Superconducting Qubits II: Decoherence

Wilhelm, Frank K.; Storcz, M. J.; Hartmann, Udo; Geller, Michael R.

doi:10.1007/978-1-4020-6137-0_6

Cited by 14 publications

(19 citation statements)

References 73 publications

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“…Then the oscillator serves as a bath for the qubit. To second order in ∆ q , the decay rate of the qubit excited state Γ e has a standard golden rule form [21][22][23][24][25],…”

Section: Golden Rule Qubit Relaxationmentioning

confidence: 99%

Relaxation of a qubit measured by a driven Duffing oscillator

2010

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We investigate the relaxation of a superconducting qubit for the case when its detector, the Josephson bifurcation amplifier, remains latched in one of its two (meta)stable states of forced vibrations. The qubit relaxation rates are different in different states. They can display strong dependence on the qubit frequency and resonant enhancement, which is due to quasienergy resonances. Coupling to the driven oscillator changes the effective temperature of the qubit.

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“…Then the oscillator serves as a bath for the qubit. To second order in ∆ q , the decay rate of the qubit excited state Γ e has a standard golden rule form [21][22][23][24][25],…”

Section: Golden Rule Qubit Relaxationmentioning

confidence: 99%

Relaxation of a qubit measured by a driven Duffing oscillator

2010

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“…This approach is valid at finite temperatures k B T κ and times t 1/ω c [3,47], which is the limit we will discuss henceforth.…”

Section: A the Interaction Phasementioning

confidence: 99%

“…The dynamics of the measurement process can be described by a coupled many-body Hamiltonian, consisting of the system to be measured and the detector with a heat bath component [1,2]. Thus, the measurement process can be investigated using the established tools of quantum mechanics of open systems [3,4,5,6].…”

Section: Introductionmentioning

confidence: 99%

Quantum nondemolition-like fast measurement scheme for a superconducting qubit

2008

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We present a measurement protocol for a flux qubit coupled to a dc-Superconducting QUantum Interference Device (SQUID), representative of any two-state system with a controllable coupling to an harmonic oscillator quadrature, which consists of two steps. First, the qubit state is imprinted onto the SQUID via a very short and strong interaction. We show that at the end of this step the qubit dephases completely, although the perturbation of the measured qubit observable during this step is weak. In the second step, information about the qubit is extracted by measuring the SQUID. This step can have arbitrarily long duration, since it no longer induces qubit errors.

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“…Refs. [15][16][17][18][19][20][21][22]). On the other hand, especially in the context of quantum gates or circuits, we often speak of just an average error channel (or simply "the" error channel) for a given quantum operation, and do not consider it as either random variable or stochastic process.…”

Section: Introductionmentioning

confidence: 99%

Exponential families for Bayesian quantum process tomography

Schultz

2019

Phys. Rev. A

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By associating the Choi matrix form of a completely positive, trace preserving (CPTP) map with a particular space of matrices with orthonormal columns, called a Stiefel manifold, we present a family of parametric probability distributions on the space of CPTP maps that is amenable to Bayesian analysis of process tomography. Using the statistical theory of exponential families, we derive a distribution that has an average Choi matrix as a sufficient statistic, and relate this to data gathered through process tomography. This results in a maximum entropy distribution completely characterized by the average Choi matrix, to our knowledge the first example of a continuous, non-unitary random CPTP map that can capture meaningful prior information about arbitrary errors for use in Bayesian estimation. As specific examples, we show how these distributions can be used for full Bayesian tomography as well as maximum a posteriori (MAP) estimates. These distributions also have relevance in recently proposed importance sampling-based Bayesian procedures for process tomography. As an aside, we show how this Stiefel manifold representation can be used to perform manifold-based optimization that maintains the CP and TP properties along the entire search path without the use of general constraint optimization techniques.

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Superconducting Qubits II: Decoherence

Abstract: Abstract. This is an introduction to elementary decoherence theory as it is typically applied to superconducting qubits.Abbreviations: SQUID -superconducting quantum interference device; qubit -quantum bit; TSS -two state system

Cited by 14 publications

References 73 publications

Relaxation of a qubit measured by a driven Duffing oscillator

Relaxation of a qubit measured by a driven Duffing oscillator

Quantum nondemolition-like fast measurement scheme for a superconducting qubit

Exponential families for Bayesian quantum process tomography

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