Locally optimal measurement-based quantum feedback with application to multiqubit entanglement generation

Zhang, S.; Martin, Leigh S.; Whaley, K. Birgitta

doi:10.1103/physreva.102.062418

“…We might consequently characterize our work above as an exploration of "open-loop conditional quantum control". Despite the importance of the measurement record, we do not require feedback to be computed instantaneously, as occurs in many feedback problems requiring non-differentiable controller trajectories that respond to diffusive conditional dynamics at each time interval [40,41,54,56].…”

Section: Discussion and Outlookmentioning

confidence: 99%

Pontryagin-optimal control of a non-Hermitian qubit

Lewalle

¹

,

Whaley²

2023

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Open-system quantum dynamics described by non-Hermitian effective Hamiltonians have become a subject of considerable interest. Studies of non-Hermitian physics have revealed general principles, including relationships between the topology of the complex eigenvalue space and the breakdown of adiabatic control strategies. We study here the control of a single non-Hermitian qubit, similar to recently realized experimental systems in which the non-Hermiticity arises from an open spontaneous emission channel. We review the topological features of the resulting non-Hermitian Hamiltonian and then present two distinct results. First, we illustrate how to realize any continuous and differentiable pure-state trajectory in the dynamics of a qubit that are conditioned on no emission. This result implicitly provides a workaround for the breakdown of standard adiabatic following in such non-Hermitian systems. Second, we use Pontryagin's maximum principle to derive optimal trajectories connecting boundary states on the Bloch sphere, using a cost function which balances the desired dynamics against the controller energy used to realize them. We demonstrate that the latter approach can effectively find trajectories which maintain high state purity even in the case of inefficient detection.

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“…We might consequently characterize our work above as an exploration of "open-loop conditional quantum control". Despite the importance of the measurement record, we do not require feedback to be computed instantaneously, as occurs in many feedback problems requiring non-differentiable controller trajectories that respond to diffusive conditional dynamics at each time interval [40,41,51,53].…”

Section: Discussion and Outlookmentioning

confidence: 99%

Pontryagin-Optimal Control of a non-Hermitian Qubit

Lewalle¹,

Whaley²

2022

Preprint

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0

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Open-system quantum dynamics described by non-Hermitian effective Hamiltonians have become a subject of considerable interest. Studies of non-Hermitian physics have revealed general principles, including relationships between the topology of the complex eigenvalue space and the breakdown of adiabatic control strategies. We study here the control of a single non-Hermitian qubit, similar to recently realized experimental systems in which the non-Hermiticity arises from an open spontaneous emission channel. We review the topological features of the resulting non-Hermitian Hamiltonian and then present two distinct results. First, we illustrate how to realize any continuous and differentiable pure-state trajectory in the dynamics of a qubit that are conditioned on no emission. This result implicitly provides a workaround for the breakdown of standard adiabatic following in such non-Hermitian systems. Second, we use Pontryagin's maximum principle to derive optimal trajectories connecting boundary states on the Bloch sphere, using a cost function which balances the desired dynamics against the controller energy used to realize them. We demonstrate that the latter approach can effectively find trajectories which maintain high state purity even in the case of inefficient detection.

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“…Feedback quantum control with deep reinforcement learning was applied to driving a system with double well potential with high fidelity toward the ground state [52]. Feedback control was proposed for controlling a solid-state qubit [47], non-linear systems [48], quantum state manipulation [49], multi-qubit entanglement generation [53], making coupled-qubit-based thermal machines [54], steering to the minimum energy eigenstate of an energy function in variational quantum algorithms [56], etc.…”

Section: Measurement-assisted Quantum Controlmentioning

confidence: 99%

“…Feedback quantum control with deep reinforcement learning was applied to driving a system with double-well potential with high fidelity toward the ground state [56]. Feedback control was proposed for the control of a solid-state qubit [57], non-linear systems [58], quantum state manipulation [59], multi-qubit entanglement generation [60], the formation of coupledqubit-based thermal machines [61], the steering of an energy function to the minimum energy eigenstate in variational quantum algorithms [29], etc. Real-time feedback control can potentially be very powerful but is difficult to realize experimentally due to the need for fast real-time processing of the measurement outcome.…”

Section: Measurement-assisted Quantum Controlmentioning

confidence: 99%

Control Landscape of Measurement-Assisted Transition Probability for a Three-Level Quantum System with Dynamical Symmetry

Elovenkova,

Pechen

2023

Quantum Reports

3

0

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Quantum systems with dynamical symmetries have conserved quantities that are preserved under coherent control. Therefore, such systems cannot be completely controlled by means of only coherent control. In particular, for such systems, the maximum transition probability between some pairs of states over all coherent controls can be less than one. However, incoherent control can break this dynamical symmetry and increase the maximum attainable transition probability. The simplest example of such a situation occurs in a three-level quantum system with dynamical symmetry, for which the maximum probability of transition between the ground and intermediate states using only coherent control is 1/2, whereas it is about 0.687 using coherent control assisted by incoherent control implemented through the non-selective measurement of the ground state, as was previously analytically computed. In this work, we study and completely characterize all critical points of the kinematic quantum control landscape for this measurement-assisted transition probability, which is considered as a function of the kinematic control parameters (Euler angles). The measurement-driven control used in this work is different from both quantum feedback and Zeno-type control. We show that all critical points are global maxima, global minima, saddle points or second-order traps. For comparison, we study the transition probability between the ground and highest excited states, as well as the case when both these transition probabilities are assisted by incoherent control implemented through the measurement of the intermediate state.

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Locally optimal measurement-based quantum feedback with application to multiqubit entanglement generation

Cited by 13 publications

References 47 publications

Pontryagin-optimal control of a non-Hermitian qubit

Pontryagin-optimal control of a non-Hermitian qubit

Pontryagin-Optimal Control of a non-Hermitian Qubit

Control Landscape of Measurement-Assisted Transition Probability for a Three-Level Quantum System with Dynamical Symmetry

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