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arXiv:2212.11929

A high on-off ratio beamsplitter interaction for gates on bosonically encoded qubits

Chapman, Benjamin J., Stijn J. de Graaf, Sophia H. Xue, Yaxing Zhang, James D. Teoh, Jacob C. Curtis, Takahiro Tsunoda, Alec Eickbusch, Alexander P. Read, Akshay Koottandavida, Shantanu Mundhada, Luigi Frunzio, Michel Devoret, S. M. Girvin, R. J. Schoelkopf

Published Dec 22, 2022• 0 citations
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Abstract

Encoding a qubit in a high quality superconducting microwave cavity offers the opportunity to perform the first layer of error correction in a single device, but presents a challenge: how can quantum oscillators be controlled while introducing a minimal number of additional error channels? We focus on the two-qubit portion of this control problem by using a 3-wave mixing coupling element to engineer a programmable beamsplitter interaction between two bosonic modes separated by more than an octave in frequency, without introducing major additional sources of decoherence. Combining this with single-oscillator control provided by a dispersively coupled transmon provides a framework for quantum control of multiple encoded qubits. The beamsplitter interaction $g_\text{bs}$ is fast relative to the timescale of oscillator decoherence, enabling over $10^3$ beamsplitter operations per coherence time, and approaching the typical rate of the dispersive coupling $χ$ used for individual oscillator control. Further, the programmable coupling is engineered without adding unwanted interactions between the oscillators, as evidenced by the high on-off ratio of the operations, which can exceed $10^5$. We then introduce a new protocol to realize a hybrid controlled-SWAP operation in the regime $g_{bs}\approxχ$, in which a transmon provides the control bit for the SWAP of two bosonic modes. Finally, we use this gate in a SWAP test to project a pair of bosonic qubits into a Bell state with measurement-corrected fidelity of $95.5\% \pm 0.2\%$.

DOI
10.48550/arxiv.2212.11929

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Encoding a qubit in a high quality superconducting microwave cavity offers the opportunity to perform the first layer of error correction in a single device, but presents a challenge: how can quantum oscillators be controlled while introducing a minimal number of additional error channels? We focus on the two-qubit portion of this control problem by using a 3-wave mixing coupling element to engineer a programmable beamsplitter interaction between two bosonic modes separated by more than an octave in frequency, without introducing major additional sources of decoherence. Combining this with single-oscillator control provided by a dispersively coupled transmon provides a framework for quantum control of multiple encoded qubits. The beamsplitter interaction gbsg_\text{bs}gbs​ is fast relative to the timescale of oscillator decoherence, enabling over 10310^3103 beamsplitter operations per coherence time, and approaching the typical rate of the dispersive coupling χχχ used for individual oscillator control. Further, the programmable coupling is engineered without adding unwanted interactions between the oscillators, as evidenced by the high on-off ratio of the operations, which can exceed 10510^5105. We then introduce a new protocol to realize a hybrid controlled-SWAP operation in the regime gbs≈χg_{bs}\approxχgbs​≈χ, in which a transmon provides the control bit for the SWAP of two bosonic modes. Finally, we use this gate in a SWAP test to project a pair of bosonic qubits into a Bell state with measurement-corrected fidelity of 95.5%±0.2%95.5\% \pm 0.2\%95.5%±0.2%.
Fast, high-fidelity operations between microwave resonators are an important tool for bosonic quantum computation and simulation with superconducting circuits. An attractive approach for implementing these operations is to couple these resonators via a nonlinear converter and actuate parametric processes with RF drives. It can be challenging to make these processes simultaneously fast and high fidelity, since this requires introducing strong drives without activating parasitic processes or introducing additional decoherence channels. We show that in addition to a careful management of drive frequencies and the spectrum of environmental noise, leveraging the inbuilt symmetries of the converter Hamiltonian can suppress unwanted nonlinear interactions, preventing converter-induced decoherence. We demonstrate these principles using a differentially-driven DC-SQUID as our converter, coupled to two high-Q microwave cavities. Using this architecture, we engineer a highly-coherent beamsplitter and fast (~100 ns) swaps between the cavities, limited primarily by their intrinsic single-photon loss. We characterize this beamsplitter in the cavities' joint single-photon subspace, and show that we can detect and post-select photon loss events to achieve a beamsplitter gate fidelity exceeding 99.98%, which to our knowledge far surpasses the current state of the art.
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In continuous-variable quantum computing with qubits encoded in the infinite-dimensional Hilbert space of bosonic modes, it is a difficult task to realize strong and on-demand interactions between the qubits. One option is to engineer a beamsplitter interaction for photons in two superconducting cavities by driving an intermediate superconducting circuit with two continuous-wave drives, as demonstrated in a recent experiment [Gao et al., Phys. Rev. X 8, 021073 (2018)]. Here we show how quantum optimal control theory (OCT) can be used in a systematic way to improve the beamsplitter interaction between the two cavities. We find that replacing the two-tone protocol by a three-tone protocol accelerates the effective beamsplitter rate between the two cavities. The third tone's amplitude and frequency are determined by gradient-free optimization and make use of cavity-transmon sideband couplings. We show how to further improve the three-tone protocol via gradient-based optimization while keeping the optimized drives experimentally feasible. Our work exemplifies how to use OCT to systematically improve practical protocols in quantum information applications.
Bosonic quantum error correction has proven to be a successful approach for extending the coherence of quantum memories, but to execute deep quantum circuits, high-fidelity gates between encoded qubits are needed.To that end, we present a family of error-detectable two-qubit gates for a variety of bosonic encodings.From a new geometric framework based on a "Bloch sphere" of bosonic operators, we construct ZZ L (θ) and exponential-SWAP(θ) gates for the binomial, four-legged cat, dual-rail, and several other bosonic codes.The gate Hamiltonian is simple to engineer, requiring only a programmable beam splitter between two bosonic qubits and an ancilla dispersively coupled to one qubit.This Hamiltonian can be realized in circuit QED hardware with ancilla transmons and microwave cavities.The proposed theoretical framework was developed for circuit QED but is generalizable to any platform that can effectively generate this Hamiltonian.Crucially, one can also detect first-order errors in the ancilla and the bosonic qubits during the gates.We show that this allows one to reach error-detected gate fidelities at the 0.01% level with today's hardware, limited only by second-order hardware errors.
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