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arXiv:1706.06562 · Physical Review Applied

Parametrically Activated Entangling Gates Using Transmon Qubits

Sam Caldwell, Nicolas Didier, Colm A. Ryan, Eyob Alebachew Sete, A. Hudson, Peter J. Karalekas, Riccardo Manenti, Marcus Palmer Da Silva, R. Sinclair, Ezer Acala, Nasser Alidoust, Jorge Angeles, Andrew J. Bestwick, Maxwell Block, Benjamin Bloom, A. Bradley, Cat-Vu H. Bui, Lauren Capelluto, Rick Chilcott, Jeff Cordova, Genya Crossman, M. Curtis, Saniya Deshpande, Tristan Ossama El Bouayadi, Daniel Girshovich, Sabrina Hong, Kat Kuang, Michael Lenihan, T. Manning, A. Marchenkov, Jayss Marshall, R. Maydra, Yuvraj Mohan, W. O’Brien, Chris Osborn, Johannes Otterbach, Alexander T. Papageorge, Jean-Philip Paquette, Michael Pelstring, Anthony Polloreno, Guen Prawiroatmodjo, Vijay Rawat, Matthew J. Reagor, Russ Renzas, Nick Rubin, Damon S. Russell, Michael Rust, Diego Scarabelli, Michael G. Scheer, Michael Selvanayagam, Robert Smith, A. Staley, Mark Suska, Nikolas Tezak, Dane C. Thompson, T.-W. To, Mehrnoosh Vahidpour, Nagesh Vodrahalli, Tyler Whyland, Kamal Yadav, William J. Zeng, Chad T. Rigetti

Published Sep 24, 2018• 206 citations

Abstract

A central challenge in building a scalable quantum computer with superconducting qubits is the execution of high-fidelity two-qubit gates in the presence of many resonant elements. As more elements are added to the architecture, and as the multiplicity of their couplings grows, the design's frequency space becomes crowded, and performance suffers. The authors present a way to address this difficulty: selective activation of interactions between transmon qubits of fixed frequency and those of tunable frequency. This activation depends on both the amplitude and frequency of modulation, and using the amplitude as an additional condition for resonance alleviates frequency crowding.

DOI: 10.1103/physrevapplied.10.034050

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A central challenge in building a scalable quantum computer with superconducting qubits is the execution of high-fidelity two-qubit gates in the presence of many resonant elements. As more elements are added to the architecture, and as the multiplicity of their couplings grows, the design's frequency space becomes crowded, and performance suffers. The authors present a way to address this difficulty: selective activation of interactions between transmon qubits of fixed frequency and those of tunable frequency. This activation depends on both the amplitude and frequency of modulation, and using the amplitude as an additional condition for resonance alleviates frequency crowding.

High-fidelity parametric gates have been demonstrated with superconducting qubits via rf flux modulation of the qubit frequency. The modulation however leads to renormalization of the bare qubit-qubit coupling, thereby reducing the gate speed. Here, we realize a parametric-resonance gate, which is activated by bringing the average frequency of the modulated qubit in resonance with a static-frequency qubit while approximately retaining the bare qubit-qubit coupling. The activation of parametric-resonance gates does not depend on the frequency of modulation, allowing us to choose the modulation frequencies and avoid frequency collisions. Moreover, we show that this approach is compatible with tunable coupler architectures, which reduce always-on residual couplings. Using these techniques, we demonstrate iswap and controlled-

Z

gates between two qubits coupled via a tunable coupler with average process fidelities as high as $99.3\mathrm{%}$ and $97.9\mathrm{%}$, respectively. The flexibility in activating parametric-resonance gates combined with a tunable coupler architecture provides a pathway for building large-scale quantum computers.

The authors address a critical scalability issue in quantum computer design by activating a resonant exchange interaction. They achieve this by coupling two fixed-frequency superconducting qubits with a bus that is modulated at the frequency difference between the qubits. This yields a high-fidelity iSWAP entangling gate, which is sought as an important component for fault-tolerant quantum circuits in the surface-code architecture. The general nature of the interaction also suggests applications in quantum simulation, annealing, and bath engineering.

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.

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 one 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 crosstalk. 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.

High-performance two-qubit gates have been reported with superconducting qubits coupled via a single-transmon coupler (STC). Most of them are implemented for qubits with a small detuning since reducing residual ZZ coupling for highly detuned qubits by an STC is challenging. In terms of the frequency crowding and crosstalk, however, highly detuned qubits are desirable. Here, we numerically demonstrate a high-performance parametric gate for highly detuned fixed-frequency qubits using a recently proposed tunable coupler called a double-transmon coupler (DTC). Applying an ac flux pulse, we can perform a maximally entangling universal gate (iSWAP) with an average fidelity over 99.99% and a short gate time of about 24 ns. This speed is comparable to resonance-based gates for slightly detuned tunable qubits. Moreover, using a dc flux pulse alternatively, we can achieve another kind of entangling gate called a CZ gate with an average fidelity over 99.99% and a gate time of about 18 ns. Given the flexibility and feasible settings, we can expect that the DTC will contribute towards realizing a high-performance quantum computer in the near future.

All-microwave control of fixed-frequency superconducting quantum systems offers the potential to reduce control circuit complexity and increase system coherence. Nevertheless, due to the limited control flexibility in qubit parameters, one has to address several issues, such as quantum crosstalk and frequency crowding, for scaling up qubit architecture with nontunable elements. This paper proposes a microwave-activated two-qubit gate scheme for two fixed-frequency transmon qubits coupled via a fixed-frequency transmon coupler. The protocol relies on applying a microwave pulse exclusively to the coupler, enabling the implementation of a controlled-

Z

gate. We show that the gate fidelity exceeding 0.999 can be achieved within 150 ns, excluding decoherence effects. Moreover, we also show that leakage from the computational subspace to noncomputational states can also be effectively suppressed.