arXiv subjects

A. T. Rezakhani

Publications and source records attributed to A. T. Rezakhani.

At least 55 records · Page 3Linked to original sources

arXiv2011

Quantum Renormalization Group for Ground-State Fidelity

Ground-state fidelity (GSF) and quantum renormalization group theory (QRG) have proven useful tools in the study of quantum critical systems. Here we lay out a general, unified formalism of GSF and QRG; specifically, we propose a method to calculate GSF through QRG, obviating the need for calculating or approximating ground states. This method thus enhances characterization of quantum criticality as well as scaling analysis of relevant properties with system size. We illustrate the formalism in the one-dimensional Ising model in a transverse field and the anisotropic spin-1/2 Heisenberg model.

quant-ph↗

arXiv2011

Substitution effects of Ag/Cu and Al/Cu on Y123 samples: Hall anomaly and transport properties

The Hall effect and its associated anomalies offer an important means for describing superconducting property in cuprate compounds. Here, we investigate the electron- and hole-doping effects (implemented through Al- and Ag-doping, respectively) on the Hall effect and transport properties of Y123 superconducting materials (YBa2Cu3-xXxO7-d; X= Ag, Al). The Hall anomaly, in both normal and vortex states, generally depends on multiple factors, such as temperature, magnetic field, and amount/type of doping. Specifically, for our samples, we observed that hole doping first enhances the critical temperature TC, whereas its excess beyond a threshold value (here x=0.15) decreases TC; electron doping, however, decreases TC. We also show how doping changes the critical current density JC at temperature 77K with magnetic field 9kOe. More importantly, all of our samples exhibited one Hall sign reversal. Interestingly, behavior of the Hall coefficient vs. temperature reveals that the Hall dip vs. magnetic field for Ag - doped samples shows a behavior opposite to that for Al-doped samples.

cond-mat.supr-con↗

arXiv2010

Effect of weak magnetic field on quantum spin correlation in an s-wave superconductor

We study the effect of a weak magnetic field on the state of the spins of a pair of electrons forming a Cooper pair in an s-wave superconductor. By perturbatively solving time-dependent Bogoliubov equations up to first order, we obtain the two-particle Green function, and whence the two-electron spin-space density matrix. It appears that up to first order approximation, the spin state of a Cooper pair retains the form of a Werner state. This state is then examined in the sense of quantum correlations, i.e., quantum discord.

cond-mat.supr-con↗

arXiv2010

Accuracy vs run time in adiabatic quantum search

Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance, yet is often poorly understood. We study the dynamics of a continuous time, adiabatic quantum search algorithm, and find rigorous results relating the accuracy and the run time. Proceeding with estimates, we show that under fairly general circumstances the adiabatic algorithmic error exhibits a behavior with two discernible regimes: the error decreases exponentially for short times, then decreases polynomially for longer times. We show that the well known quadratic speedup over classical search is associated only with the exponential error regime. We illustrate the results through examples of evolution paths derived by minimization of the adiabatic error. We also discuss specific strategies for controlling the adiabatic error and run time.

quant-ph↗

arXiv2010

Bound entanglement in quantum phase transitions

We investigate quantum phase transitions in which a change in the type of entanglement from bound entanglement to either free entanglement or separability may occur. In particular, we present a theoretical method to construct a class of quantum spin-chain Hamiltonians that exhibit this type of quantum criticality. Given parameter-dependent two-site reduced density matrices (with prescribed entanglement properties), we lay out a reverse construction for a compatible pure state for the whole system, as well as a class of Hamiltonians for which this pure state is a ground state. This construction is illustrated through several examples.

quant-ph↗

arXiv2010

Control-Induced Decoherence-Free Manifolds

Quantum coherence of open quantum systems is usually compromised because of the interaction with the ambient environment. A "decoherence-free subspace" (DFS) of the system Hilbert space is defined where the evolution remains unitary. In the absence of a priori existence of such subspaces, it seems natural that utilizing quantum control may help generate and/or retain a DFS. Here, we introduce a time-varying DFS wherein the system's density matrix has a unitarily evolving sub-density corresponding to some given set of its eigenvalues (which we aim to preserve). This subspace is characterized from both topological and algebraic perspectives. In particular, we show that this DFS admits a complex vector bundle structure over a real-analytic manifold (the decoherence-free manifold).

quant-ph↗

arXiv2009

Equation of motion for process matrix: Hamiltonian identification and dynamical control of open quantum systems

We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of the process matrix acting on a system. This equation is applicable to non-Markovian and/or strong coupling regimes. We propose two distinct applications for this dynamical equation. We first demonstrate identification of quantum Hamiltonians generating dynamics of closed or open systems via performing process tomography. In particular, we argue how one can efficiently estimate certain classes of sparse Hamiltonians by performing partial tomography schemes. In addition, we introduce a novel optimal control theoretic setting for manipulating quantum dynamics of Hamiltonian systems, specifically for the task of decoherence suppression.

quant-ph↗

arXiv2009

Quantum Process Estimation via Generic Two-Body Correlations

Performance of quantum process estimation is naturally limited to fundamental, random, and systematic imperfections in preparations and measurements. These imperfections may lead to considerable errors in the process reconstruction due to the fact that standard data analysis techniques presume ideal devices. Here, by utilizing generic auxiliary quantum or classical correlations, we provide a framework for estimation of quantum dynamics via a single measurement apparatus. By construction, this approach can be applied to quantum tomography schemes with calibrated faulty state generators and analyzers. Specifically, we present a generalization of "Direct Characterization of Quantum Dynamics" [M. Mohseni and D. A. Lidar, Phys. Rev. Lett. 97, 170501 (2006)] with an imperfect Bell-state analyzer. We demonstrate that, for several physically relevant noisy preparations and measurements, only classical correlations and small data processing overhead are sufficient to accomplish the full system identification. Furthermore, we provide the optimal input states for which the error amplification due to inversion on the measurement data is minimal.

quant-ph↗

arXiv2009

Quantum Adiabatic Brachistochrone

We formulate a time-optimal approach to adiabatic quantum computation (AQC). A corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. This geometrization of AQC is demonstrated through two examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance.

quant-ph↗

arXiv2009

Adiabatic approximation with exponential accuracy for many-body systems and quantum computation

We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is controllable. Assuming that the Hamiltonian is analytic in a finite strip around the real time axis, that some number of its time-derivatives vanish at the initial and final times, and that the target adiabatic eigenstate is non-degenerate and separated by a gap from the rest of the spectrum, we show that one can obtain an error between the final adiabatic eigenstate and the actual time-evolved state which is exponentially small in the evolution time, where this time itself scales as the square of the norm of the time-derivative of the Hamiltonian, divided by the cube of the minimal gap.

quant-ph↗

arXiv2009

Temperature effects on quantum cloning of states and entanglement

Performances of the symmetric universal and phase-covariant cloning transformations and entanglement cloners -- qubit case -- are investigated when the initial state of the hardware or the original state to be cloned is weakly coupled to a thermal environment. Different behaviors of each of these transformations are analyzed and contrasted with the ideal cases.

quant-ph↗

arXiv2008

Correlation effects in a discrete quantum random walk

We introduce history-dependent discrete-time quantum random walk models by adding uncorrelated memory terms and also by modifying Hamiltonian of the walker to include couplings with memory-keeping agents. We next numerically study the correlation effects in these models. We also propose a correlation exponent as a relevant and promising tool for investigation of correlation or memory (hence non-Markovian) effects. Our analysis can easily be applied to more realistic models in which different regimes may emerge because of competition between different underlying physical mechanisms.

quant-ph↗

arXiv2008

Separability in Asymmetric Phase-Covariant Cloning

Here, asymmetric phase-covariant quantum cloning machines are defined and trade-off between qualities of their outputs and its impact on entanglement properties of the outputs are studies. In addition, optimal families among these cloners are introduced and also their entanglement properties are investigated. An explicit proof of optimality is presented for the case of qubits, which is based on the no-signaling condition. Our optimality proof can also be used to derive an upper bound on trade-off relations for a more general class of optimal cloners which clone states on a specific orbit of the Bloch sphere. It is shown that the optimal cloners of the equatorial states, as in the case of symmetric phase-covariant cloning, give rise to two separable clones, and in this sense these states are unique. For these cloners it is shown that total output is of GHZ-type.

quant-ph↗

arXiv2008

Direct Estimation of Single- and Two-Qubit Hamiltonians and Relaxation Rates

We provide a novel approach for characterization of quantum Hamiltonian systems via utilizing a single measurement device. Specifically, we demonstrate how external quantum correlations can be used for Hamiltonian identification tasks. We explicitly introduce experimental procedures for direct estimation of single- and two-qubit Hamiltonian parameters, and also for simultaneous estimation of transverse and longitudinal relaxation rates, using a single Bell-state analyzer. An advantage of our method over the earlier approaches is that it has a built-in feature which makes it suitable for partial characterization of Hamiltonian parameters.

quant-ph↗

arXiv2008

Quantum Process Tomography: Resource Analysis of Different Strategies

Characterization of quantum dynamics is a fundamental problem in quantum physics and quantum information science. Several methods are known which achieve this goal, namely Standard Quantum Process Tomography (SQPT), Ancilla-Assisted Process Tomography (AAPT), and the recently proposed scheme of Direct Characterization of Quantum Dynamics (DCQD). Here, we review these schemes and analyze them with respect to some of the physical resources they require. Although a reliable figure-of-merit for process characterization is not yet available, our analysis can provide a benchmark which is necessary for choosing the scheme that is the most appropriate in a given situation, with given resources. As a result, we conclude that for quantum systems where two-body interactions are not naturally available, SQPT is the most efficient scheme. However, for quantum systems with controllable two-body interactions, the DCQD scheme is more efficient than other known QPT schemes in terms of the total number of required elementary quantum operations.

quant-ph↗

arXiv2006

Temperature effects on mixed state geometric phase

Geometric phase of an open quantum system that is interacting with a thermal environment (bath) is studied through some simple examples. The system is considered to be a simple spin-half particle which is weakly coupled to the bath. It is seen that even in this regime the geometric phase can vary with temperature. In addition, we also consider the system under an adiabatically time-varying magnetic field which is weakly coupled to the bath. An important feature of this model is that it reveals existence of a temperature-scale in which adiabaticity condition is preserved and beyond which the geometric phase is varying quite rapidly with temperature. This temperature is exactly the one in which the geometric phase vanishes. This analysis has some implications in realistic implementations of geometric quantum computation.

quant-ph↗

arXiv2005

A General Setting for Geometric Phase of Mixed States Under an Arbitrary Nonunitary Evolution

The problem of geometric phase for an open quantum system is reinvestigated in a unifying approach. Two of existing methods to define geometric phase, one by Uhlmann's approach and the other by kinematic approach, which have been considered to be distinct, are shown to be related in this framework. The method is based upon purification of a density matrix by its uniform decomposition and a generalization of the parallel transport condition obtained from this decomposition. It is shown that the generalized parallel transport condition can be satisfied when Uhlmann's condition holds. However, it does not mean that all solutions of the generalized parallel transport condition are compatible with those of Uhlmann's one. It is also shown how to recover the earlier known definitions of geometric phase as well as how to generalize them when degeneracy exists and varies in time.

quant-ph↗

arXiv2004

TC suppression in Pr-doped 123-systems: Hole clustering

Doping Pr in 123-systems gives rise to some anomalies, such as TC suppression. Here, we show that a modification of hole localization theory based on a geometrical modeling by band percolation theory can put forward a good explanations for TC suppression for whole range of Pr-doping value. In this model the central effect of hole clustering is introduced. Also we have provided some experimental evidences which manifest an agreement between simulation based on hole clustering effect and the experimental data.

cond-mat.supr-con↗