Session W39: Focus Session: Superconducting Qubits: Measurement and Novel Architectures

Parity Protection in Flux-Pairing Qubits

We have studied a novel qubit whose logical states are decoupled from the environment due to parity protection. The flux-pairing qubit (FPQ) is a superconducting loop consisting of a 4$\pi $ periodic Josephson element (a Cooper pair box with the $e$ charge on the central island) and a superinductor [1]. This device is dual to the charge-pairing qubit [2]. The FPQ design suppresses tunneling of single flux lines through the junctions in the Cooper pair box and enforces simultaneous tunneling of pairs of flux lines. The lowest-energy quantum states of the FPQ are encoded in the parity of the magnetic flux quanta inside the loop. Parity protection prohibits the mixing of these states, and reduces both the decay and dephasing rates. We will discuss the experimental aspects of the FPQ optimization and the possibility of fault-tolerant operations with these qubits. \\[4pt] [1] M.T. Bell, I.A. Sadovskyy, L.B. Ioffe, A.Yu. Kitaev, and M.E. Gershenson. \textit{Phys. Rev. Lett.} \textbf{109,} 137003 (2012).\\[0pt] [2] M.T. Bell, J. Paramanandam, L.B. Ioffe, and M.E. Gershenson. \textit{Phys. Rev. Lett.} \textbf{112,} 167001 (2014).   

Adjusting the dc-SQUID working point by a flux trapping loop for readout of gap-tunable flux qubit

When the flux qubit is readout by a dc-SQUID, normally people use a coil to bias both the qubit and the dc-SQUID. However, if the working point of the qubit is located on the bottom or the top of the dc-SQUID's critical current modulation region, the readout is hardly carried out. We insert a flux trapping loop into the readout dc-SQUID. By trapping different numbers of fluxoids in the loop, the flux bias of the dc-SQUID can be changed accordingly, while the flux bias of the qubit changes very little because of the very small mutual inductance between the qubit and the trap loop. This improvement enables us to carry out the readout in the complicate experiments of gap-tunable flux qubit.   

cQED readout error from leakage to a neighboring qubit

In a circuit QED setup, we consider the readout error of a dispersively measured superconducting qubit caused by its coupling to a detuned neighboring qubit. This readout error is significant if the logical qubit is encoded in the bare basis, but can be substantially reduced by encoding the logical qubit in the eigenbasis. The process of measurement leads to quantum jumps in the eigenbasis. As a result, the excitation of the measured qubit may switch between the two qubits at a rate that depends on the qubit-qubit detuning and coupling, as well as the linewidth of the readout resonator. The switching produces readout misidentification error, which cannot be eliminated with a longer measurement. However, we show that this error can be made negligible by using a readout resonator with a sufficiently narrow linewidth.   

Microwave Photon Detection Using an Impedance-Matched $\Lambda$ System

We demonstrate microwave photon detection using an impedance-matched $\Lambda$ system consisting of dressed states in a circuit QED system~$[1, 2]$. When a microwave photon resonant with the $\Lambda$ system is input, it deterministically induces a Raman transition in the system and excites the qubit, enabling its applications to the single photon detection by reading out a qubit state before its relaxation. The resonant microwave pulses with an average photon number of $\sim 0.1$ are applied to the $\Lambda$ system. The qubit state is read out by using a parametric phase-locked oscillator, which enables a fast, single-shot, and non-destructive readout~$[3]$. The photon detection efficiency of $\sim 70\%$ has been achieved. The loss of the efficiency is mainly attributed to the relaxation of the qubit state due to short $T_1$.\\ \\ $[1]$ K. Koshino {\it et al}., Phys. Rev. Lett. {\bf 111}, 153606 (2013).\\ $[2]$ K. Inomata {\it et al}., Phys. Rev. Lett. {\bf 113}, 063604 (2014).\\ $[3]$ Z.~R. Lin {\it et al}., Nat. Commun. {\bf 5}, 4480 (2014).\\   

High-fidelity dispersive readout using squeezed light. Part I

High-fidelity and fast qubit readout is essential for quantum information processing. For interferometric measurements of small static phase shifts, it is well-known that squeezing permits one to surpass the standard quantum limit scaling of imprecision with photon number. We show here how to obtain a similar improvement (and Heisenberg-limited scaling) using squeezed light for qubit measurement in circuit QED. In contrast to the standard problem, the phase shifts here are not small, and are in general time-dependent. We first explain that because of these features, only a limited improvement of measurement fidelity is possible if one uses single-mode squeezed states. We then show that by using two-mode squeezed states in a novel two-cavity geometry, one can achieve a dramatic fidelity enhancement, and true Heisenberg-limited scaling.   

High-fidelity dispersive readout using squeezed light. Part II

Protocols employing squeezed radiation for quantum measurement have been realized in a gamut of systems. The central idea is to squeeze noise associated with the measured observable to enhance the signal-to-noise ratio (SNR) beyond the standard shot noise limit of detection. A similar strategy may be exploited to achieve fast, high-fidelity dispersive readout of superconducting qubits. Nonetheless, most of the reported schemes would require small dispersive shifts and/or encode information in vacuum fluctuations of the output quadrature, limiting their applicability in circuit-QED (cQED). In this talk, I will present further details on a new scheme using two-mode squeezing to dramatically enhance SNR in cQED measurement, in a setup where the qubit couples to two readout modes. I will discuss how the scheme is not limited to small dispersive couplings, and how it is robust even against various imperfections. Details on implementation of this protocol in practical cQED setups will also be discussed.\\[4pt] This work was sponsored by the Army Research Office (ARO) and by the Assistant Secretary of Defense for Research \& Engineering (ASDR\&E). Opinions, interpretations, conclusions and recommendations are those of the author and are not necessarily endorsed by the United States Government   

Optimal Control of Quantum Measurement for Superconducting Phase Qubits

Pulses to steer the time evolution of quantum systems can be designed with optimal control theory. In most cases it is the coherent processes that can be controlled and one optimizes the time evolution towards a target unitary process, sometimes also in the presence of non-controllable incoherent processes. Here we show how to extend the GRAPE algorithm in the case where the incoherent processes are controllable and the target time evolution is a non-unitary quantum channel. We perform a gradient search on a fidelity measure based on Choi matrices. We illustrate our algorithm by optimizing a phase qubit measurement pulse. We show how this technique can lead to large measurement contrast close to 99\%. We also show, within the validity of our model, that this algorithm can produce short 1.4 ns pulses with 98.2\% contrast. Work posted at arXiv:1408.6086, in press at Physical Review A   

Fast Resonator Depopulation with a Simple Measurement Pulse Shape

Recent innovations have enabled fast, accurate qubit readout in the circuit QED architecture, but often it is also important to quickly return the readout resonator to its ground state afterward: any residual photons continue to measure and Stark-shift the qubit, preventing high-fidelity gates. Simply waiting several times the resonator decay constant is inadequate for multi-qubit operations in which some qubits need to be measured and reused while others remain in superpositions, which would lose coherence during this time. Here we demonstrate fast, qubit-state-independent resonator reset using a readout pulse with a simple piecewise-constant envelope. The pulse differs from a square pulse only by the addition of two segments at the end, whose width and amplitude depend on the resonator linewidth and qubit-resonator coupling strength. To quantify the effectiveness of the pulse at resetting the cavity, we extract the residual photon population using a Ramsey experiment performed shortly after the pulse. Comparing the result to that obtained using a square pulse followed by a delay of the same length as the extra segments, we find that the extra segments shorten the total wait time needed to recover high qubit coherence by about 300 ns, more than twice the cavity time constant.   

Adjustable Josephson Coupler for Transmon Qubit Measurement

Transmon qubits are measured via a dispersive interaction with a linear resonator. In order to be scalable this measurement must be fast, accurate, and not disrupt the state of the qubit. Speed is of particular importance in a scalable architecture with error correction as the measurement accounts for substantial portion of the cycle time and waiting time associated with measurement is a major source of decoherence. We have found that measurement speed and accuracy can be improved by driving the qubit beyond the critical photon number $n_{crit} = \frac{\Delta}{4g}$ by a factor of 2-3 without compromising the QND nature of the measurement. While it is expected that such strong drive will cause qubit state transitions, we find that as long as the readout is sufficiently fast, those transitions are negligible, however they grow rapidly with time, and are not described by a simple rate. Measuring in this regime requires parametric amplifiers with very high saturation power, on the order of -105 dBm in order to avoid losing SNR when increasing the power. It also requires a Purcell filter to allow fast ring-up and ring-down. Adjustable couplers can be used to further increase the measurement performance, by switching the dispersive interaction on and off much faster than the cavity ring-down time. This technique can also be used to investigate the dynamics of the qubit cavity interaction beyond the weak dispersive limit $n_{cavity} \geq n_{crit}$ not easily accessible to standard dispersive measurement due to the cavity time constant.   

Quantum analysis of a bandpass Purcell filter for accurate qubit readout

In a circuit QED setup the readout fidelity of a superconducting qubit is partially limited by the qubit relaxation through the resonator into a transmission line, which is also known as the Purcell effect. One way to suppress this effect is to employ a filter, which impedes microwave propagation at the qubit frequency. We present a quantum analysis for the bandpass Purcell filter that was recently realized by E. Jeffrey et al. [PRL 112, 190504 (2014)]. Using experimental parameters, we show that the bandpass filter suppresses the qubit relaxation rate by two orders of magnitude while keeping the measurement rate the same. We also show that in the presence of a microwave drive the qubit relaxation rate further decreases with increasing drive strength.   

Characterizing a Superconducting Resonator with Frequency-Compensated Tunable Coupling

Deterministic quantum state transfer between devices on different chips requires the ability to transfer quantum states between traveling qubits and fixed logic qubits. Reflections must be minimized to avoid energy loss and phase interference; this requires tunable coupling to an inter-chip line while the two devices are at equal frequencies. To achieve this, we present a 6GHz superconducting coplanar resonator with tunable coupling to a 50 Ohm transmission line. We compensate for the resulting shift in resonator frequency by simultaneously tuning a second SQUID. We further demonstrate the device coherence and the ability both to release a single-frequency shaped pulse into the transmission line and to efficiently capture a shaped pulse, prerequisites for efficient inter-chip deterministic quantum state transfer.   

Design of a Tunable 3D Microwave Cavity for Use in Coupling to Quantum Superconducting Circuits

We have designed a tunable 3D cavity system for use with transmon qubits. We use an rf SQUID loop as a variable inductive element that perturbs the cavity modes and produces a shift in the cavity frequency that depends on the flux applied to the loop. Our 3D cavity is made of aluminum and has a lowest mode TE101 frequency of 6.2 GHz. Following a method developed by E. U. Condon, we estimate our cavity to have an effective inductance of 100 nH [1]. Our inductive SQUID loop is made of thermally deposited aluminum on a sapphire substrate, with dimensions 250$\mu$m x 250$\mu$m, which yields an expected geometric inductance of 0.9 nH. We use a single junction in our inductive loop with a critical current of approximately 1$\mu$A. We tune the effective inductance of the loop by using a modulation coil that is well isolated from the cavity at the resonance frequency. \\[4pt] [1] Condon, E. U. Reviews of Modern Physics. Volume 14, Number 4 (1942)   

Scalable architecture for coherent microwave control of weakly anharmonic qubits

As the number of qubits in quantum processors continues to increase in the near future, architectures offering scalability of control signals will be essential. We describe an architecture and prototype for improved scalability in microwave control of weakly anharmonic qubits in quantum processors based on repeated unit cells. We present the scalable architecture and test results on a multi-qubit processor based on circuit quantum electrodynamics.