Correction

Pechen and Tannor Reply (vol 108, 198902 2012)

Journal

PHYSICAL REVIEW LETTERS
Volume 108, Issue 21, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.108.229901

Keywords

-

Ask authors/readers for more resources

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Recommended

Article Physics, Multidisciplinary

Quantum control landscape for ultrafast generation of single-qubit phase shift quantum gates

Boris O. Volkov, Oleg Morzhin, Alexander N. Pechen

Summary: The mathematical analysis of quantum control landscapes is crucial in determining the absence or presence of traps in quantum control objectives. In this study, a rigorous analysis of control landscapes for ultrafast generation of single-qubit quantum gates was conducted, showing that the control landscape for ultrafast phase shift gate generation is trap-free using a combination of analytical methods and numerical optimization techniques.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2021)

Article Physics, Multidisciplinary

Reachable sets for two-level open quantum systems driven by coherent and incoherent controls

Lev Lokutsievskiy, Alexander Pechen

Summary: This study investigates the controllability of all density matrices in a two-level open quantum system driven by coherent and incoherent controls. It shows that high precision density matrices can be achieved in the Bloch ball, and demonstrates the complete controllability of the system in the set of all density matrices. The reachable set as a function of final time exhibits a non-trivial structure.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2021)

Article Mathematics, Applied

On Reachable and Controllability Sets for Minimum-Time Control of an Open Two-Level Quantum System

Oleg Morzhin, Alexander N. Pechen

Summary: The study investigated a two-level open quantum system governed by the Gorini-Kossakowski-Sudarshan-Lindblad equation, with controls depending on coherent and incoherent factors. Results regarding reachability, controllbility, and minimum-time control were obtained through Bloch parametrization.

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS (2021)

Article Mathematics, Applied

Constrained Optimization Criterion for Zirconium Isotope Separation by the Method of Laser-Assisted Retardation of Condensation

K. A. Lyakhov, A. N. Pechen

Summary: A new optimization criterion for iterative zirconium isotope recovery by laser-assisted retardation of condensation is proposed, with optimization performed over parameters such as gas flow pressure and temperature, target gas molar fraction, laser pulse intensity, nozzle dimensions, and total processing time. The evolution of the objective function for zirconium isotope separation has been evaluated as a function of gas flow core temperature at different ambient gas pressures, with the laser intensity variation range needing to satisfy the condition of the isotope separation method used.

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS (2021)

Article Physics, Multidisciplinary

Complete structural restoring of transferred multi-qubit quantum state

E. B. Fel'dman, A. N. Pechen, A. I. Zenchuk

Summary: This work focuses on optimal transfer of quantum states via spin chains, proposing a protocol for restoring multi-quantum coherence matrices of multi-qubit quantum states and developing a method for constructing a 0-order coherence matrix that can be perfectly transferred in this process. The restoring protocol is based on a specially constructed unitary transformation applied to the state of the extended receiver, which is universally optimal for any higher-order coherence matrices.

PHYSICS LETTERS A (2021)

Article Mathematics

On the Construction of a Quantum Channel Corresponding to Non-commutative Graph for a Qubit Interacting with Quantum Oscillator

G. G. Amosov, A. S. Mokeev, A. N. Pechen

Summary: In this study, error correction based on the theory of non-commutative graphs for a model of a qubit interacting with a quantum oscillator is considered. The dynamics of the composite system is governed by the Schrodinger equation, which generates a positive operator-valued measure (POVM) for the system dynamics. A quantum channel is constructed to generate the non-commutative graph as a linear envelope of the POVM, by applying a generalized version of a quantum channel using the apparatus of von Neumann algebras. The results analyze a non-commutative graph generated by a qubit interacting with a quantum oscillator, where the quantum anticlique determining the error correcting subspace has an explicit expression.

LOBACHEVSKII JOURNAL OF MATHEMATICS (2021)

Article Mathematics

Enrichment Factor for Molybdenum Isotopes Separation by the Method of Laser-assisted Retardation of Condensation

K. A. Lyakhov, A. N. Pechen

Summary: This paper evaluates the enrichment factor and product cut for molybdenum isotopes separation using the laser assisted retardation of condensation method under different gas flow temperatures and pressures. The stabilization rate of the system with diffusion and nonlinear reaction term is estimated. The laser excitation rate is determined based on the photo-absorption cross section as a function of gas flow pressure and temperature from experimental data.

LOBACHEVSKII JOURNAL OF MATHEMATICS (2021)

Article Physics, Nuclear

Optimal control for state preparation in two-qubit open quantum systems driven by coherent and incoherent controls via GRAPE approach

Vadim N. Petruhanov, Alexander N. Pechen

Summary: In this work, we investigate a model of two qubits driven by coherent and incoherent time-dependent controls. We analyze the optimal control problem of state preparation and derive analytical expressions for the gradients of the objective. By studying the evolution of various parameters, we observe distinct behaviors in the optimization process for different classes of coherent control.

INTERNATIONAL JOURNAL OF MODERN PHYSICS A (2022)

Article Mathematics, Interdisciplinary Applications

Energy control in a quantum oscillator using coherent control and engineered environment

Alexander N. Pechen, Sergey Borisenok, Alexander L. Fradkov

Summary: This article presents a new method for manipulating the energy of a quantum harmonic oscillator using coherent and incoherent control. The proposed algorithm allows for complete control over the oscillator's energy. Additionally, a robust control algorithm is introduced, which ensures system stability.

CHAOS SOLITONS & FRACTALS (2022)

Article Optics

Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search

Vadim N. N. Petruhanov, Alexander N. N. Pechen

Summary: In this work, an environment formed by incoherent photons is considered as a resource for controlling open quantum systems via incoherent control. Single-qubit gates for a two-level open quantum system are generated by exploiting coherent and incoherent controls. The control problem is formulated as minimization of an objective functional and the gradient of the objective functional with respect to piecewise constant controls is obtained. Optimal trajectories in the Bloch ball are computed and the relation of quantum gate generation with optimization on complex Stiefel manifolds is discussed. The developed methodology is applied to unitary gates as a testing example.

PHOTONICS (2023)

Article Physics, Multidisciplinary

GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls

V. N. Petruhanov, A. N. Pechen

Summary: The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimizing in quantum control. In this work, the GRAPE method is applied to open quantum systems driven by both coherent and incoherent controls. The gradient of various objectives for general N-level open quantum systems is computed, with a focus on the case of a single qubit which is solved analytically. The efficiency of the algorithm is demonstrated through numerical simulations, and the robustness of the optimal controls is also studied.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2023)

Article Quantum Science & Technology

Optimal state manipulation for a two-qubit system driven by coherent and incoherent controls

Oleg V. Morzhin, Alexander N. Pechen

Summary: This article investigates the optimal state manipulation of a two-qubit system governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation. Both coherent and incoherent controls are considered and the Hilbert-Schmidt overlap between final and target density matrices is optimized.

QUANTUM INFORMATION PROCESSING (2023)

Article Optics

Quantum feedback control in quantum photosynthesis

Sergei V. Kozyrev, Alexander N. Pechen

Summary: This paper introduces a model of charge separation in quantum photosynthesis as a model of quantum feedback control in a system of interacting excitons and vibrons. It is found that quantum feedback can induce a nonlinear evolution equation, describing the Landau-Zener transition with decoherence. This model explains the irreversibility in the process of charge separation for quantum photosynthesis and the coincidence of the energy of the vibron paired to the transition and the Bohr frequency of the transition.

PHYSICAL REVIEW A (2022)

Article Quantum Science & Technology

Transfer of zero-order coherence matrix along spin-1/2 chain

G. A. Bochkin, E. B. Fel'dman, I. D. Lazarev, A. N. Pechen, A. Zenchuk

Summary: In this work, the transfer of coherence matrices along spin-1/2 chains of various length is studied. The perfect transfer of zero-order coherence matrix is possible if its elements are properly fixed. In some cases, an extended receiver with optimized unitary transformation is required for achieving perfect transfer. The study considers the asymptotic perfectly transferable zero-order coherence matrix for an infinitely long chain and examines the deviation of a perfectly transferred state from this asymptotic state as a function of the chain length for different sizes of the extended receiver. The transfer of arbitrary parameters via the nondiagonal elements of the zero-order coherence matrix is also examined and optimized using the unitary transformation of the extended receiver.

QUANTUM INFORMATION PROCESSING (2022)

Article Optics

Noncommutative graphs based on finite-infinite system couplings: Quantum error correction for a qubit coupled to a coherent field

G. G. Amosov, A. S. Mokeev, A. N. Pechen

Summary: Quantum error correction is crucial for quantum information transmission and quantum computing. This study utilizes the theory of noncommutative operator graphs to analyze error correction in scenarios where a finite-dimensional quantum system is coupled to an infinite-dimensional system, with a specific focus on a qubit coupled via the Jaynes-Cummings Hamiltonian with a bosonic coherent field. By extending the theory and constructing noncommutative graphs using coherent states, the researchers identify the quantum anticlique and analyze its behavior in relation to the frequencies of the qubit and bosonic field. The proposed scheme can be applied to systems with similar spectrum decompositions as the JC model, providing insights into error-correcting subspaces for experimental parameter values.

PHYSICAL REVIEW A (2021)

No Data Available