Quantum control through measurement feedback

Uys, Hermann; Bassa, Humairah; Toit, Pieter du; Ghosh, Sibasish; Konrad, Thomas

doi:10.1103/physreva.97.060102

Cited by 12 publications

(15 citation statements)

References 21 publications

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“…Equation ( 6) guarantees that, once the target state is reached, the q-controllers do not force the system to leave it. A more restrictive condition was discovered with different reasoning in the context of a measurement-based quantum feedback control scheme [34]. In addition to the fixed point condition (6), initialstate-independent convergence to the target state further requires that the fixed point be globally attractive.…”

Section: A Coherent Feedback Control With Sequential Q-controllersmentioning

confidence: 99%

Robust control of quantum systems by quantum systems

Konrad,

Rouillard,

Kastner

et al. 2020

Preprint

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Quantum systems can be controlled by other quantum systems in a reversible way, without any information leaking to the outside of the system-controller compound. Such coherent quantum control is deterministic, is less noisy than measurement-based feedback control, and has potential applications in a variety of quantum technologies, including quantum computation, quantum communication and quantum metrology. Here we introduce a coherent feedback protocol, consisting of a sequence of identical interactions with controlling quantum systems, that steers a quantum system from an arbitrary initial state towards a target state. We determine the broad class of such coherent feedback channels that achieve convergence to the target state, and then stabilise as well as protect it against noise. Our results imply that also weak system-controller interactions can counter noise if they occur with suitably high frequency. We provide an example of a control scheme that does not require knowledge of the target state encoded in the controllers, which could be the result of a quantum computation. It thus provides a mechanism for autonomous, purely quantum closed-loop control.

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Section: A Coherent Feedback Control With Sequential Q-controllersmentioning

confidence: 99%

Robust control of quantum systems by quantum systems

Konrad,

Rouillard,

Kastner

et al. 2020

Preprint

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show abstract

“…After an unsharp measurement

{\hat{M}}_{n}

is imposed on the state

false| ψ^{e} false⟩

, we immediately execute feedback operation

{\hat{U}}_{n}

on the post‐measurement state. The feedback operation

{\hat{U}}_{n}

should satisfy the condition of restoring the corresponding post‐measurement state of

false| ψ^{T} false⟩

to its pre‐measurement state, that is,

\begin{matrix} true \\ right | ψ^{T} ⟩ = {\hat{U}}_{n} \frac{{\overset{M}{true}}_{n}}{\sqrt{w_{n}}} | ψ^{T} ⟩ = {\hat{U}}_{n} | ψ_{n}^{T^{'}} ⟩ \end{matrix}

where

false| ψ_{n}^{T^{'}} false⟩ = \frac{{\hat{M}}_{n}}{\sqrt{w_{n}}} false| ψ^{T} false⟩

is the post‐measurement state of

false| ψ^{T} false⟩

and the normalization constant

w_{n} = false⟨ ψ^{T} false| {\overset{E}{true}}_{n} false| ψ^{T} false⟩

. Then, a sequence of measurement‐feedback operations (MFOs)

{{\overset{U}{true}}_{n}^{(j)} {\overset{M}{true}}_{n}^{(j)}}

would drive the initial state

false| ψ^{e} false⟩

to the target state

false| ψ^{T} false⟩

, as is depicted in Figure a (the color of the star‐points change from blue to red).…”

Section: Control Tasks and Overview Of Sfpmentioning

confidence: 99%

“…In order to get a more clear insight into the physical process of SFP, we define a fidelity

F^{(j)} \equiv {| false⟨ ψ^{e, j} false| ψ^{T, j} false⟩ |}^{2}

to quantify the proximity between the state

false| ψ^{e, j} false⟩

and the target state

false| ψ^{T, j} false⟩

. The change between the fidelity

F^{false(j false)}

and the average post‐measurement fidelity

{\bar{F}}_{M}^{false(j false)}

over all possible measurement results reads,

\begin{matrix} true \\ right normalΔ F^{false(j false)} & = & left {\bar{F}}_{M}^{false(j false)} - F^{false(j false)} = \sum_{n}^{N} P_{n}^{e, j} | ⟨ ψ_{n}^{e, j} | ψ_{n}^{T, j} ⟩ |^{2} - {false| ⟨ ψ^{e, j} | ψ^{T, j} ⟩ false|}^{2} \\ = & left \sum_{n}^{N} \frac{1}{w_{n}} | ⟨ ψ^{e, j} | {\hat{M}}_{n}^{false(j false) †} {\hat{M}}_{n}^{false(j false)} | ψ^{T, j} {false⟩ false|}^{2} - {false| ⟨ ψ^{e, j} | ψ^{T, j} ⟩ false|}^{2} \\ = & left \end{matrix}

…”

Section: Control Tasks and Overview Of Sfpmentioning

confidence: 99%

“…The change between the fidelity

F^{false(j false)}

and the average post‐measurement fidelity

{\bar{F}}_{M}^{false(j false)}

over all possible measurement results reads,

\begin{matrix} true \\ right normalΔ F^{false(j false)} & = & left {\bar{F}}_{M}^{false(j false)} - F^{false(j false)} = \sum_{n}^{N} P_{n}^{e, j} | ⟨ ψ_{n}^{e, j} | ψ_{n}^{T, j} ⟩ |^{2} - {false| ⟨ ψ^{e, j} | ψ^{T, j} ⟩ false|}^{2} \\ = & left \sum_{n}^{N} \frac{1}{w_{n}} | ⟨ ψ^{e, j} | {\hat{M}}_{n}^{false(j false) †} {\hat{M}}_{n}^{false(j false)} | ψ^{T, j} {false⟩ false|}^{2} - {false| ⟨ ψ^{e, j} | ψ^{T, j} ⟩ false|}^{2} \\ = & left \sum_{n}^{N} | ⟨ ψ^{e, j} | {\hat{E}}_{n}^{false(j false)} | ψ^{T, j} ⟩ - ⟨ ψ^{e, j} | ψ^{T, j} ⟩ ⟨ ψ^{T, j} | {\hat{E}}_{n}^{false(j false)} | \end{matrix}

…”

Section: Control Tasks and Overview Of Sfpmentioning

confidence: 99%

“…Although the measurement feedback methods are widely applied for manipulating quantum systems, how one could effectively manipulate arbitrary dimension quantum systems as desired with such methods remains less explored. Recently, a sufficiently ground‐breaking technique called self‐fulfilling prophesy (SFP) was formulated by H. Uys et al., which aims at achieving arbitrary quantum control. SFP is based on a sequence of unsharp measurements and unitary feedback operations, where the feedback reverses the effect of unsharp measurement if the measurement is carried out on the system which is assumed initially in target state .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Manipulation of Multi‐Level Quantum Systems via Unsharp Measurements and Feedback Operations

et al. 2019

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In this paper, we propose a scheme to eliminate the influence of noises on system dynamics, by means of a sequential unsharp measurements and unitary feedback operations. The unsharp measurements are carried out periodically during system evolution, while the feedback operations are well designed based on the eigenstates of the density matrices of the exact (noiseless) dynamical states and its corresponding post-measurement states. For illustrative examples, we show that the dynamical trajectory errors caused by both static and non-static noises are successfully eliminated in typical two-level and multi-level systems, i.e., the high-fidelity quantum dynamics can be maintained. Furthermore, we discuss the influence of noise strength and measurement strength on the degree of precise quantum control. Crucially, the measurement-feedback scheme is quite universal in that it can be applied to precise quantum control for any dimension systems. Thus, it naturally finds extensive applications in quantum information processing.

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Unravelling-based (auto)control of back-action in atomic Bose–Einstein condensate

Tomilin,

Il’ichov

2024

Front. Phys.

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Quantum control through measurement feedback

Cited by 12 publications

References 21 publications

Robust control of quantum systems by quantum systems

Robust control of quantum systems by quantum systems

Manipulation of Multi‐Level Quantum Systems via Unsharp Measurements and Feedback Operations

Unravelling-based (auto)control of back-action in atomic Bose–Einstein condensate

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