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Nikesh S Dattani - One of the best experts on this subject based on the ideXlab platform.
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feyndyn a matlab program for fast numerical feynman integral calculations for open Quantum System dynamics on gpus
Computer Physics Communications, 2013Co-Authors: Nikesh S DattaniAbstract:Abstract This MATLAB program calculates the dynamics of the reduced density matrix of an open Quantum System modeled either by the Feynman–Vernon model or the Caldeira–Leggett model. The user gives the program a Hamiltonian matrix that describes the open Quantum System as if it were in isolation, a matrix of the same size that describes how that System couples to its environment, and a spectral distribution function and temperature describing the environment’s influence on it, in addition to the open Quantum System’s initial density matrix and a grid of times. With this, the program returns the reduced density matrix of the open Quantum System at all moments specified by that grid of times (or just the last moment specified by the grid of times if the user makes this choice). This overall calculation can be divided into two stages: the setup of the Feynman integral, and the actual calculation of the Feynman integral for time propagation of the density matrix. When this program calculates this propagation on a multi-core CPU, it is this propagation that is usually the rate-limiting step of the calculation, but when it is calculated on a GPU, the propagation is calculated so quickly that the setup of the Feynman integral can actually become the rate-limiting step. The overhead of transferring information from the CPU to the GPU and back seems to have a negligible effect on the overall runtime of the program. When the required information cannot fit on the GPU, the user can choose to run the entire program on a CPU. Program summary Program title: FeynDyn. Catalogue identifier: AEPX_v1_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEPX_v1_0.html . Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland. Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html . No. of lines in distributed program, including test data, etc.: 703. No. of bytes in distributed program, including test data, etc.: 11026. Distribution format: tar.gz. Programming language: MATLAB R2012a. Computer: See “Operating System”. Operating System: Any operating System that can run MATLAB R2007a or above. Classification: 4.4. Nature of problem: Calculating the dynamics of the reduced density operator of an open Quantum System. Solution method: Numerical Feynman integral. Running time: Depends on the input parameters. See the main text for examples.
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feyndyn a matlab program for fast numerical feynman integral calculations for open Quantum System dynamics on gpus
Computer Physics Communications, 2013Co-Authors: Nikesh S DattaniAbstract:Abstract This MATLAB program calculates the dynamics of the reduced density matrix of an open Quantum System modeled either by the Feynman–Vernon model or the Caldeira–Leggett model. The user gives the program a Hamiltonian matrix that describes the open Quantum System as if it were in isolation, a matrix of the same size that describes how that System couples to its environment, and a spectral distribution function and temperature describing the environment’s influence on it, in addition to the open Quantum System’s initial density matrix and a grid of times. With this, the program returns the reduced density matrix of the open Quantum System at all moments specified by that grid of times (or just the last moment specified by the grid of times if the user makes this choice). This overall calculation can be divided into two stages: the setup of the Feynman integral, and the actual calculation of the Feynman integral for time propagation of the density matrix. When this program calculates this propagation on a multi-core CPU, it is this propagation that is usually the rate-limiting step of the calculation, but when it is calculated on a GPU, the propagation is calculated so quickly that the setup of the Feynman integral can actually become the rate-limiting step. The overhead of transferring information from the CPU to the GPU and back seems to have a negligible effect on the overall runtime of the program. When the required information cannot fit on the GPU, the user can choose to run the entire program on a CPU. Program summary Program title: FeynDyn. Catalogue identifier: AEPX_v1_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEPX_v1_0.html . Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland. Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html . No. of lines in distributed program, including test data, etc.: 703. No. of bytes in distributed program, including test data, etc.: 11026. Distribution format: tar.gz. Programming language: MATLAB R2012a. Computer: See “Operating System”. Operating System: Any operating System that can run MATLAB R2007a or above. Classification: 4.4. Nature of problem: Calculating the dynamics of the reduced density operator of an open Quantum System. Solution method: Numerical Feynman integral. Running time: Depends on the input parameters. See the main text for examples.
Hartmut Neven - One of the best experts on this subject based on the ideXlab platform.
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artificial Quantum thermal bath engineering temperature for a many body Quantum System
Physical Review A, 2016Co-Authors: Alireza Shabani, Hartmut NevenAbstract:Temperature determines the relative probability of observing a physical System in an energy state when that System is energetically in equilibrium with its environment. In this paper, we present a theory for engineering the temperature of a Quantum System different from its ambient temperature. We define criteria for an engineered Quantum bath that, when coupled to a Quantum System with Hamiltonian $H$, drives the System to the equilibrium state $\frac{e^{-H/T}}{{{\rm{Tr}}}(e^{-H/T})}$ with a tunable parameter $T$. This is basically an analog counterpart of the digital Quantum metropolis algorithm. For a System of superconducting qubits, we propose a circuit-QED approximate realization of such an engineered thermal bath consisting of driven lossy resonators. Our proposal opens the path to simulate thermodynamical properties of many-body Quantum Systems of size not accessible to classical simulations. Also we discuss how an artificial thermal bath can serve as a temperature knob for a hybrid Quantum-thermal annealer.
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artificial Quantum thermal bath engineering temperature for a many body Quantum System
Physical Review A, 2016Co-Authors: Alireza Shabani, Hartmut NevenAbstract:Temperature determines the relative probability of observing a physical System in an energy state when that System is energetically in equilibrium with its environment. In this paper we present a theory for engineering the temperature of a Quantum System different from its ambient temperature. We define criteria for an engineered Quantum bath that, when coupled to a Quantum System with Hamiltonian $H$, drives the System to the equilibrium state $\frac{{e}^{\ensuremath{-}H/T}}{\mathrm{Tr}({e}^{\ensuremath{-}H/T})}$ with a tunable parameter $T$. This is basically an analog counterpart of the digital Quantum metropolis algorithm. For a System of superconducting qubits, we propose a circuit-QED approximate realization of such an engineered thermal bath consisting of driven lossy resonators. Our proposal opens the path to simulate thermodynamical properties of many-body Quantum Systems of size not accessible to classical simulations. Also we discuss how an artificial thermal bath can serve as a temperature knob for a hybrid Quantum-thermal annealer.
Herschel Rabitz - One of the best experts on this subject based on the ideXlab platform.
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Quantum System compression a hamiltonian guided walk through hilbert space
Physical Review A, 2021Co-Authors: Robert Kosut, Herschel RabitzAbstract:We present a Systematic study of Quantum System compression for the evolution of generic many-body problems. The necessary numerical simulations of such Systems are seriously hindered by the exponential growth of the Hilbert-space dimension with the number of particles. For a constant Hamiltonian System of Hilbert-space dimension $n$ with frequencies ranging from ${f}_{min}$ to ${f}_{max}$, we show via a proper orthogonal decomposition that for a run time $T$ the dominant dynamics are compressed in the neighborhood of a subspace whose dimension is the smallest integer larger than the time-bandwidth product $\mathrm{\ensuremath{\Delta}}=({f}_{max}\ensuremath{-}{f}_{min})T$. We also show how the distribution of initial states can further compress the System dimension. Under the stated conditions, the time-bandwidth estimate reveals the existence of an effective compressed model whose dimension is derived solely from System properties and not dependent on the particular implementation of a variational simulator, such as a machine learning System, or Quantum device, or possibly even specially adapting traditional methods of solving the time-dependent Schr\"odinger equation. However, finding an efficient solution procedure $\mathit{is}$ dependent on the simulator implementation, which is not discussed in this paper. In addition, we show that the compression rendered by the proper orthogonal decomposition encoding method can be further strengthened via a multilayer autoencoder. Finally, we present numerical illustrations to affirm the compression behavior in time-varying Hamiltonian dynamics in the presence of external fields. The essential time-bandwidth product is also simply estimated for a wide class of physical Systems, where typically localized high-frequency motion occurs at or around each of the many particles, and with low-frequency dynamics associated with globally distributed characteristic degrees of freedom. This estimate for the bandwidth has a generic character indicating the wide significance of expected Quantum System dynamics compression. We also discuss the potential implications of the findings for machine learning tools to efficiently solve the many-body or other high-dimensional Schr\"odinger equations.
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environment invariant measure of distance between evolutions of an open Quantum System
New Journal of Physics, 2010Co-Authors: Matthew D Grace, Jason Dominy, Robert L Kosut, Constantin Brif, Herschel RabitzAbstract:The problem of quantifying the difference between evolutions of an open Quantum System (in particular, between the actual evolution of an open System and the ideal target operation on the corresponding closed System) is important in Quantum control, especially in control of Quantum information processing. Motivated by this problem, we develop a measure for evaluating the distance between unitary evolution operators of a composite Quantum System that consists of a sub-System of interest (e.g. a Quantum information processor) and environment. The main characteristic of this measure is the invariance with respect to the effect of the evolution operator on the environment, which follows from an equivalence relation that exists between unitary operators acting on the composite System, when the effect on only the sub-System of interest is considered. The invariance to the environment's transformation makes it possible to quantitatively compare the evolution of an open Quantum System and its closed counterpart. The distance measure also determines the fidelity bounds of a general Quantum channel (a completely positive and trace-preserving map acting on the sub-System of interest) with respect to a unitary target transformation. This measure is also independent of the initial state of the System and straightforward to numerically calculate. As an example, the measure is used in numerical
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environment invariant measure of distance between evolutions of an open Quantum System
arXiv: Quantum Physics, 2009Co-Authors: Matthew D Grace, Jason Dominy, Robert L Kosut, Constantin Brif, Herschel RabitzAbstract:The problem of quantifying the difference between evolutions of an open Quantum System (in particular, between the actual evolution of an open System and the ideal target operation on the corresponding closed System) is important in Quantum control, especially in control of Quantum information processing. Motivated by this problem, we develop a measure for evaluating the distance between unitary evolution operators of a composite Quantum System that consists of a sub-System of interest (e.g., a Quantum information processor) and environment. The main characteristic of this measure is the invariance with respect to the effect of the evolution operator on the environment, which follows from an equivalence relation that exists between unitary operators acting on the composite System, when the effect on only the sub-System of interest is considered. The invariance to the environment's transformation makes it possible to quantitatively compare the evolution of an open Quantum System and its closed counterpart. The distance measure also determines the fidelity bounds of a general Quantum channel (a completely positive and trace-preserving map acting on the sub-System of interest) with respect to a unitary target transformation. This measure is also independent of the initial state of the System and straightforward to numerically calculate. As an example, the measure is used in numerical simulations to evaluate fidelities of optimally controlled Quantum gate operations (for one- and two-qubit Systems), in the presence of a decohering environment. This example illustrates the utility of this measure for optimal control of Quantum operations in the realistic case of open-System dynamics.
Alireza Shabani - One of the best experts on this subject based on the ideXlab platform.
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artificial Quantum thermal bath engineering temperature for a many body Quantum System
Physical Review A, 2016Co-Authors: Alireza Shabani, Hartmut NevenAbstract:Temperature determines the relative probability of observing a physical System in an energy state when that System is energetically in equilibrium with its environment. In this paper, we present a theory for engineering the temperature of a Quantum System different from its ambient temperature. We define criteria for an engineered Quantum bath that, when coupled to a Quantum System with Hamiltonian $H$, drives the System to the equilibrium state $\frac{e^{-H/T}}{{{\rm{Tr}}}(e^{-H/T})}$ with a tunable parameter $T$. This is basically an analog counterpart of the digital Quantum metropolis algorithm. For a System of superconducting qubits, we propose a circuit-QED approximate realization of such an engineered thermal bath consisting of driven lossy resonators. Our proposal opens the path to simulate thermodynamical properties of many-body Quantum Systems of size not accessible to classical simulations. Also we discuss how an artificial thermal bath can serve as a temperature knob for a hybrid Quantum-thermal annealer.
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artificial Quantum thermal bath engineering temperature for a many body Quantum System
Physical Review A, 2016Co-Authors: Alireza Shabani, Hartmut NevenAbstract:Temperature determines the relative probability of observing a physical System in an energy state when that System is energetically in equilibrium with its environment. In this paper we present a theory for engineering the temperature of a Quantum System different from its ambient temperature. We define criteria for an engineered Quantum bath that, when coupled to a Quantum System with Hamiltonian $H$, drives the System to the equilibrium state $\frac{{e}^{\ensuremath{-}H/T}}{\mathrm{Tr}({e}^{\ensuremath{-}H/T})}$ with a tunable parameter $T$. This is basically an analog counterpart of the digital Quantum metropolis algorithm. For a System of superconducting qubits, we propose a circuit-QED approximate realization of such an engineered thermal bath consisting of driven lossy resonators. Our proposal opens the path to simulate thermodynamical properties of many-body Quantum Systems of size not accessible to classical simulations. Also we discuss how an artificial thermal bath can serve as a temperature knob for a hybrid Quantum-thermal annealer.
A I Zenchuk - One of the best experts on this subject based on the ideXlab platform.
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unitary invariant discord as a measures of bipartite Quantum correlations in an n qubit Quantum System
Quantum Information Processing, 2012Co-Authors: A I ZenchukAbstract:We introduce a measure of Quantum correlations in the N-qubit Quantum System which is invariant with respect to the SU(2 N ) group of transformations of this System. This measure is a modification of the Quantum discord introduced earlier and is referred to as the unitary or SU(2 N )-invariant discord. Since the evolution of a Quantum System is equivalent to the proper unitary transformation, the introduced measure is an integral of motion and is completely defined by eigenvalues of the density matrix. As far as the calculation of the unitary invariant discord is rather complicated computational problem, we propose its modification which may be found in a simpler way. The case N = 2 is considered in details. In particular, it is shown that the modified SU(4)-invariant discord reaches the maximum value for a pure state. A geometric measure of the unitary invariant discord of an N-qubit state is introduced and a simple formula for this measure is derived, which allows one to consider this measure as a witness of Quantum correlations. The relation of the unitary invariant discord with the Quantum state transfer along the spin chain is considered. We also compare the modified SU(4)-invariant discord with the geometric measure of SU(4)-invariant discord of the two-qubit Systems in the thermal equilibrium states governed by the different Hamiltonians.
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unitary invariant discord as a measure of bipartite Quantum correlations in an n qubit Quantum System
arXiv: Quantum Physics, 2011Co-Authors: A I ZenchukAbstract:We introduce a measure of Quantum correlations in the $N$-qubit Quantum System which is invariant with respect to the $SU(2^N)$ group of transformations of this System. This measure is a modification of the Quantum discord introduced earlier and is referred to as the unitary or $SU(2^N)$-invariant discord. Since the evolution of a Quantum System is equivalent to the proper unitary transformation, the introduced measure is an integral of motion and is completely defined by eigenvalues of the density matrix. As far as the calculation of the unitary invariant discord is rather complicated computational problem, we propose its modification which may be found in a simpler way. The case N=2 is considered in details. In particular, it is shown that the modified SU(4)-invariant discord reaches the maximum value for a pure state. {A geometric measure of the unitary invariant discord of an $N$-qubit state is introduced and a simple formula for this measure is derived, which allows one to consider this measure as a witness of Quantum correlations.} The relation of the unitary invariant discord with the Quantum state transfer along the spin chain is considered. We also compare the modified SU(4)-invariant discord with the geometric measure of SU(4)-invariant discord of the two-qubit Systems in the thermal equilibrium states governed by the different Hamiltonians.
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the minimal entanglement of bipartite decompositions as a witness of strong entanglement in a Quantum System
arXiv: Quantum Physics, 2010Co-Authors: A I ZenchukAbstract:We {characterize the multipartite entanglement in a Quantum System by the quantity} which vanishes if only the Quantum System may be decomposed into two weakly entangled subSystems, unlike measures of multipartite entanglement introduced before. We refer to this {quantity} as the minimal entanglement of bipartite decompositions (MEBD). Big MEBD means that the System may not be decomposed into two weakly entangled subSystems. MEBD allows one to define, for instance, whether the given Quantum System may be a candidate for a Quantum register, where the above decomposition is undesirable. A method of lower estimation of MEBD is represented. Examples of big MEBD in spin-1/2 chains governed by the $H_{dz}$ Hamiltonian in the strong external magnetic field are given.
