In circuit-based quantum computing, the available gate set typically consists of single-qubit gates acting on each individual qubit and at least one entangling gate between pairs ofqubits. In certain physical architectures, however, some qubits may be ‚hidden‘ and lacking direct addressability through dedicated control and readout lines, for instance because of limited on-chip routing capabilities, or because the number of control lines becomes a limiting factor for many-qubit systems. In this case, no single-qubit operations can be applied to the hidden qubits and their state cannot be measured directly. Instead, they may be controlled and read out only via single-qubit operations on connected ‚control‘ qubits and a suitable set of two-qubit gates. We first discuss the impact of such restricted control capabilities on the quantum volume of specific qubit coupling networks. We then experimentally demonstrate full control and measurement capabilities in a superconducting two-qubit device with local single-qubit control and iSWAP and controlled-phase two-qubit interactions enabled by a tunable coupler. We further introduce an iterative tune-up process required to completely characterize the gate set used for quantum process tomography and evaluate the resulting gate fidelities.
The possibility to utilize different types of two-qubit gates on a single quantum computing platform adds flexibility in the decomposition of quantum algorithms. A larger hardware-nativegate set may decrease the number of required gates, provided that all gates are realized with high fidelity. Here, we benchmark both controlled-Z (CZ) and exchange-type (iSWAP) gates using a parametrically driven tunable coupler that mediates the interaction between two superconducting qubits. Using randomized benchmarking protocols we estimate an error per gate of 0.9±0.03% and 1.3±0.4% fidelity for the CZ and the iSWAP gate, respectively. We argue that spurious ZZ-type couplings are the dominant error source for the iSWAP gate, and that phase stability of all microwave drives is of utmost importance. Such differences in the achievable fidelities for different two-qubit gates have to be taken into account when mapping quantum algorithms to real hardware.
The speed of quantum gates and measurements is a decisive factor for the overall fidelity of quantum protocols when performed on physical qubits with finite coherence time. Reducingthe time required to distinguish qubit states with high fidelity is therefore a critical goal in quantum information science. The state-of-the-art readout of superconducting qubits is based on the dispersive interaction with a readout resonator. Here, we bring this technique to its current limit and demonstrate how the careful design of system parameters leads to fast and high-fidelity measurements without affecting qubit coherence. We achieve this result by increasing the dispersive interaction strength, by choosing an optimal linewidth of the readout resonator, by employing a Purcell filter, and by utilizing phase-sensitive parametric amplification. In our experiment, we measure 98.25% readout fidelity in only 48 ns, when minimizing read-out time, and 99.2% in 88 ns, when maximizing the fidelity, limited predominantly by the qubit lifetime of 7.6 us. The presented scheme is also expected to be suitable for integration into a multiplexed readout architecture.
A switch capable of routing microwave signals at cryogenic temperatures is a desirable component for state-of-the-art experiments in many fields of applied physics, including but notlimited to quantum information processing, communication and basic research in engineered quantum systems. Conventional mechanical switches provide low insertion loss but disturb operation of dilution cryostats and the associated experiments by heat dissipation. Switches based on semiconductors or microelectromechanical systems have a lower thermal budget but are not readily integrated with current superconducting circuits. Here we design and test an on-chip switch built by combining tunable transmission-line resonators with microwave beam-splitters. The device is superconducting and as such dissipates a negligible amount of heat. It is compatible with current superconducting circuit fabrication techniques, operates with a bandwidth exceeding 100MHz, is capable of handling photon fluxes on the order of 105μs−1, equivalent to powers exceeding −90dBm, and can be switched within approximately 6−8ns. We successfully demonstrate operation of the device in the quantum regime by integrating it on a chip with a single-photon source and using it to route non-classical itinerant microwave fields at the single-photon level.
A quantum system interacting with its environment is subject to dephasing which ultimately destroys the information it holds. Using a superconducting qubit, we experimentally show thatthis dephasing has both dynamic and geometric origins. It is found that geometric dephasing, which is present even in the adiabatic limit and when no geometric phase is acquired, can either reduce or restore coherence depending on the orientation of the path the qubit traces out in its projective Hilbert space. It accompanies the evolution of any system in Hilbert space subjected to noise.
In the circuit quantum electrodynamics architecture, both the resonance frequency and the coupling of superconducting qubits to microwave field modes can be controlled via externalelectric and magnetic fields to explore qubit — photon dynamics in a wide parameter range. Here, we experimentally demonstrate and analyze a scheme for tuning the coupling between a transmon qubit and a microwave resonator using a single coherent drive tone. We treat the transmon as a three-level system with the qubit subspace defined by the ground and the second excited states. If the drive frequency matches the difference between the resonator and the qubit frequency, a Jaynes-Cummings type interaction is induced, which is tunable both in amplitude and phase. We show that coupling strengths of about 10 MHz can be achieved in our setup, limited only by the anharmonicity of the transmon qubit. This scheme has been successfully used to generate microwave photons with controlled temporal shape [Pechal et al., Phys. Rev. X 4, 041010 (2014)] and can be directly implemented with superconducting quantum devices featuring larger anharmonicity for higher coupling strengths.
Coherent generation of single photons with waveforms of a given shape plays an important role in many protocols for quantum information exchange between distant quantum bits. Here wecreate shaped microwave photons in a superconducting system consisting of a transmon circuit coupled to a transmission line resonator. Using the third level of the transmon, we exploit a second-order transition induced by a modulated microwave drive to controllably transfer an excitation to the resonator from which it is emitted into a transmission line as a travelling photon. We demonstrate the single-photon nature of the emitted field and the ability to generate photons with a controlled amplitude and phase. In contrast to similar schemes, the presented one requires only a single control line, allowing for a simple implementation with fixed-frequency qubits.
We make use of a superconducting qubit to study the effects of noise on
adiabatic geometric phases. The state of the system, an effective spin one-half
particle, is adiabatically guidedalong a closed path in parameter space and
thereby acquires a geometric phase. By introducing artificial fluctuations in
the control parameters, we measure the geometric contribution to dephasing for
a variety of noise powers and evolution times. Our results clearly show that
only fluctuations which distort the path lead to geometric dephasing. In a
direct comparison with the dynamic phase, which is path-independent, we observe
that the adiabatic geometric phase is less affected by noise-induced dephasing.
This observation directly points towards the potential of geometric phases for
quantum gates or metrological applications.
Geometric phases, which accompany the evolution of a quantum system and
depend only on its trajectory in state space, are commonly studied in two-level
systems. Here, however, we studythe adiabatic geometric phase in a weakly
anharmonic and strongly driven multi-level system, realised as a
superconducting transmon-type circuit. We measure the contribution of the
second excited state to the two-level geometric phase and find good agreement
with theory treating higher energy levels perturbatively. By changing the
evolution time, we confirm the independence of the geometric phase of time and
explore the validity of the adiabatic approximation at the transition to the
non-adiabatic regime.