scholarly journals Quantum speed limit time in the presence of disturbance

2020 ◽  
pp. 2150009
Author(s):  
S. Haseli ◽  
S. Salimi ◽  
H. Dolatkhah ◽  
A. S. Khorashad
Keyword(s):  
Quantum Theory ◽  
Quantum System ◽  
Open Quantum System ◽  
Quantum Systems ◽  
Quantum Evolution ◽  
Speed Limit ◽  
Initial State ◽  
Limit Time ◽  
Maximal Speed ◽  
Disturbed Environment

Quantum theory sets a bound on the minimal time it takes for a system to evolve from initial state to target state. This bound is called the quantum speed limit (QSL) time. The quantum speed limit time is used to quantify the maximal speed of the quantum evolution. The quantum evolution will be faster if the quantum speed limit time decreases. In this work, we study the quantum speed limit time for an open quantum system in the presence of disturbance in an environment. We use the model which is provided by Ban [Phys. Rev. A 99, 012116 (2019)]. In this model, two quantum systems [Formula: see text] and [Formula: see text] interact with environment sequentially. At first, quantum system [Formula: see text] interacts with the environment [Formula: see text] as an auxiliary system, then quantum system [Formula: see text] starts its interaction with disturbed environment immediately. In this work, we consider the dephasing coupling with two types of environment that has different spectral density: Ohmic and Lorentzian. We observe that, non-Markovian effects will appear in the dynamics of the second quantum system [Formula: see text] due to the interaction of the first quantum system [Formula: see text] with the environment. Given the fact that the quantum speed limit time reduces due to the non-Markovian feature of quantum evolution, we show that disturbance effects will reduce the quantum speed limit time for the dynamics of the second quantum system [Formula: see text].

Lyapunov control on quantum systems

2014 ◽  
Vol 28 (30) ◽  
pp. 1430020 ◽  
Author(s):  
L. C. Wang ◽  
X. X. Yi
Keyword(s):  
Quantum System ◽  
Open Quantum System ◽  
Open Quantum Systems ◽  
Logic Gates ◽  
Quantum Systems ◽  
Open Quantum ◽  
Quantum Operations ◽  
Lyapunov Control ◽  
Decoherence Free Subspace ◽  
General Method

We review the scheme of quantum Lyapunov control and its applications into quantum systems. After a brief review on the general method of quantum Lyapunov control in closed and open quantum systems, we apply it into controlling quantum states and quantum operations. The control of a spin-1/2 quantum system, driving an open quantum system into its decoherence free subspace (DFS), constructing single qubit and two-qubit logic gates are taken to illustrate the scheme. The optimalization of the Lyapunov control is also reviewed in this article.

scholarly journals Hilbert–Schmidt speed as an efficient figure of merit for quantum estimation of phase encoded into the initial state of open n-qubit systems

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hossein Rangani Jahromi ◽  
Rosario Lo Franco
Keyword(s):  
Figure Of Merit ◽  
Open Quantum System ◽  
Open Quantum Systems ◽  
Quantum Fisher Information ◽  
Quantum Systems ◽  
Phase Estimation ◽  
System State ◽  
Initial State ◽  
Open Quantum ◽  
Derivatives Of

AbstractHilbert–Schmidt speed (HSS) is a special type of quantum statistical speed which is easily computable, since it does not require diagonalization of the system state. We find that, when both HSS and quantum Fisher information (QFI) are calculated with respect to the phase parameter encoded into the initial state of an n-qubit register, the zeros of the HSS dynamics are actually equal to those of the QFI dynamics. Moreover, the signs of the time-derivatives of both HSS and QFI exactly coincide. These findings, obtained via a thorough investigation of several paradigmatic open quantum systems, show that HSS and QFI exhibit the same qualitative time evolution. Therefore, HSS reveals itself as a powerful figure of merit for enhancing quantum phase estimation in an open quantum system made of n qubits. Our results also provide strong evidence for both contractivity of the HSS under memoryless dynamics and its sensitivity to system-environment information backflows to detect the non-Markovianity in high-dimensional systems, as suggested in previous studies.

scholarly journals Hermitian–Non-Hermitian Interfaces in Quantum Theory

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Miloslav Znojil
Keyword(s):  
Quantum Theory ◽  
Quantum System ◽  
Quantum Systems ◽  
Interaction Potentials ◽  
The Individual

In the global framework of quantum theory, the individual quantum systems seem clearly separated into two families with the respective manifestly Hermitian and hiddenly Hermitian operators of their Hamiltonian. In the light of certain preliminary studies, these two families seem to have an empty overlap. In this paper, we will show that whenever the interaction potentials are chosen to be weakly nonlocal, the separation of the two families may disappear. The overlapsaliasinterfaces between the Hermitian and non-Hermitian descriptions of a unitarily evolving quantum system in question may become nonempty. This assertion will be illustrated via a few analytically solvable elementary models.

scholarly journals A Quantum System Control Method Based on Enhanced Reinforcement Learning

2021 ◽  
Author(s):  
Wenjie Liu ◽  
Bosi Wang ◽  
Jihao Fan ◽  
Yebo Ge ◽  
Mohammed Zidan
Keyword(s):  
Reinforcement Learning ◽  
Quantum System ◽  
Control Method ◽  
Quantum Systems ◽  
System Control ◽  
Control Task ◽  
Initial State ◽  
Simulation Experiments ◽  
Switch Control ◽  
Control Of Quantum Systems

Abstract The design of quantum system control is a key task to a powerful quantum information technology. In practical, traditional quantum system control methods often face different constraints, and are easy to cause both leakage and stochastic control errors under the condition of limited resources. Reinforcement learning has been proved as an efficient way to complete the quantum system control task. So a quantum system control method based on enhanced reinforcement learning (QSC-ERL) is proposed. A satisfactory control strategy is obtained through enhanced reinforcement learning so that the quantum system can be evolved accurately from the initial state to the target state. According to the number of candidate unitary operations, the three-switch control is used for simulation experiments. Compared with other methods, the QSC-ERL can achieve high fidelity learning control of quantum systems and improve the efficiency of quantum system control.

scholarly journals Fast-forwarding quantum evolution

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 577
Author(s):  
Shouzhen Gu ◽  
Rolando D. Somma ◽  
Burak Şahinoğlu
Keyword(s):  
Positive Semidefinite ◽  
Quantum Circuit ◽  
Quantum Systems ◽  
Spin Systems ◽  
Quantum Evolution ◽  
Diagonal Form ◽  
Initial State ◽  
Local Spin ◽  
Low Energies ◽  
Asymptotic Complexity

We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that considers the model of quantum computation, the Hamiltonians that induce the evolution, and the properties of the initial states. Our definition accounts for any asymptotic complexity improvement of the general case and we use it to demonstrate fast-forwarding in several quantum systems. In particular, we show that some local spin systems whose Hamiltonians can be taken into block diagonal form using an efficient quantum circuit, such as those that are permutation-invariant, can be exponentially fast-forwarded. We also show that certain classes of positive semidefinite local spin systems, also known as frustration-free, can be polynomially fast-forwarded, provided the initial state is supported on a subspace of sufficiently low energies. Last, we show that all quadratic fermionic systems and number-conserving quadratic bosonic systems can be exponentially fast-forwarded in a model where quantum gates are exponentials of specific fermionic or bosonic operators, respectively. Our results extend the classes of physical Hamiltonians that were previously known to be fast-forwarded, while not necessarily requiring methods that diagonalize the Hamiltonians efficiently. We further develop a connection between fast-forwarding and precise energy measurements that also accounts for polynomial improvements.

Quantum speed limit time of a spin qubit in noninteracting spin bath

2019 ◽  
Vol 17 (07) ◽  
pp. 1950054
Author(s):  
Muhammad Musadiq ◽  
Salman Khan ◽  
Muhammad Javed ◽  
Mahmood Shamirzaie
Keyword(s):  
Approximate Solutions ◽  
Temperature Limit ◽  
Quantum Evolution ◽  
Speed Limit ◽  
Spin Bath ◽  
Driving Time ◽  
Potential Capacity ◽  
Limit Time ◽  
Speed Up ◽  
Spin Qubit

We study the dynamic of quantum speed limit (QSL) time of a qubit coupled to a bath of noninteracting spins. The investigations are carried under both exact and approximate solutions of the model and the results of the two approaches are compared with each other. Under the exact solution and in the low temperature limit, QSL time becomes independent of the number of spins in the environment with potential capacity for quantum speed up. Beyond a critical value of temperature, there exists a frequency of the spins that reduces the capacity for speeding up quantum evolution. The effects of driving time, nonuniform frequencies of the bath’s spins and coupling strength on QSL time are also investigated.

scholarly journals On the connection between microscopic description and memory effects in open quantum system dynamics

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 439
Author(s):  
Andrea Smirne ◽  
Nina Megier ◽  
Bassano Vacchini
Keyword(s):  
System Dynamics ◽  
Quantum System ◽  
Open System ◽  
Open Quantum System ◽  
Memory Effects ◽  
Initial State ◽  
System Environment ◽  
Open Quantum ◽  
Microscopic Models ◽  
Environment Evolution

The exchange of information between an open quantum system and its environment allows us to discriminate among different kinds of dynamics, in particular detecting memory effects to characterize non-Markovianity. Here, we investigate the role played by the system-environment correlations and the environmental evolution in the flow of information. First, we derive general conditions ensuring that two generalized dephasing microscopic models of the global system-environment evolution result exactly in the same open-system dynamics, for any initial state of the system. Then, we use the trace distance to quantify the distinct contributions to the information inside and outside the open system in the two models. Our analysis clarifies how the interplay between system-environment correlations and environmental-state distinguishability can lead to the same information flow from and toward the open system, despite significant qualitative and quantitative differences at the level of the global evolution.

scholarly journals Canonical structure of A and B maps

Quanta ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 34-41
Author(s):  
Sudha Sudha ◽  
B. N. Karthik ◽  
A. R. Usha Devi ◽  
A. K. Rajagopal
Keyword(s):  
Quantum System ◽  
Open Quantum System ◽  
Quantum Systems ◽  
The Novel ◽  
Canonical Structure ◽  
Completely Positive ◽  
Open Quantum ◽  
Finite Dimensional ◽  
Positive Nature

In their seminal 1961 paper, Sudarshan, Mathews and Rau investigated properties of the dynamical A and B maps acting on n-dimensional quantum systems. The nature of dynamical maps in open quantum system evolutions has attracted great deal of attention in the later years. However, the novel paper on the A and B dynamical maps has not received its due attention. In this tutorial article, we review the properties of A and B forms associated with the dynamics of finite dimensional quantum systems. In particular, we investigate a canonical structure associated with the A form and establish its equivalence with the associated B form. We show that the canonical structure of the A form captures the completely positive (not completely positive) nature of the dynamics in a succinct manner. This feature is illustrated through physical examples of qubit channels.Quanta 2021; 10: 34–41.

Entanglement

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Physical Condition ◽  
Physical System ◽  
Polarization State ◽  
Quantum Systems ◽  
Ghz State ◽  
Mathematical Representation ◽  
Entangled State ◽  
Physical Relation

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

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