Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback

Vijay, R.; Macklin, Chris; Slichter, Daniel; Weber, Steven; Murch, Kater; Naik, Ravi; Korotkov, Alexander N.; Siddiqi, Irfan

doi:10.1038/nature11505

Cited by 458 publications

(523 citation statements)

References 27 publications

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“…These results points to both the Kerr nonlinearity and the non-optimal choice of measurement phase as a possible explanation for a series of experiments that have reported smaller than expected quantum efficiencies for JPAs [17,29,31,32]. A more detailed experimental study of the quantum efficiency as a function of both detuning and measurement phase could confirm these results and would allow for a better understanding of these nonlinear effects.…”

Section: Phase-sensitive Quantum Efficiencymentioning

confidence: 70%

“…This correction also leads to non-Gaussian signatures observed both in the intracavity field Wigner function and the fourth order cumulants of the output field. Our combined numerical and experimental results allow to explain a broad range of experimental observations, such as the smaller than expected quantum efficiency of the JPA [17,29,31,32], the saturation and decrease of squeezing at high gain in JPAs [14,15,28,29], and nonGaussian signatures of the output field [15,28]. In particular, this work presents a new experimental characterization of the output field of a flux-driven JPA, as well as a direct experimental imaging of the non-Gaussian distortions of the output field.…”

Section: Discussionmentioning

confidence: 90%

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Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

et al. 2017

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Single-mode Josephson junction-based parametric amplifiers are often modeled as perfect amplifiers and squeezers. We show that, in practice, the gain, quantum efficiency, and output field squeezing of these devices are limited by usually neglected higher-order corrections to the idealized model. To arrive at this result, we derive the leading corrections to the lumped-element Josephson parametric amplifier of three common pumping schemes: monochromatic current pump, bichromatic current pump, and monochromatic flux pump. We show that the leading correction for the last two schemes is a single Kerr-type quartic term, while the first scheme contains additional cubic terms. In all cases, we find that the corrections are detrimental to squeezing. In addition, we show that the Kerr correction leads to a strongly phase-dependent reduction of the quantum efficiency of a phase-sensitive measurement. Finally, we quantify the departure from ideal Gaussian character of the filtered output field from numerical calculation of third and fourth order cumulants. Our results show that, while a Gaussian output field is expected for an ideal Josephson parametric amplifier, higher-order corrections lead to non-Gaussian effects which increase with both gain and nonlinearity strength. This theoretical study is complemented by experimental characterization of the output field of a flux-driven Josephson parametric amplifier. In addition to a measurement of the squeezing level of the filtered output field, the Husimi Q-function of the output field is imaged by the use of a deconvolution technique and compared to numerical results. This work establishes nonlinear corrections to the standard degenerate parametric amplifier model as an important contribution to Josephson parametric amplifier's squeezing and noise performance.

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Section: Phase-sensitive Quantum Efficiencymentioning

confidence: 70%

Section: Discussionmentioning

confidence: 90%

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

et al. 2017

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“…The time local measurement averaging results in a Markovian feedback that is applicable to both discrete and continuous time implementation. In the continuous time limit, the optimal ASLO quantum feedback becomes equivalent to simple proportional feedback, which is easily modelled using a Wiseman-Milburn equation [5,41] and which may be realized in an autonomous fashion in experiments using a mixer (multiplier) [8]. The ASLO strategy was then used to develop a discrete time step, semiclassical protocol, suitable for low measurement efficiencies and large time steps, in which only the classical probabilities for being in the entangled or unentangled states are taken into account.…”

Section: Resultsmentioning

confidence: 99%

Deterministic generation of remote entanglement with active quantum feedback

Martin¹,

Motzoi²,

Li³

et al. 2015

Phys. Rev. A

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We consider the task of deterministically entangling two remote qubits using joint measurement and feedback, but no directly entangling Hamiltonian. In order to formulate the most effective experimentally feasible protocol, we introduce the notion of average sense locally optimal (ASLO) feedback protocols, which do not require real-time quantum state estimation, a difficult component of real-time quantum feedback control. We use this notion of optimality to construct two protocols which can deterministically create maximal entanglement: a semiclassical feedback protocol for low efficiency measurements and a quantum feedback protocol for high efficiency measurements. The latter reduces to direct feedback in the continuous-time limit, whose dynamics can be modeled by a Wiseman-Milburn feedback master equation which yields an analytic solution in the limit of unit measurement efficiency. Our formalism can smoothly interpolate between continuous-time and discrete-time descriptions of feedback dynamics, and we exploit this feature to then derive a superior hybrid protocol for arbitrary non-unit measurement efficiency that switches between quantum and semiclassical protocols. Finally, we show using simulations incorporating experimental imperfections that deterministic entanglement of remote superconducting qubits may be achieved with current technology using the continuous-time feedback protocol alone.

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“…An alternative strategy, inspired by the success of classical control, is feedback control [5]. Because of the complications introduced by quantum measurement [6], closed-loop control is less pervasive in the quantum settings and, with exceptions [7,8], its experimental implementations have been mainly limited to quantum optics experiments. Here we implement a feedback control algorithm with a solid-state spin qubit system associated with the Nitrogen Vacancy (NV) centre in diamond, using coherent feedback [9] to overcome limitations of measurement-based feedback, and show that it can protect the qubit against intrinsic dephasing noise for milliseconds.…”

mentioning

confidence: 99%

Coherent feedback control of a single qubit in diamond

Hirose

Cappellaro

2016

Nature

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Engineering desired operations on qubits subjected to the deleterious effects of their environment is a critical task in quantum information processing, quantum simulation and sensing. The most common approach is to rely on open-loop quantum control techniques, including optimal control algorithms, based on analytical [1] or numerical [2] solutions, Lyapunov design [3] and Hamiltonian engineering [4]. An alternative strategy, inspired by the success of classical control, is feedback control [5]. Because of the complications introduced by quantum measurement [6], closed-loop control is less pervasive in the quantum settings and, with exceptions [7,8], its experimental implementations have been mainly limited to quantum optics experiments. Here we implement a feedback control algorithm with a solid-state spin qubit system associated with the Nitrogen Vacancy (NV) centre in diamond, using coherent feedback [9] to overcome limitations of measurement-based feedback, and show that it can protect the qubit against intrinsic dephasing noise for milliseconds. In coherent feedback, the quantum system is connected to an auxiliary quantum controller (ancilla) that acquires information about the system's output state (by an entangling operation) and performs an appropriate feedback action (by a conditional gate). In contrast to open-loop dynamical decoupling (DD) techniques [10], feedback control can protect the qubit even against Markovian noise and for an arbitrary period of time (limited only by the ancilla coherence time), while allowing gate operations. It is thus more closely related to Quantum Error Correction schemes [11][12][13][14], which however require larger and increasing qubit overheads. Increasing the number of fresh ancillas allows protection even beyond their coherence time. We can further evaluate the robustness of the feedback protocol, which could be applied to quantum computation and sensing, by exploring an interesting tradeoff between information gain and decoherence protection, as measurement of the ancilla-qubit correlation after the feedback algorithm voids the protection, even if the rest of the dynamics is unchanged.To demonstrate coherent feedback with spin qubits, we choose two of the most common tasks for qubits, implementing the no-operation (NOOP) and NOT gates, while cancelling the effects of noise. A simple, measurementbased feedback scheme, exploiting one ancillary qubit, was proposed in [16]. The correction protocol (Fig. 1a) works by entangling the qubit-ancilla system before the desired gate operation. By selecting an entangling operation U c appropriate for the type of bath acting on the system, information about the noise action is encoded in the ancilla state. After undoing the entangling operation, the qubit coherence can be restored by a feedback action, Hadamard gates prepare and read out a superposition state of the qubit, |φ q = 1 √ 2 (|0 + |1 ). Amid entangling gates between qubit and ancilla, the qubit is subjected to noise (and possibly unitary gates U ). We assume the ancil...

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Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback

Cited by 458 publications

References 27 publications

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

Deterministic generation of remote entanglement with active quantum feedback

Coherent feedback control of a single qubit in diamond

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