Catch-Disperse-Release Readout for Superconducting Qubits

Abstract

We analyze a single-shot readout for superconducting qubits via the controlled catch, dispersion, and release of a microwave field. A tunable coupler is used to decouple the microwave resonator from the transmission line during the dispersive qubit-resonator interaction, thus circumventing damping from the Purcell effect. We show that if the qubit frequency tuning is sufficiently adiabatic, a fast high-fidelity qubit readout is possible even in the strongly nonlinear dispersive regime. Interestingly, the Jaynes-Cummings nonlinearity leads to the quadrature squeezing of the resonator field below the standard quantum limit, resulting in a significant decrease of the measurement error.PACS numbers: 03.67. Lx, 03.65.Yz, 42.50.Pq, 85.25.Cp A fast high-fidelity qubit readout plays an important role in quantum information processing. For superconducting qubits various nonlinear processes have been used to realize a singleshot readout [1][2][3][4][5][6]. The linear dispersive readout in the circuit quantum electrodynamics (cQED) setup [7,8] became sufficiently sensitive for the single-shot qubit measurement only recently [9,10], with development of near-quantum-limited superconducting parametric amplifiers [9][10][11]. In particular, readout fidelity of 94% for flux qubits [9] and 97% for transmon qubits [10] has been realized (see also [12]). With increasing coherence time of superconducting qubits into 10-100 µs range [13,14], fast high-fidelity readout becomes practically important, for example, for reaching the threshold of quantum error correction codes [15], for which the desired readout time is less than 100 ns, with fidelity above 99%.A significant source of error in the currently available cQED readout schemes is the Purcell effect [16] -the cavityinduced relaxation of the qubit due to the always-on coupling between the resonator and the outgoing transmission line. The Purcell effect can be reduced by increasing the qubit-resonator detuning; however, this reduces the dispersive interaction and increases measurement time. Several proposals to overcome the Purcell effect have been put forward, including the use of the Purcell filter [17] and the use of a Purcell-protected qubit [18]. Here we propose and analyze a cQED scheme which avoids the Purcell effect altogether by decoupling the resonator from the transmission line during the dispersive qubitresonator interaction.Similar to the standard cQED measurement [7][8][9][10], in our method (Fig. 1) the qubit state affects the dispersive shift of the resonator frequency, that in turn changes the phase of the microwave field in the resonator, which is then measured via homodyne detection. However, instead of measuring continuously, we perform a sequence of three operations: "catch", "disperse", and "release" of the microwave field. During the first two stages a tunable coupler decouples the outgoing transmission line from the resonator (we assume using the coupler recently realized in [19]; see also [20]). This automatically eliminates the problems associated with...

Entanglement generated by the dispersive interaction: The dressed coherent state

“…To the best of our knowledge this state was first described in Ref. [10]. Schematic diagrams of the dressed coherent states |g, α and |e, α for |α| (20), and highlight the fact that the dressed coherent state has the same distribution of superposition coefficients as the coherent state, only for the dressed states instead of the bare states.…”

“…In this manuscript, we will show that in the lab frame of the experiment a more accurate description of the joint state is the dressed coherent state |g/e, α [10]. Unlike the description in the dispersive frame, the dressed coherent state of the lab frame is entangled, even if the qubit is not initially in a superposition state.…”

Hybrid phase-space–Fock-space approach to evolution of a driven nonlinear resonator

“…In particular, it can be shown that a nonlinear resonator near the bifurcation point at large photon numbers is equivalent to a degenerate parametric amplifier driven with a detuned pump [33]. Squeezed states can be used to improve measurement accuracy [34,35] in a range of applications, such as gravitational wave detectors [36], superconducting qubit readout [37][38][39][40][41][42], and nano/micromechanical position measurement [11,43,44]. There is currently a significant experimental interest in producing squeezed microwave states with Josephson parametric amplifiers [21,[45][46][47][48][49]; the self-developing squeezing due to the nonlinearity of a microwave resonator (with revival and formation of "cat" states) has also been demonstrated experimentally [50].…”

Perfect squeezing by damping modulation in circuit quantum electrodynamics

“…A catch and release protocol for qubit readout based on the setup of Ref. [16] was already theoretically studied by Sete and co-authors [28].…”

“…If the goal is to improve qubit readout, there is an optimal value of the modulation amplitude where the overlap between the two Wigner functions is minimal. To quantify the state discrimination, we compute the measurement error E = 1 2 dx Min[P 0 (x), P 1 (x)] [28]. In this expression, P i is the marginal of the Wigner function corresponding to |i and integrated along the imaginary axis (see Appendix E).…”