Reachability in Infinite-Dimensional Unital Open Quantum Systems with Switchable GKS–Lindblad Generators

Abstract By extending the concept of energy-constrained diamond norms, we obtain continuity bounds on the dynamics of both closed and open quantum systems in infinite dimensions, which are stronger than previously known bounds. We extensively discuss applications of our theory to quantum speed limits, attenuator and amplifier channels, the quantum Boltzmann equation, and quantum Brownian motion. Next, we obtain explicit log-Lipschitz continuity bounds for entropies of infinite-dimensional quantum systems, and classical capacities of infinite-dimensional quantum channels under energy-constraints. These bounds are determined by the high energy spectrum of the underlying Hamiltonian and can be evaluated using Weyl’s law.

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Local Spin and Open Quantum Systems: Clarifying Misconceptions, Unifying Approaches

10.26434/chemrxiv.13200245.v1 ◽

2020 ◽

Author(s):

Angel Martín Pendás ◽

Evelio Francisco

Keyword(s):

Quantum Control ◽

Open Systems ◽

Open Quantum Systems ◽

Real Space ◽

Quantum Systems ◽

Spin Coupling ◽

Molecular Systems ◽

Open Quantum ◽

Local Spin

We now show that Clark and Davidson local spins operators are perfectly defined subsystem operators if a fragment is taken as an open quantum system (OQS). Open systems have become essential in quantum control and quantum computation, but have not received much attention in Chemistry. We have already shown (J. Chem. Theory Comput. 2018, 15, 1079) how real space OQSs can be defined in molecular systems and how they offer new insights relating quantum mechanical entaglement and chemical bonding. The OQS account of local spin that we offer yields a rigorous, yet easily accessible way to rationalize local spin values. A fragment is found in a mixed state direct sum of sectors characterized by different number of electrons that occur with different probabilities. The local spin is then a weighted sum of otherwise standard S(S+1) values. With OQS glasses, it is obvious that atomic or fragment spins should not vanish. Our approach thus casts doubts on any procedure used to annihilate them, like those used by Mayer and coworkers. OQS local spins allow for a fruitful use of models. One can propose easily sector probabilities for localized, covalent, ionic, zwitterionic, etc. situations, and examine their ideal local spins. We have mapped all 2c-2e cases, and shown how to do that in general multielectron cases. The role of electron correlation is also studied by tuning the Hubbard U/t parameter for H chains. Correlation induced localization changes the spin-coupling patterns even qualitatively, and show how the limiting antiferromagnet arises.

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

Scientific Reports ◽

10.1038/s41598-021-86461-2 ◽

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.

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Shortcuts to adiabaticity for open systems in circuit quantum electrodynamics

Nature Communications ◽

10.1038/s41467-021-27900-6 ◽

2022 ◽

Vol 13 (1) ◽

Author(s):

Zelong Yin ◽

Chunzhen Li ◽

Jonathan Allcock ◽

Yicong Zheng ◽

Xiu Gu ◽

...

Keyword(s):

Quantum Electrodynamics ◽

Quantum Control ◽

Open Systems ◽

Open Quantum Systems ◽

Quantum Systems ◽

Circuit Quantum Electrodynamics ◽

Open Quantum ◽

Shortcuts To Adiabaticity ◽

Potential Applications ◽

Closed Systems

AbstractShortcuts to adiabaticity are powerful quantum control methods, allowing quick evolution into target states of otherwise slow adiabatic dynamics. Such methods have widespread applications in quantum technologies, and various shortcuts to adiabaticity protocols have been demonstrated in closed systems. However, realizing shortcuts to adiabaticity for open quantum systems has presented a challenge due to the complex controls in existing proposals. Here, we present the experimental demonstration of shortcuts to adiabaticity for open quantum systems, using a superconducting circuit quantum electrodynamics system. By applying a counterdiabatic driving pulse, we reduce the adiabatic evolution time of a single lossy mode from 800 ns to 100 ns. In addition, we propose and implement an optimal control protocol to achieve fast and qubit-unconditional equilibrium of multiple lossy modes. Our results pave the way for precise time-domain control of open quantum systems and have potential applications in designing fast open-system protocols of physical and interdisciplinary interest, such as accelerating bioengineering and chemical reaction dynamics.

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On non-Markovian Time Evolution in Open Quantum Systems

Open Systems & Information Dynamics ◽

10.1007/s11080-007-9051-5 ◽

2007 ◽

Vol 14 (03) ◽

pp. 265-274 ◽

Cited By ~ 27

Author(s):

Andrzej Kossakowski ◽

Rolando Rebolledo

Keyword(s):

Time Evolution ◽

Open System ◽

Open Quantum Systems ◽

Vacuum State ◽

Quantum Systems ◽

Initial State ◽

Completely Positive ◽

Open Quantum

Non-Markovian reduced dynamics of an open system is investigated. In the case when the initial state of the reservoir is the vacuum state, an approximation is introduced which makes it possible to construct a reduced dynamics which is completely positive.

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“What Is Life?”: Open Quantum Systems Approach

10.21203/rs.3.rs-143923/v1 ◽

2021 ◽

Author(s):

Andrei Khrennikov ◽

Irina Basieva

Keyword(s):

Steady State ◽

Quantum Dynamics ◽

Systems Approach ◽

Open Quantum Systems ◽

Quantitative Measure ◽

Second Law Of Thermodynamics ◽

Quantum Systems ◽

Order Structure ◽

Initial State ◽

Open Quantum

Abstract Recently the quantum formalism and methodology started to be applied to modeling of information processing in biosystems, mainly to the process of decision making and psychological behavior (but some applications to microbiology and genetics are considered as well). Since a living system is fundamentally open (an isolated biosystem is dead), the theory of open quantum systems is the most powerful tool for life-modeling. In this paper, we turn to the famous Schrödinger book “What is life?” and reformulate his speculations in terms of this theory. Schrödinger pointed toorder preservation as one of the main distinguishing features of biosystems. Entropy is the basic quantitative measure of order. In physical systems, entropy has the tendency to increase (Second Law of Thermodynamics for isolated classical systems and dissipation in open classical and quantum systems). Schrödinger emphasized the ability of biosystems to beat this tendency. We demonstrate that systems processing information in the quantum-like way can preservethe order-structure expressed by the quantum (von Neumann or linear) entropy. We emphasize the role of the special class of quantum dynamics and initial states generating the camel-like graphs for entropy-evolution in the process of interaction with a new environment ℰ: 1) entropy (disorder) increasing in the process of adaptation to the specific features of ℰ; 2) entropy decreasing (order increasing) resulting from adaptation; 3) the restoration of order or even its increase for limiting steady state. In the latter case the steady state entropy can be even lower than the entropy of the initial state.

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Local Spin and Open Quantum Systems: Clarifying Misconceptions, Unifying Approaches

10.26434/chemrxiv.13200245 ◽

2020 ◽

Author(s):

Angel Martín Pendás ◽

Evelio Francisco

Keyword(s):

Quantum Control ◽

Open Systems ◽

Open Quantum Systems ◽

Real Space ◽

Quantum Systems ◽

Spin Coupling ◽

Molecular Systems ◽

Open Quantum ◽

Local Spin

We now show that Clark and Davidson local spins operators are perfectly defined subsystem operators if a fragment is taken as an open quantum system (OQS). Open systems have become essential in quantum control and quantum computation, but have not received much attention in Chemistry. We have already shown (J. Chem. Theory Comput. 2018, 15, 1079) how real space OQSs can be defined in molecular systems and how they offer new insights relating quantum mechanical entaglement and chemical bonding. The OQS account of local spin that we offer yields a rigorous, yet easily accessible way to rationalize local spin values. A fragment is found in a mixed state direct sum of sectors characterized by different number of electrons that occur with different probabilities. The local spin is then a weighted sum of otherwise standard S(S+1) values. With OQS glasses, it is obvious that atomic or fragment spins should not vanish. Our approach thus casts doubts on any procedure used to annihilate them, like those used by Mayer and coworkers. OQS local spins allow for a fruitful use of models. One can propose easily sector probabilities for localized, covalent, ionic, zwitterionic, etc. situations, and examine their ideal local spins. We have mapped all 2c-2e cases, and shown how to do that in general multielectron cases. The role of electron correlation is also studied by tuning the Hubbard U/t parameter for H chains. Correlation induced localization changes the spin-coupling patterns even qualitatively, and show how the limiting antiferromagnet arises.

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Strategy of state transfer for open quantum systems by no-knowledge feedback control: Via reverse engineering

International Journal of Modern Physics B ◽

10.1142/s0217979222500138 ◽

2021 ◽

Author(s):

Juju Hu ◽

Qiang Ke ◽

Yinghua Ji

Keyword(s):

Feedback Control ◽

Reverse Engineering ◽

State Transition ◽

Open Quantum Systems ◽

Quantum Systems ◽

Control Pulse ◽

Initial State ◽

Open Quantum ◽

Knowledge Measurement ◽

State Transfer

It has long been interest to control the transfer of population between specified quantum states and protect the coherence of the system at the same time. In this paper, we investigate a scheme to improve the strategy of state transfer for open quantum systems using no-knowledge measurement-based feedback control and reverse engineering. In order to ensure that the system can process information effectively, we first design the control pulse in advance from the perspective of population and coherence and then verify it through numerical simulations. The research results show that, based on the designed control pulse, we can indeed drive the system from any initial state to the desired target state, and the coherence of the system can be effectively protected during the state transition.

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