ≠ 0, the electron essentially behaves as a free particle. [ABSTRACT FROM AUTHOR]