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Qubit state guidance without feedback

Mauro Paternostro, M S Kim

Published Oct 4, 2004• 8 citations
OpenAlex

Abstract

We study a protocol for two-qubit state guidance that does not rely on feedback mechanisms. In our scheme, entanglement can be concentrated by arranging the interactions of the qubits with a continuous variable ancilla. By properly post-selecting the outcomes of repeated measurements of the state of the ancilla, the qubit state is driven to have a desired amount of purity and entanglement. We stress the primary role played by the first iterations of the protocol. Inefficiencies in the detection operations can be fully taken into account.

Related papers

Qubit state guidance without feedback

Mauro Paternostro, M S Kim

We study a protocol for two-qubit-state guidance that does not rely on feedback mechanisms. In our scheme, entanglement can be concentrated by arranging the interactions of the qubits with a continuous variable ancilla. By properly post-selecting the outcomes of repeated measurements performed on the state of the ancilla, the qubit state is driven to have a desired amount of purity and entanglement. We stress the primary role played by the first iterations of the protocol. Inefficiencies in the detection operations can be fully taken into account. We also discuss the robustness of the guidance protocol to the effects of an experimentally motivated model for mixedness of the ancillary states.

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We propose and analyze a protocol for stabilizing a maximally entangled state of two noninteracting qubits using active state-dependent feedback from a continuous two-qubit half-parity measurement in coordination with a concurrent, noncommuting dynamical decoupling drive. We demonstrate that such a drive can be simultaneous with the measurement and feedback, while also playing a key part in the feedback protocol itself. We show that robust stabilization with near-unit fidelity can be achieved even in the presence of realistic nonidealities, such as time delay in the feedback loop, imperfect state-tracking, inefficient measurements, dephasing from $1/f$-distributed qubit-frequency noise, and relaxation. We mitigate feedback-delay error by introducing a forward-state-estimation strategy in the feedback controller that tracks the effects of control signals already in transit. More generally, the steady state is globally attractive without the need for ancillas, regardless of the error state, in contrast to most known feedback and error-correction schemes.

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We study the correction of errors intervening in two qubits dissipating into their own environments. This is done by resorting to local feedback actions with the aim of preserving as much as possible the initial amount of entanglement. Optimal control is found first by gaining insights from the subsystem purity and then by numerical analysis on the concurrence. This is tantamount to a double optimization on the actuation and on the measurement processes. Repeated feedback action is also investigated, thus paving the way for a continuous-time formulation and a solution of the problem.

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Entangling unitary gates on distant qubits with ancilla feedback

Kerem Halil Shah, Daniel K. L. Oi

By using an ancilla qubit as a mediator, two distant qubits can undergo a non-local entangling unitary operation. This is desirable for when attempting to scale up or distribute quantum computation by combining fixed static local sets of qubits with ballistic mediators. Using a model driven by measurements on the ancilla, it is possible to generate a maximally entangling CZ gate while only having access to a less entangling gate between the pair qubits and the ancilla. However this results in a stochastic process of generating control phase rotation gates where the expected time for success does not correlate with the entangling power of the connection gate. We explore how one can use feedback into the preparation and measurement parameters of the ancilla to speed up the expected time to generate a CZ gate between a pair of separated qubits and to leverage stronger coupling strengths for faster times. Surprisingly, by choosing an appropriate strategy, control of a binary discrete parameter achieves comparable speed up to full continuous control of all degrees of freedom of the ancilla.

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Efficient generation of a maximally entangled state by repeated on- and off-resonant scattering of ancilla qubits

Kazuya Yuasa, Daniel Klaus Burgarth, Vittorio Giovannetti +1 more

A scheme for preparing two fixed noninteracting qubits in a maximally entangled state is presented. By repeating on- and off-resonant scattering of ancilla qubits, the target qubits are driven from an arbitrary initial state into a singlet state with probability 1 (perfect efficiency). Neither the preparation nor the post-selection of the ancilla spin state is required. The convergence from an arbitrary input state to the unique fixed point (mixing property) is proved rigorously, and its robustness is investigated by scrutinizing the effects of imperfections in the incident wave of the ancilla—such as mistuning to a resonant momentum, imperfect monochromatization, and fluctuation of the incident momentum—as well as detector efficiency.

arXiv:0909.3401•New Journal of Physics•Dec 21, 2009•20 citations
We study a protocol for two-qubit state guidance that does not rely on feedback mechanisms. In our scheme, entanglement can be concentrated by arranging the interactions of the qubits with a continuous variable ancilla. By properly post-selecting the outcomes of repeated measurements of the state of the ancilla, the qubit state is driven to have a desired amount of purity and entanglement. We stress the primary role played by the first iterations of the protocol. Inefficiencies in the detection operations can be fully taken into account.
We study a protocol for two-qubit-state guidance that does not rely on feedback mechanisms. In our scheme, entanglement can be concentrated by arranging the interactions of the qubits with a continuous variable ancilla. By properly post-selecting the outcomes of repeated measurements performed on the state of the ancilla, the qubit state is driven to have a desired amount of purity and entanglement. We stress the primary role played by the first iterations of the protocol. Inefficiencies in the detection operations can be fully taken into account. We also discuss the robustness of the guidance protocol to the effects of an experimentally motivated model for mixedness of the ancillary states.
We propose and analyze a protocol for stabilizing a maximally entangled state of two noninteracting qubits using active state-dependent feedback from a continuous two-qubit half-parity measurement in coordination with a concurrent, noncommuting dynamical decoupling drive. We demonstrate that such a drive can be simultaneous with the measurement and feedback, while also playing a key part in the feedback protocol itself. We show that robust stabilization with near-unit fidelity can be achieved even in the presence of realistic nonidealities, such as time delay in the feedback loop, imperfect state-tracking, inefficient measurements, dephasing from 1/f1/f1/f-distributed qubit-frequency noise, and relaxation. We mitigate feedback-delay error by introducing a forward-state-estimation strategy in the feedback controller that tracks the effects of control signals already in transit. More generally, the steady state is globally attractive without the need for ancillas, regardless of the error state, in contrast to most known feedback and error-correction schemes.
Abstract A protocol is proposed to generate Bell states in two non-directly interacting qubits by means of repeated measurements of the state of a central ancilla connected to both qubits. An optimal measurement rate is found that minimizes the time to stably encode a Bell state in the target qubits, being of advantage in order to reduce detrimental effects from possible interactions with the environment. The quality of the entanglement is assessed in terms of the concurrence and the distance between the qubits state and the target Bell state is quantified by the fidelity.
We study the correction of errors intervening in two qubits dissipating into their own environments. This is done by resorting to local feedback actions with the aim of preserving as much as possible the initial amount of entanglement. Optimal control is found first by gaining insights from the subsystem purity and then by numerical analysis on the concurrence. This is tantamount to a double optimization on the actuation and on the measurement processes. Repeated feedback action is also investigated, thus paving the way for a continuous-time formulation and a solution of the problem.
By using an ancilla qubit as a mediator, two distant qubits can undergo a non-local entangling unitary operation. This is desirable for when attempting to scale up or distribute quantum computation by combining fixed static local sets of qubits with ballistic mediators. Using a model driven by measurements on the ancilla, it is possible to generate a maximally entangling CZ gate while only having access to a less entangling gate between the pair qubits and the ancilla. However this results in a stochastic process of generating control phase rotation gates where the expected time for success does not correlate with the entangling power of the connection gate. We explore how one can use feedback into the preparation and measurement parameters of the ancilla to speed up the expected time to generate a CZ gate between a pair of separated qubits and to leverage stronger coupling strengths for faster times. Surprisingly, by choosing an appropriate strategy, control of a binary discrete parameter achieves comparable speed up to full continuous control of all degrees of freedom of the ancilla.
A scheme for preparing two fixed noninteracting qubits in a maximally entangled state is presented. By repeating on- and off-resonant scattering of ancilla qubits, the target qubits are driven from an arbitrary initial state into a singlet state with probability 1 (perfect efficiency). Neither the preparation nor the post-selection of the ancilla spin state is required. The convergence from an arbitrary input state to the unique fixed point (mixing property) is proved rigorously, and its robustness is investigated by scrutinizing the effects of imperfections in the incident wave of the ancilla—such as mistuning to a resonant momentum, imperfect monochromatization, and fluctuation of the incident momentum—as well as detector efficiency.