Linear quantum systems: A tutorial

Dong, Zhiyuan

doi:10.1016/j.arcontrol.2022.04.013

Cited by 18 publications

(7 citation statements)

References 187 publications

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“…The operator W is defined on a special Hilbert space F called Fock space. When the input fields are in the vacuum states, the fundamental annihilation process W and creation process W † are quantum Wiener processes satisfying the quantum Itô rule [40][41][42][43].…”

Section: Linear Quantum Passive Systemsmentioning

confidence: 99%

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Synthesis of robust memory modes for linear quantum systems with unknown inputs

Miao,

Chen,

Pan

et al. 2024

EPJ Quantum Technol.

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In this paper, the synthesis of robust memory modes for linear quantum passive systems in the presence of unknown inputs has been studied, aimed at facilitating secure storage and communication of quantum information. In particular, we can switch on decoherence-free (DF) modes in the storage stage by placing the poles on the imaginary axis via a coherent feedback control scheme, and these memory modes can further be simultaneously made robust against perturbations to the system parameters by minimizing the condition number associated with imaginary poles. The DF modes can also be switched off by tuning the controller parameters to place the poles in the left half of the complex plane in the writing/reading stage. We develop explicit algebraic conditions guiding the design of such a coherent quantum controller, which involves employing an augmented system model to counter the influence of unknown inputs. Examples are provided to illustrate the procedure of synthesizing robust memory modes for linear optical quantum systems.

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Section: Linear Quantum Passive Systemsmentioning

confidence: 99%

“…( 5) can be physically realized as linear quantum systems corresponding to quantum harmonic oscillators unless the physical realizabity condition is satisfied; see e.g. [24,43] and the references therein for more details.…”

Section: Linear Quantum Passive Systemsmentioning

confidence: 99%

Synthesis of robust memory modes for linear quantum systems with unknown inputs

Miao,

Chen,

Pan

et al. 2024

EPJ Quantum Technol.

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“…. , X n (0), such as polynomials or Weyl quantization integrals [27] (see also Equation (32) in [47]). The dependence of H 0 , L 0 on X(0) is inherited by H, L as functions of X and, along with a given commutation structure of the system variables, specifies a particular form of the resulting QSDEs ( 14) and ( 16), thereby influencing their tractability.…”

Section: Quantum Stochastic Systems Being Consideredmentioning

confidence: 99%

“…In particular, quadratic dependence of the system Hamiltonian and linear dependence of the system-field coupling operators on the quantum mechanical position-momentum variables [28] lead to linear QSDEs for open quantum harmonic oscillators (OQHOs) [11,18], which play the role of building blocks in linear quantum control theory [10,21,[29][30][31][32]. The dynamics of such systems are relatively well understood and are similar to the classical linear SDEs in a number of respects, including the preservation of the Gaussian nature of quantum states [33,34] in the case of vacuum input fields.…”

Section: Introductionmentioning

confidence: 99%

A Transverse Hamiltonian Approach to Infinitesimal Perturbation Analysis of Quantum Stochastic Systems

Vladimirov¹

2023

Preprint

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This paper is concerned with variational methods for open quantum systems with Markovian dynamics governed by Hudson-Parthasarathy quantum stochastic differential equations. These QSDEs are driven by quantum Wiener processes of the external bosonic fields and are specified by the system Hamiltonian and system-field coupling operators. We consider the system response to perturbations in these operators and introduce a transverse Hamiltonian which encodes the propagation of the perturbations through the unitary system-field evolution. This approach provides an infinitesimal perturbation analysis tool which can be used for the development of optimality conditions in quantum control and filtering problems. Such settings employ, as performance criteria, quadratic (or more complicated) cost functionals of the system and field variables to be minimised over the energy and coupling parameters of system interconnections. We demonstrate an application of the transverse Hamiltonian variational approach to a mean square optimal coherent quantum filtering problem for a measurement-free field-mediated cascade connection of a quantum system with a quantum observer.

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Section: Introductionmentioning

confidence: 99%

A Transverse Hamiltonian Approach to Infinitesimal Perturbation Analysis of Quantum Stochastic Systems

Vladimirov

2023

Entropy

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This paper is concerned with variational methods for open quantum systems with Markovian dynamics governed by Hudson–Parthasarathy quantum stochastic differential equations. These QSDEs are driven by quantum Wiener processes of the external bosonic fields and are specified by the system Hamiltonian and system–field coupling operators. We consider the system response to perturbations in these operators and introduce a transverse Hamiltonian which encodes the propagation of the perturbations through the unitary system–field evolution. This approach provides an infinitesimal perturbation analysis tool which can be used for the development of optimality conditions in quantum control and filtering problems. As performance criteria, such settings employ quadratic (or more complicated) cost functionals of the system and field variables to be minimized over the energy and coupling parameters of system interconnections. We demonstrate an application of the transverse Hamiltonian variational approach to a mean square optimal coherent quantum filtering problem for a measurement-free field-mediated cascade connection of a quantum system with a quantum observer.

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Linear quantum systems: A tutorial

Cited by 18 publications

References 187 publications

Synthesis of robust memory modes for linear quantum systems with unknown inputs

Synthesis of robust memory modes for linear quantum systems with unknown inputs

A Transverse Hamiltonian Approach to Infinitesimal Perturbation Analysis of Quantum Stochastic Systems

A Transverse Hamiltonian Approach to Infinitesimal Perturbation Analysis of Quantum Stochastic Systems

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