Linear feedback stabilization of a dispersively monitored qubit

L., Patti, Taylor; Chantasri, Areeya; García-Pintos, Luis Pedro; Jordan, Andrew N.; Dressel, Justin

doi:10.1103/physreva.96.022311

Cited by 18 publications

(21 citation statements)

References 67 publications

(160 reference statements)

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“…Since the dynamics is no longer Markovian, it is necessary to simulate the stochastic master equation ( 9) explicitly [77] and average over many trajectories. We find that the effect of time delay in the feedback loop is negligible so long as Γτ 1, in accordance with previous studies [50]. As the time delay τ increases, shot-to-shot fluctuations grow and attaining numerical convergence of the trajectory average becomes increasingly demanding.…”

Section: Effect Of Feedback Delaysupporting

confidence: 91%

“…Here, we propose an alternative route based on continuous weak measurements and feedback control. This effectively recasts the problem of dissipative bat-tery charging as a feedback stabilisation protocol [47][48][49][50]. More precisely, we consider a homodyne-like measurement scheme, which leads to a dynamical description in terms of diffusive quantum trajectories [51?…”

Section: Introductionmentioning

confidence: 99%

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Charging a quantum battery with linear feedback control

Mitchison

Goold

Prior

2021

Quantum

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Energy storage is a basic physical process with many applications. When considering this task at the quantum scale, it becomes important to optimise the non-equilibrium dynamics of energy transfer to the storage device or battery. Here, we tackle this problem using the methods of quantum feedback control. Specifically, we study the deposition of energy into a quantum battery via an auxiliary charger. The latter is a driven-dissipative two-level system subjected to a homodyne measurement whose output signal is fed back linearly into the driving field amplitude. We explore two different control strategies, aiming to stabilise either populations or quantum coherences in the state of the charger. In both cases, linear feedback is shown to counteract the randomising influence of environmental noise and allow for stable and effective battery charging. We analyse the effect of realistic control imprecisions, demonstrating that this good performance survives inefficient measurements and small feedback delays. Our results highlight the potential of continuous feedback for the control of energetic quantities in the quantum regime.

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Section: Effect Of Feedback Delaysupporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Charging a quantum battery with linear feedback control

Mitchison

Goold

Prior

2021

Quantum

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“…(For an alternative recent derivation of a simple continuous measurement model that includes some of these nonidealities in the context of feedback, see also Ref. [58]. )…”

Section: Observable Dynamics From Anterior Measurementsmentioning

confidence: 99%

“…In the continuum limit as dt → 0 and N → ∞, keeping T = N dt constant, the unitary and measurement operators will commute up to second order in dt such that each pair of operators M rj U effectively describe the evolution within the same time step [t j , t j + dt), and the evolution in Eq. (6) becomes equivalent to a stochastic master equation [33,38,39,58] that describes truly continuous-in-time observable monitoring. In what follows, however, we retain the explicitly discrete time steps dt for numerical stability and conceptual clarity.…”

Section: Observable Dynamics From Anterior Measurementsmentioning

confidence: 99%

Past observable dynamics of a continuously monitored qubit

García-Pintos

Dressel

2017

Phys. Rev. A

Self Cite

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Monitoring a quantum observable continuously in time produces a stochastic measurement record that noisily tracks the observable. For a classical process such noise may be reduced to recover an average signal by minimizing the mean squared error between the noisy record and a smooth dynamical estimate. We show that for a monitored qubit this usual procedure returns unusual results. While the record seems centered on the expectation value of the observable during causal generation, examining the collected past record reveals that it better approximates a moving-mean Gaussian stochastic process centered at a distinct (smoothed) observable estimate. We show that this shifted mean converges to the real part of a generalized weak value in the time-continuous limit without additional postselection. We verify that this smoothed estimate minimizes the mean squared error even for individual measurement realizations. We go on to show that if a second observable is weakly monitored concurrently, then that second record is consistent with the smoothed estimate of the second observable based solely on the information contained in the first observable record. Moreover, we show that such a smoothed estimate made from incomplete information can still outperform estimates made using full knowledge of the causal quantum state.Over the past decade, time-continuous quantum measurements [1-9] of superconducting qubits (such as transmons [10]) have become an important and increasingly well-controlled component of emerging quantum computing technology . Indeed, the primary method for extracting information from a superconducting transmon is to dispersively couple it to a pumped microwave resonator, then amplify and mix the leaked microwave field with a local oscillator to perform a homodyne measurement of the traveling field, which produces a stochastic time-dependent voltage that encodes information about the transmon energy basis [33][34][35]. Understanding what information is contained in the resulting stochastic readout is thus an essential theoretical issue.In simple terms, a continuous measurement can be understood as a sequence of weak measurements [36,37] on the qubit. In the superconducting case, each temporal segment of the steady-state traveling coherent microwave field acts as an independent and approximately Gaussian meter that becomes entangled with the qubit and later measured [35]. During the measurement of the field, the finite bandwidth of the circuitry typically discretizes the field into time bins of size dt. Provided that dt is longer than the correlation timescale of the traveling field, the statistics of the averaged homodyne voltage collected in each independent time bin are approximately Gaussian, producing a discrete temporal sequence of Gaussian-distributed measurement results {r j } with a wide variance that inversely depends upon the time step size dt. All information about the qubit must be extracted by processing this stochastic time series.For convenience, this time series is traditionally interpolated ...

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“…Observing such a signal r induces a partial state collapse that has the form of a hyperbolic boost matrix [65,66],…”

mentioning

confidence: 99%

Monitoring fast superconducting qubit dynamics using a neural network

Koolstra¹,

Stevenson²,

Barzili³

et al. 2021

Preprint

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Weak measurements of a superconducting qubit produce noisy voltage signals that are weakly correlated with the qubit state. To recover individual quantum trajectories from these noisy signals, traditional methods require slow qubit dynamics and substantial prior information in the form of calibration experiments. Monitoring rapid qubit dynamics, e.g. during quantum gates, requires more complicated methods with increased demand for prior information. Here, we experimentally demonstrate an alternative method for accurately tracking rapidly driven superconducting qubit trajectories that uses a Long-Short Term Memory (LSTM) artificial neural network with minimal prior information. Despite few training assumptions, the LSTM produces trajectories that include qubit-readout resonator correlations due to a finite detection bandwidth. In addition to revealing rotated measurement eigenstates and a reduced measurement rate in agreement with theory for a fixed drive, the trained LSTM also correctly reconstructs evolution for an unknown drive with rapid modulation. Our work enables new applications of weak measurements with faster or initially unknown qubit dynamics, such as the diagnosis of coherent errors in quantum gates.

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Linear feedback stabilization of a dispersively monitored qubit

Cited by 18 publications

References 67 publications

Charging a quantum battery with linear feedback control

Charging a quantum battery with linear feedback control

Past observable dynamics of a continuously monitored qubit

Monitoring fast superconducting qubit dynamics using a neural network

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