Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect

Gambetta, Jay; Blais, Alexandre; Boissonneault, Maxime; Houck, Andrew; Schuster, David I.; Girvin, S. M.

doi:10.1103/physreva.77.012112

Cited by 266 publications

(444 citation statements)

References 52 publications

(129 reference statements)

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“…As shown in Refs. [13,27] this can be done in the limit γ 1j κ, which is easily satisfied with current Purcell limited qubits 28 . In a frame of reference given by the transformation…”

Section: The Model a Effective Two Qubit Stochastic Master Equamentioning

confidence: 99%

High-fidelity feedback-assisted parity measurement in circuit QED

Tornberg

Johansson

2010

Phys. Rev. A

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We analyze a two qubit parity measurement based on dispersive read-out in circuit quantum electrodynamics. The back-action on the qubits has two qualitatively different contributions. One is an unavoidable dephasing in one of the parity subspaces, arising during the transient time of switching on the measurement. The other part is a stochastic rotation of the phase in the same subspace, which persists during the whole measurement. The latter can be determined from the full measurement record, using the method of state estimation. Our main result is that the outcome of this phase determination process is independent of the initial state in the state estimation procedure. The procedure can thus be used in a measurement situation, where the initial state is unknown. We discuss how this feed-back method can be used to achieve a high fidelity parity measurement for realistic values of the cavity-qubit coupling strength. Finally, we discuss the robustness of the feed-back procedure towards errors in the measurement record.

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“…As shown in Refs. [13,27] this can be done in the limit γ 1j κ, which is easily satisfied with current Purcell limited qubits 28 . In a frame of reference given by the transformation…”

Section: The Model a Effective Two Qubit Stochastic Master Equamentioning

confidence: 99%

High-fidelity feedback-assisted parity measurement in circuit QED

Tornberg

Johansson

2010

Phys. Rev. A

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“…This results in a qubit-state dependent shift of the cavity mode frequency. By applying a microwave tone to a single cavity mode, one can infer the qubit state from the phase of the reflected signal 16 ; this readout scheme has been used extensively with superconducting qubits for quantum information processing, and also to perform weak measurements 17 and track quantum trajectories of a single qubit 18 . In our configuration, each cavity mode constitutes a measurement channel which extracts the projection of the qubit spin along the σ z axis of the Bloch sphere.…”

mentioning

confidence: 99%

Quantum dynamics of simultaneously measured non-commuting observables

Hacohen-Gourgy

Martin

Flurin

et al. 2016

Nature

143

181

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In quantum mechanics, measurements cause wavefunction collapse that yields precise outcomes, whereas for non-commuting observables such as position and momentum Heisenbergs uncertainty principle limits the intrinsic precision of a state.Although theoretical work 1 has demonstrated that it should be possible to perform simultaneous non-commuting measurements and has revealed the limits on measurement outcomes, only recently 2,3 has the dynamics of the quantum state been discussed. To realize this unexplored regime, we simultaneously apply two continuous quantum non-demolition probes of non-commuting observables to a superconducting qubit. We implement multiple readout channels by coupling the qubit to multiple modes of a cavity. To control the measurement observables, we implement a single quadrature measurement by driving the qubit and applying cavity sidebands with a relative phase that sets the observable. Here, we use this approach to show that the uncertainty principle governs the dynamics of the wavefunction by enforcing a lower bound on the measurement-induced disturbance. Consequently, as we transition from measuring identical to measuring non-commuting observables, the dynamics make a smooth transition from standard wavefunction collapse to localized persistent diffusion and then to isotropic persistent diffusion. Although the evolution of the state differs markedly from that of a conventional measurement, information about both non-commuting observables is extracted by keeping track of the time ordering of the measurement record, enabling quantum state tomography without alternating measurements. Our work creates novel capabilities for quantum control, including rapid state purification 4 , adaptive measurement 5,6 , measurement-based state steering and continuous quantum error correction 7 . As physical systems often interact continuously with their environment via non-commuting degrees of freedom, our work offers a way 8,9 to * shayhh@berkeley.edushayhh@berkeley.edu study how notions of contemporary quantum foundations 10-14 arise in such settings.In this work, we implement two high quantum efficiency readouts of the angular momenta about two different axes of an artificial spin-1/2 system and observe in real-time the resulting dynamics. Importantly, our measurements are designed to be individually quantum non-demolition, which ensures that the back-action arises only from the competition between incompatible observables.Our experiment utilizes a single superconducting transmon qubit coupled dispersively to a multimode waveguide cavity 15 . This results in a qubit-state dependent shift of the cavity mode frequency. By applying a microwave tone to a single cavity mode, one can infer the qubit state from the phase of the reflected signal 16 ; this readout scheme has been used extensively with superconducting qubits for quantum information processing, and also to perform weak measurements 17 and track quantum trajectories of a single qubit 18 . In our configuration, each cavity mode constitutes a measure...

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“…Third, the desirable operation U y1 could be constructed as: U y1 = exp(iπσ y1 /4) = exp(iπσ z1 /4) exp(i3πσ x1 /4) exp(i3πσ z1 /4). It should be pointed out that the durations t x (or t y ) of the single-qubit operations required above for implementing the desirable tomographies is estimated as ∼ 100ps using the experimental parameters: ǫ ∼ 2π ×20MHz [18], and ∆ dr ∼ κ/2 [24]. This is significantly less by at least two orders than the qubit decoherence time, which is measured as ∼ 500ns [24].…”

Section: B Tomographic Reconstruction Of a Single-qubit Statementioning

confidence: 98%

“…In recent years, the QND measurement has also been successfully applied to probe the atomic qubits in the cavity quantum electrodynamics (QED) [12,13]. Furthermore, this technique was extensively used to the circuit QED systems [14][15][16][17][18][19][20] for nondestructively reading out the superconducting qubits. This QND measurement is implemented by measuring the transmission of the driven microwave signals through a transmission line resonator, which is dispersively coupled to the detected qubits.…”

Section: Introductionmentioning

confidence: 99%

“…Thus by detecting the signals of the shifted frequency of the resonator, the qubit state will be read out. However, the QND measurements in the above works [14][15][16][17][18][19][20] are only utilized to effectively distinguish the different logic states of the detected qubit(s), which is (are) not prepared initially at their superposed state.…”

Section: Introductionmentioning

confidence: 99%

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High-efficiency tomographic reconstruction of quantum states by quantum nondemolition measurements

Huang¹,

Wei²,

Oh³

2011

Phys. Rev. A

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We propose a high efficiency tomographic scheme to reconstruct an unknown quantum state of the qubits by using a series of quantum nondemolition (QND) measurements. The proposed QND measurements of the qubits are implemented by probing the the stationary transmissions of the dispersively-coupled resonator. It is shown that only one kind of QND measurements is sufficient to determine all the diagonal elements of the density matrix of the detected quantum state. The remaining non-diagonal elements of the density matrix can be determined by other spectral measurements by beforehand transferring them to the diagonal locations using a series of unitary operations. Compared with the pervious tomographic reconstructions based on the usual destructively projective (DP) measurements (wherein one kind of such measurements could only determine one diagonal element of the density matrix), the present approach exhibits significantly high efficiency for N -qubit (N > 1). Specifically, our generic proposal is demonstrated by the experimental circuit-quantumelectrodynamics (circuit-QED) systems with a few Josephson charge qubits.

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Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect

Cited by 266 publications

References 52 publications

High-fidelity feedback-assisted parity measurement in circuit QED

High-fidelity feedback-assisted parity measurement in circuit QED

Quantum dynamics of simultaneously measured non-commuting observables

High-efficiency tomographic reconstruction of quantum states by quantum nondemolition measurements

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