All-optical input-agnostic polarization transformer via experimental Kraus-map control

Zhang, Wenlei; Saripalli, Ravi K.; Leamer, Jacob M.; Glasser, Ryan T.; Bondar, Denys I.

doi:10.1140/epjp/s13360-022-03104-9

Cited by 8 publications

(6 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another approach that allows for the experimental modification of decoherence rates was realized via the experimental control of the system-reservoir interaction and hydrogen spin relaxation rates [33]. Non-unitary control is also necessary for the experimental realization of all-to-one Kraus maps [31].…”

Section: Environment-assisted Control Of a Qubitmentioning

confidence: 99%

“…The generation of some maps of this class was also discussed recently in [17]. There was a non-trivial problem of the experimental realization of such all-to-one Kraus maps, which was recently solved for an open single qubit [31]. Other various experimental works have been conducted using control by incoherent photons or the modification of relaxation rates.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum Control Landscapes for Generation of H and T Gates in an Open Qubit with Both Coherent and Environmental Drive

Petruhanov,

Pechen

2023

Photonics

View full text Add to dashboard Cite

An important problem in quantum computation is the generation of single-qubit quantum gates such as Hadamard (H) and π/8 (T) gates, which are components of a universal set of gates. Qubits in experimental realizations of quantum computing devices are interacting with their environment. While the environment is often considered as an obstacle leading to a decrease in the gate fidelity, in some cases, it can be used as a resource. Here, we consider the problem of the optimal generation of H and T gates using coherent control and the environment as a resource acting on the qubit via incoherent control. For this problem, we studied the quantum control landscape, which represents the behavior of the infidelity as a functional of the controls. We considered three landscapes, with infidelities defined by steering between two, three (via Goerz–Reich–Koch approach), and four matrices in the qubit Hilbert space. We observed that, for the H gate, which is a Clifford gate, for all three infidelities, the distributions of minimal values obtained with a gradient search have a simple form with just one peak. However, for the T gate, which is a non-Clifford gate, the situation is surprisingly different—this distribution for the infidelity defined by two matrices also has one peak, whereas distributions for the infidelities defined by three and four matrices have two peaks, which might indicate the possible existence of two isolated minima in the control landscape. It is important that, among these three infidelities, only those defined with three and four matrices guarantee the closeness of the generated gate to a target and can be used as a good measure of closeness. We studied sets of optimized solutions for the most general and previously unexplored case of coherent and incoherent controls acting together and discovered that they form sub-manifolds in the control space, and unexpectedly, in some cases, two isolated sub-manifolds.

show abstract

Section: Environment-assisted Control Of a Qubitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum Control Landscapes for Generation of H and T Gates in an Open Qubit with Both Coherent and Environmental Drive

Petruhanov,

Pechen

2023

Photonics

View full text Add to dashboard Cite

show abstract

“…(3) A simple explicit analytic solution for incoherent control was obtained. (4) The control scheme is robust to variations of the initial state the optimal control steers simultaneously all initial states into the target state, thereby physically realizing all-to-one Kraus maps theoretically exploited for quantum control in [69] and recently experimentally for an open single qubit in [70]. In [22], coherent and incoherent controls were separated in time (first coherent control, followed by incoherent) and were applied to the system on different time scales determined by the parameters of the system.…”

Section: Incoherent Control and Time-dependent Decoherence Ratesmentioning

confidence: 99%

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

Моржин

Pechen

2021

Proc. Steklov Inst. Math.

View full text Add to dashboard Cite

This article is devoted to developing an approach for manipulating the von Neumann entropy S(ρ(t)) of an open two-qubit system with coherent control and incoherent control inducing time-dependent decoherence rates. The following goals are considered: (a) minimizing or maximizing the final entropy S(ρ(T )); (b) steering S(ρ(T )) to a given target value; (c) steering S(ρ(T )) to a target value and satisfying the pointwise state constraint S(ρ(t)) ≤ S for a given S; (d) keeping S(ρ(t)) constant at a given time interval. Under the Markovian dynamics determined by a Gorini-Kossakowski-Sudarshan-Lindblad type master equation, which contains coherent and incoherent controls, one-and two-step gradient projection methods and genetic algorithm have been adapted, taking into account the specifics of the objective functionals. The corresponding numerical results are provided and discussed.

show abstract

“…Exact description of reachable sets for a qubit via geometric control tehcnique was obtained in [15]. The first experimental realization of Kraus maps studied in [16] for an open single qubit was done in [17].…”

Section: Introductionmentioning

confidence: 99%

“…(4) The scheme is robust to variations of the initial state-the optimal control steers simultaneously all initial states into the target state, thereby physically realizing all-to-one Kraus maps previously theoretically exploited for quantum control [78]. The first experimental realization of Kraus maps studied in [78] for an open single qubit was done in [79]. However, after when the existence of optimal controls is established, the next question is how to find optimal coherent and incoherent controls.…”

Section: Introductionmentioning

confidence: 99%

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

Petruhanov¹,

Pechen²

2023

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimization in quantum control. GRAPE is gradient search method based on exact expressions for gradient of the control objective. It has been applied to various coherently controlled closed and open quantum systems. In this work, we adopt the GRAPE method for optimizing objective functionals in open quantum systems driven by both coherent and incoherent controls. In our case, a tailored or engineered environment acts on the controlled system as control via time-dependent decoherence rates γ i ( t ) or, equivalently, via spectral density n ω ( t ) of the environment. To develop the GRAPE approach for this problem, we compute gradient of various objectives for general N-level open quantum systems for the piecewise constant class of control. The case of a single qubit is considered in details and solved analytically. For this case, an explicit analytical expression for evolution and objective gradient is obtained via diagonalization of a 3 × 3 matrix determining the system’s dynamics in the Bloch ball. The diagonalization is obtained by solving a cubic equation via Cardano’s method. The efficiency of the algorithm is demonstrated through numerical simulations for the state-to-state transition problem and its complexity is estimated. Robustness of the optimal controls is also studied.

show abstract

All-optical input-agnostic polarization transformer via experimental Kraus-map control

Cited by 8 publications

References 52 publications

Quantum Control Landscapes for Generation of H and T Gates in an Open Qubit with Both Coherent and Environmental Drive

Quantum Control Landscapes for Generation of H and T Gates in an Open Qubit with Both Coherent and Environmental Drive

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

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

Contact Info

Product

Resources

About