In modern circuit QED architectures, superconducting transmon qubits are measured via the state-dependent phase and amplitude shift of a microwave field leaking from a coupled resonator.Determining this shift requires integrating the field quadratures for a nonzero duration, which can permit unwanted concurrent evolution. Here we investigate such dynamical degradation of the measurement fidelity caused by a detuned neighboring qubit. We find that in realistic parameter regimes, where the qubit ensemble-dephasing rate is slower than the qubit-qubit detuning, the joint qubit-qubit eigenstates are better discriminated by measurement than the bare states. Furthermore, we show that when the resonator leaks much more slowly than the qubit-qubit detuning, the measurement tracks the joint eigenstates nearly adiabatically. However, the measurement process also causes rare quantum jumps between the eigenstates. The rate of these jumps becomes significant if the resonator decay is comparable to or faster than the qubit-qubit detuning, thus significantly degrading the measurement fidelity in a manner reminiscent of energy relaxation processes.
The readout fidelity of superconducting transmon and Xmon qubits is partially limited by the qubit energy relaxation through the resonator into the transmission line, which is alsoknown as the Purcell effect. One way to suppress this energy relaxation is to employ a filter which impedes microwave propagation at the qubit frequency. We present semiclassical and quantum analyses for the bandpass Purcell filter realized by E.\ Jeffrey \textit{et al}.\ [Phys.\ Rev.\ Lett.\ 112, 190504 (2014)]. For typical experimental parameters, the bandpass filter suppresses the qubit relaxation rate by up to two orders of magnitude while maintaining the same measurement rate. We also show that in the presence of a microwave drive the qubit relaxation rate further decreases with increasing drive strength.
We analyze the transfer of a quantum state between two resonators connected by a superconducting transmission line. Nearly perfect state-transfer efficiency can be achieved by usingadjustable couplers and destructive interference to cancel the back-reflection into the transmission line at the receiving coupler. We show that the transfer protocol is robust to parameter variations affecting the transmission amplitudes of the couplers. We also show that the effects of Gaussian filtering, pulse-shape noise, and multiple reflections on the transfer efficiency are insignificant. However, the transfer protocol is very sensitive to frequency mismatch between the two resonators. Moreover, the tunable coupler we considered produces time-varying frequency detuning caused by the changing coupling. This detuning requires an active frequency compensation with an accuracy better than 90% to yield the transfer efficiency above 99%.
We apply the method of compressed sensing (CS) quantum process tomography (QPT) to characterize quantum gates based on superconducting Xmon and phase qubits. Using experimental datafor a two-qubit controlled-Z gate, we obtain an estimate for the process matrix χ with reasonably high fidelity compared to full QPT, but using a significantly reduced set of initial states and measurement configurations. We show that the CS method still works when the amount of used data is so small that the standard QPT would have an underdetermined system of equations. We also apply the CS method to the analysis of the three-qubit Toffoli gate with numerically added noise, and similarly show that the method works well for a substantially reduced set of data. For the CS calculations we use two different bases in which the process matrix χ is approximately sparse, and show that the resulting estimates of the process matrices match each ther with reasonably high fidelity. For both two-qubit and three-qubit gates, we characterize the quantum process by not only its process matrix and fidelity, but also by the corresponding standard deviation, defined via variation of the state fidelity for different initial states.
The creation of a quantum network requires the distribution of coherent information across macroscopic distances. We demonstrate the entanglement of two superconducting qubits, separatedby more than a meter of coaxial cable, by designing a joint measurement that probabilistically projects onto an entangled state. By using a continuous measurement scheme, we are further able to observe single quantum trajectories of the joint two-qubit state, confirming the validity of the quantum Bayesian formalism for a cascaded system. Our results allow us to resolve the dynamics of continuous projection onto the entangled manifold, in quantitative agreement with theory.
We analyze the Purcell relaxation rate of a superconducting qubit coupled to a resonator, which is coupled to a transmission line and pumped by an external microwave drive. Consideringthe typical regime of the qubit measurement, we focus on the case when the qubit frequency is significantly detuned from the resonator frequency. Surprisingly, the Purcell rate decreases when the strength of the microwave drive is increased. This suppression becomes significant in the nonlinear regime. In the presence of the microwave drive, the loss of photons to the transmission line also causes excitation of the qubit; however, the excitation rate is typically much smaller than the relaxation rate. Our analysis also applies to a more general case of a two-level quantum system coupled to a cavity.
We describe a method to perform any generalized purity-preserving measurement of a qubit with techniques tailored to superconducting systems. We start with considering two methods forrealizing a two-outcome partial projection: using a thresholded continuous measurement in the circuit QED setup and using an indirect ancilla qubit measurement. Then we decompose an arbitrary purity-preserving two-outcome measurement into single qubit unitary rotations and a partial projection. Finally, we systematically reduce any multiple-outcome measurement to a sequence of two-outcome measurements and unitary operations.
Quantum information systems require high fidelity quantum operations. It is particularly challenging to convert flying qubits to stationary qubits for deterministic quantum networks,since absorbing naturally shaped emission has a maximum fidelity of only 54%. Theoretical protocols reaching 100% efficiency rely upon sculpting the time dependence of photon wavepackets and receiver coupling. Using these schemes, experimental fidelities have reached up to 20% for optical photons and 81% for microwave photons, although with drive pulses much longer than the cavity decay rate. Here, we demonstrate a particularly simple „time reversed“ photon shape and gated receiver with an absorption fidelity of 99.4% and a receiver efficiency of 97.4% for microwave photons. We classically drive a superconducting coplanar waveguide resonator an order of magnitude shorter than the intrinsic decay time. With the fidelity now at the error threshold for fault tolerant quantum communication (96%) and computation (99.4%) and comparable to fidelities of good logic gates and measurements, new designs may be envisioned for quantum communication and computation systems.
We analyze single-shot readout for superconducting qubits via controlled catch, dispersion, and release of a microwave field. A tunable coupler is used to decouple the microwave resonatorfrom 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.