results for au:Gardas_B in:quant-ph

- May 16 2018 quant-ph arXiv:1805.05462v1We conduct experimental simulations of many body quantum systems using a \emphhybrid classical-quantum algorithm. In our setup, the wave function of the transverse field quantum Ising model is represented by a restricted Boltzmann machine. This neural network is then trained using variational Monte Carlo assisted by a D-Wave quantum sampler to find the ground state energy. Our results clearly demonstrate that already the first generation of quantum computers can be harnessed to tackle non-trivial problems concerning physics of many body quantum systems.
- Jan 23 2018 quant-ph cond-mat.stat-mech arXiv:1801.06925v1Near term quantum hardware promises unprecedented computational advantage. Crucial in its development is the characterization and minimization of computational errors. We propose the use of the quantum fluctuation theorem to benchmark the performance of quantum annealers. This versatile tool provides simple means to determine whether the quantum dynamics are unital, unitary, and adiabatic, or whether the system is prone to thermal noise. Our proposal is experimentally tested on two generations of the D-Wave machine, which illustrates the sensitivity of the fluctuation theorem to the smallest aberrations from ideal annealing.
- Aug 01 2017 quant-ph arXiv:1707.09463v2The shift of interest from general purpose quantum computers to adiabatic quantum computing or quantum annealing calls for a broadly applicable and easy to implement test to assess how quantum or adiabatic is a specific hardware. Here we propose such a test based on an exactly solvable many body system -- the quantum Ising chain in transverse field -- and implement it on the D-Wave machine. An ideal adiabatic quench of the quantum Ising chain should lead to an ordered broken symmetry ground state with all spins aligned in the same direction. An actual quench can be imperfect due to decoherence, noise, flaws in the implemented Hamiltonian, or simply too fast to be adiabatic. Imperfections result in topological defects: Spins change orientation, kinks punctuating ordered sections of the chain. The number of such defects quantifies the extent by which the quantum computer misses the ground state, and is, therefore, imperfect.
- Dec 16 2016 cond-mat.stat-mech quant-ph arXiv:1612.05084v3The ground state of the one-dimensional Bose-Hubbard model at unit filling undergoes the Mott-superfluid quantum phase transition. It belongs to the Kosterlitz-Thouless universality class with an exponential divergence of the correlation length in place of the usual power law. We present numerical simulations of a linear quench both from the Mott insulator to superfluid and back. The results satisfy the scaling hypothesis that follows from the Kibble-Zurek mechanism (KZM). In the superfluid-to-Mott quenches there is no significant excitation in the superfluid phase despite its gaplessness. Since all critical superfluid ground states are qualitatively similar, the excitation begins to build up only after crossing the critical point when the ground state begins to change fundamentally. The last process falls into the KZM framework.
- Jul 21 2016 quant-ph arXiv:1607.05778v1We investigate $\mathcal{P}\mathcal{T}$-symmetric quantum systems ultra-weakly coupled to an environment. We find that such open systems evolve under $\mathcal{P}\mathcal{T}$-symmetric, purely dephasing and unital dynamics. The dynamical map describing the evolution is then determined explicitly using a quantum canonical transformation. Furthermore, we provide an explanation of why $\mathcal{P}\mathcal{T}$-symmetric dephasing type interactions lead to \emphcritical slowing down of decoherence. This effect is further exemplified with an experimentally relevant system -- a $\mathcal{P}\mathcal{T}$-symmetric qubit easily realizable, \emphe.g., in optical or microcavity experiments.
- Mar 02 2016 quant-ph arXiv:1603.00066v1A non-commuting measurement transfers, via the apparatus, information encoded in a system's state to the external "observer". Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Therefore, even a possibility to describe physical reality by means of non-hermitian operators should \emphvolens nolens be excluded as their eigenstates are not orthogonal. Here, we show that non-hermitian operators with real spectrum can be treated within the standard framework of quantum mechanics. Furthermore, we propose a quantum canonical transformation that maps hermitian systems onto non-hermitian ones. Similar to classical inertial forces this transformation is accompanied by an energetic cost pinning the system on the unitary path.
- Nov 20 2015 quant-ph arXiv:1511.06256v2Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum. This equality expresses the second law of thermodynamics for isothermal processes arbitrarily far from equilibrium. In the quasistatic limit however, the second law leads to the Carnot bound which is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Furthermore, we propose two setups to test our predictions. Namely with strongly interacting excitons and photons in a semiconductor microcavity and in the non-hermitian tight-binding model.
- Oct 22 2015 cond-mat.stat-mech cond-mat.mes-hall cond-mat.quant-gas hep-th quant-ph arXiv:1510.06132v2When a system is driven across a quantum critical point at a constant rate its evolution must become non-adiabatic as the relaxation time $\tau$ diverges at the critical point. According to the Kibble-Zurek mechanism (KZM), the emerging post-transition excited state is characterized by a finite correlation length $\hat\xi$ set at the time $\hat t=\hat \tau$ when the critical slowing down makes it impossible for the system to relax to the equilibrium defined by changing parameters. This observation naturally suggests a dynamical scaling similar to renormalization familiar from the equilibrium critical phenomena. We provide evidence for such KZM-inspired spatiotemporal scaling by investigating an exact solution of the transverse field quantum Ising chain in the thermodynamic limit.
- Mar 12 2015 cond-mat.stat-mech quant-ph arXiv:1503.03455v3The Carnot statement of the second law of thermodynamics poses an upper limit on the efficiency of all heat engines. Recently, it has been studied whether generic quantum features such as coherence and quantum entanglement could allow for quantum devices with efficiencies larger than the Carnot efficiency. The present study shows that this is not permitted by the laws of thermodynamics. In particular, we will show that rather the definition of heat has to be modified to account for the thermodynamic cost for maintaining coherence and entanglement. Our theoretical findings are numerically illustrated for an experimentally relevant example from optomechanics.
- Jan 25 2013 quant-ph arXiv:1301.5661v2It is possible to prepare a composite qubit-environment system so that its time evolution will guarantee the conservation of a preselected qubit's observable. In general, this observable is not associated with a symmetry. The latter may not even be present in the subsystem. The initial states which lead to such a quantity conserved dynamics form a subspace of the qubit-environment space of states. General construction of this subspace is presented and illustrated by two examples. The first one is the exactly soluble Jaynes-Cummings model and the second is the multi-photon Rabi model.
- Jan 25 2013 quant-ph arXiv:1301.5660v2It is recognised that, apart from the total energy conservation, there is a nonlocal $\mathbb{Z}_2$ and a somewhat hidden symmetry in this model. Conditions for the existence of this observable, its form, and its explicit construction are presented.
- Jan 17 2013 quant-ph arXiv:1301.3747v1Quantum multi--photon spin--boson model is considered. We solve an operator Riccati equation associated with that model and present a candidate for a generalized parity operator allowing to transform spin--boson Hamiltonian to a block diagonal form what indicates an existence of the related symmetry of the model.
- We address the problem of obtaining the exact reduced dynamics of the spin-half (qubit) immersed within the bosonic bath (enviroment). An exact solution of the Schrodinger equation with the paradigmatic spin-boson Hamiltonian is obtained. We believe that this result is a major step ahead and may ultimately contribute to the complete resolution of the problem in question. We also construct the constant of motion for the spin-boson system. In contrast to the standard techniques available within the framework of the open quantum systems theory, our analysis is based on the theory of block operator matrices.
- A problem of finding stationary states of open quantum systems is addressed. We focus our attention on a generic type of open system: a qubit coupled to its environment. We apply the theory of block operator matrices and find stationary states of two--level open quantum systems under certain conditions applied both on the qubit and the surrounding.
- In this paper we revisit the problem of decoherence applying the block operator matrices analysis. Riccati algebraic equation associated with the Hamiltonian describing the process of decoherence is studied. We prove that if the environment responsible for decoherence is invariant with respect to the antylinear transformation then the antylinear operator solves Riccati equation in question. We also argue that this solution leads to neither linear nor antilinear operator similarity matrix. This fact deprives us the standard procedure for solving linear differential equation (e.g, Schrodinger equation). Furthermore, the explicit solution of the Riccati equation is found for the case where the environment operators commute with each other. We discuss the connection between our results and the standard description of decoherence (one that uses the Kraus representation). We show that reduced dynamics we obtain does not have the Kraus representation if the initial correlations between the system and its environment are present. However, for any initial state of the system (even when the correlations occur) reduced dynamics can be written in a manageable way.
- May 29 2010 quant-ph arXiv:1005.5182v2The two-level quantum system (qubit) in a precessing magnetic field and in contact with a heat bath is investigated. The exact reduced dynamics for the qubit in question is obtained. We apply the approach based on the block operator matrices theory, in contrast with the standard methods provided by the theory of the open quantum systems. We also present the solution of the Riccati operator equation associated with the Hamiltonian of the system. Next, we study the adiabatic approximation for the system under consideration using quantum fidelity as a way to measure validity of the adiabatic theory. We find that in the weak coupling domain the standard condition that ensures adiabatic behavior of the spin in the magnetic field also guarantees its adiabatic evolution in the open system variant of this model. Therefore, we provide the explicit example of the open quantum system that satisfies the adiabatic approximation firstly formulated for the closed quantum systems.
- Jan 21 2010 quant-ph arXiv:1001.3541v6The block operator matrix theory is used to investigate the problem of a single qubit. We will establish a connection between the Riccati operator equation and the possibility of obtaining an exact reduced dynamics for the qubit in question. The model of the half spin particle in the rotating magnetic field coupling with the external environment is discussed. We show that the model defined in such a way can be reduced to a time independent problem.
- Nov 04 2009 quant-ph arXiv:0911.0567v1We present two measures of distance between quantum processes based on the superfidelity, introduced recently to provide an upper bound for quantum fidelity. We show that the introduced measures partially fulfill the requirements for distance measure between quantum processes. We also argue that they can be especially useful as diagnostic measures to get preliminary knowledge about imperfections in an experimental setup. In particular we provide quantum circuit which can be used to measure the superfidelity between quantum processes. As the behavior of the superfidelity between quantum processes is crucial for the properties of the introduced measures, we study its behavior for several families of quantum channels. We calculate superfidelity between arbitrary one-qubit channels using affine parametrization and superfidelity between generalized Pauli channels in arbitrary dimensions. Statistical behavior of the proposed quantities for the ensembles of quantum operations in low dimensions indicates that the proposed measures can be indeed used to distinguish quantum processes.