Quantum nondemolition-like fast measurement scheme for a superconducting qubit

I. Serban, B. L. T. Plourde, and F. K. Wilhelm

Phys. Rev. B 78, 054507 – Published 12 August 2008

Abstract

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 a 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.

Received 31 March 2008

DOI:https://doi.org/10.1103/PhysRevB.78.054507

Authors & Affiliations

I. Serban^1,2, B. L. T. Plourde³, and F. K. Wilhelm²

¹Physics Department, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-Universität, Theresienstrasse 37, 80333 Munich, Germany
²IQC and Department of Physics and Astronomy, University of Waterloo, 200 University Avenue W, Waterloo, Ontario, Canada N2L 3G1
³Department of Physics, Syracuse University, Syracuse, New York 13244-1130, USA

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Vol. 78, Iss. 5 — 1 August 2008

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Images

Figure 1
(Color online) (a) Simplified circuit consisting of a flux qubit inductively coupled to a SQUID with two identical junctions and shunt capacitance $C_{S}$ . The SQUID is driven by a bias step-like dc pulse $I_{B} (t)$ and the voltage drop $V (t)$ is measured by a device with internal resistance $R$ . (b) Illustration of the measurement scheme: coupling $(t = 0)$ and decoupling $(t = τ)$ of the qubit and the SQUID (oscillator) and the evolution of a point of mass in the transition of potential from one harmonic oscillator to a superposition of two displaced oscillators and back. The dashed (red) and the continuous (green) lines correspond to the different states of the qubit.Reuse & Permissions
Figure 2
(a) Evolution of $⟨ {\hat{σ}}_{z} ⟩$ with qubit initially in $| ↑ ⟩$ state. (b) Dephasing from the $1 / \sqrt{2} (| ↑ ⟩ + | ↓ ⟩)$ state for the time $τ$ that the qubit is in contact with the oscillator. For both plots, the following parameters were used: $Ω / (2 π) = 0.97 GHz$ , $κ / Ω = 10^{- 2}$ , $w = Ω$ , $Ω τ = 1.83$ , $δ τ = 0.015$ , $γ τ = 3$ , and $T = 30 mK$ . The assumed values of the circuit parameters are given in Appendix .Reuse & Permissions
Figure 3
(Color online) Phase space representation of the oscillator trajectories $[⟨ \hat{x} ⟩ (t), ⟨ \hat{p} ⟩ (t), t]$ corresponding to the two qubit states $| ↓ ⟩$ (dashed, red) and $| ↑ ⟩$ (continuous, green) for the parameters given in Appendix an oscillator quality factor of 10, with (a) $K = 0$ and (b) $K \neq 0$ . Projections on the $(x, p)$ , $(x, t)$ , and $(p, t)$ planes are included. Both trajectories start at the origin and move away from it under the influence of the interaction with the qubit. At the point marked with $●$ the interaction is switched off, and the system evolves freely spiraling around the origin. The trajectories circle around each other without crossing.Reuse & Permissions
Figure 4
(Color online) Probability distribution of output voltage (density plot: dark color indicates high and white low density) and expectation value of momentum for the two qubit states $| ↓ ⟩$ (dashed, red) and $| ↑ ⟩$ (continuous, green). Here $Ω / (2 π) = 0.97 GHz$ , $Ω / κ = 20$ , $w = Ω$ , $Ω τ = 1.83$ , $δ τ = 0.015$ , $γ τ = 3$ , and $T = 30 mK$ . The assumed values of the circuit parameters are given in Appendix .Reuse & Permissions
Figure 5
Circuit diagram for SQUID oscillator and qubit, along with reference SQUID oscillator, dual-input gradiometer microstrip amplifier, and a cryogenic high electron mobility transistor (HEMT). Dashed boxes indicate different chips and/or different temperatures.Reuse & Permissions
Figure 6
(Color online) Probability distribution of output voltage (density plot: dark color indicates high and white low density) and expectation value of momentum for the two qubit states $| ↓ ⟩$ (dashed, red) and $| ↑ ⟩$ (continuous, green). Here the contribution of the reference SQUID has been introduced. Parameters: $Ω / (2 π) = 0.97 GHz$ , $Ω / κ = 20$ , $w = Ω$ , $Ω τ = 1.83$ , $δ τ = 0.015$ , $γ τ = 3$ , and $T = 30 mK$ . The assumed values of the circuit parameters are given in Appendix .Reuse & Permissions

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