Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quantum computing platform
Marc Ganzhorn, Gian Salis, Daniel J. Egger, Andreas Fuhrer, Matthias Mergenthaler, Clemens Müller, P. Müller, Stephan Paredes, Marek Pechal, Max Werninghaus, Stefan Filipp
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-native gate 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% 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 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-native gate 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% 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.
Abstract It is advantageous for any quantum processor to support different classes of two-qubit quantum logic gates when compiling quantum circuits, a property that is typically not present in existing platforms. In particular, access to a gate set that includes support for the CZ-, iSWAP-, and SWAP-type families of gates renders conversions between these gate families unnecessary during compilation, as any two-qubit Clifford gate can be executed using at most one two-qubit gate from this set, plus additional single-qubit gates. We experimentally demonstrate that a SWAP gate can be decomposed into one iSWAP gate followed by one CZ gate, affirming a more efficient compilation strategy over the conventional approach that relies on three iSWAP or three CZ gates to replace a SWAP gate. Our implementation makes use of a superconducting quantum processor design based on fixed-frequency transmon qubits coupled together by a parametrically modulated tunable transmon coupler, extending this platform’s native gate set so that any two-qubit Clifford unitary matrix can be realized using no more than two two-qubit gates and single-qubit gates.
Future quantum information processors require tunable coupling architectures that can produce high-fidelity logical gates between two or more qubits. Parametric coupling is a powerful technique for generating tunable interactions between many qubits. Here, we present a highly flexible parametric coupling scheme with superconducting qubits that provides complete removal of residual Z Z coupling and the implementation of driven SWAP or SWAP-free controlled- Z ( C Z ) gates. Our fully integrated two-dimensional on-chip coupler design is only weakly flux tunable, cancels static linear coupling between the qubits, avoids internal coupler dynamics or excitations, and is extensible to multiqubit circuit-QED systems. Exploring gate fidelity versus gate duration allows us to maximize two-qubit gate fidelity, while providing insights into possible error sources for these gates. Randomized benchmarking over several hours reveals that the parametric SWAP C Z gate achieves an average fidelity of 99.44 ± 0.09 % in a gate duration of 70 ns and that a dispersively driven parametric SWAP-free C Z gate attains an average fidelity of 99.47 ± 0.07 % in only 30 ns. The fidelity remained above this value for over 8 h and peaked twice with a maximum of 99.67 ± 0.14 % . Overall, our parametric approach combines versatility, precision, speed, and high performance in one compact coupler design.
Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable ZZ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off resonantly. We show tunable coupling over 1 order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave cross talk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of 99.43(1)% as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors.
A current bottleneck for quantum computation is the realization of high-fidelity two-qubit quantum operations between two or more quantum bits in arrays of coupled qubits. Gates based on parametrically driven tunable couplers offer a convenient method to entangle multiple qubits by selectively activating different interaction terms in the effective Hamiltonian. Here, we theoretically and experimentally study a superconducting qubit setup with two transmon qubits connected via a capacitively coupled tunable bus. We develop a time-dependent Schrieffer-Wolff transformation and derive analytic expressions for exchange-interaction gates swapping excitations between the qubits (iswap) and for two-photon gates creating and annihilating simultaneous two-qubit excitations (bswap). We find that the bswap gate is generally slower than the more commonly used iswap gate, but features favorable scalability properties with less severe frequency-crowding effects, which typically degrade the fidelity in multiqubit setups. Our theoretical results are backed by experimental measurements as well as exact numerical simulations including the effects of higher transmon levels and dissipation.
Superconducting quantum processors could significantly profit from enhanced connectivity together with precise control of interactions and gates between qubits. Here we investigate plaquettes of four qubits that are coupled via a central tunable coupling circuit, so that not only gates between qubits connected by an edge of the plaquette can be executed but also between qubits across the diagonal. By numerically and analytically analyzing parametrically driven processes, we explore iSWAP-gates between any pair of qubits, also across the diagonal, as well as three-qubit interactions and gates. For experimentally available circuit parameters, we for example find iSWAP-gates with a gate time of 50 ns and 99.9\% fidelity, which is decreased to 99.4\% if two such gates are executed in parallel on disjoint qubit pairs in the plaquette. For three-qubit gates we find fidelities of 95\% fidelity at a gate time of 200 ns.
We experimentally demonstrate a parametric iswap gate in a superconducting circuit based on a tunable coupler for achieving a continuous tunability to eliminate unwanted qubit interactions. We implement the two-qubit iswap gate by applying a fast-flux bias modulation pulse on the coupler to turn on parametric exchange interaction between computational qubits. The controllable interaction can provide an extra degree of freedom to verify the optimal condition for constructing the parametric gate. Aiming to fully investigate error sources of the two-qubit gates, we perform quantum process tomography measurements and numerical simulations as varying static ZZ coupling strength. We quantitatively calculate the dynamic ZZ coupling parasitizing in two-qubit gate operation, and extract the particular gate error from the decoherence, dynamic ZZ coupling, and high-order oscillation terms. Our results reveal that the main gate error comes from the decoherence, while the increase in the dynamic ZZ coupling and high-order oscillation error degrades the parametric gate performance. This approach, which has not yet been previously explored, provides a guiding principle to improve gate fidelity of a parametric iswap gate by suppression of the unwanted qubit interactions. This controllable interaction, together with the parametric modulation technique, is desirable for crosstalk-free multiqubit quantum circuits and quantum simulation applications.