Quantum computation presents a powerful new paradigm for information processing. A robust universal quantum computer can be realized with any well controlled quantum system, but a successful platform will ultimately require the combination of highly coherent, error-correctable quantum elements with at least one entangling operation between them1,2. Quantum information stored in a continuous-variable system—for example, a harmonic oscillator—can take advantage of hardware-efficient quantum error correction protocols that encode information in the large available Hilbert space of each element3,4,5. However, such encoded states typically have no controllable direct couplings, making deterministic entangling operations between them particularly challenging. Here we develop an efficient implementation of the exponential-SWAP operation6 and present its experimental realization between bosonic qubits stored in two superconducting microwave cavities. This engineered operation is analogous to the exchange interaction between discrete spin systems, but acts within any encoded subspace of the continuous-variable modes. Based on a control rotation, the operation produces a coherent superposition of identity and SWAP operations between arbitrary states of two harmonic oscillator modes and can be used to enact a deterministic entangling gate within quantum error correction codes. These results provide a valuable building block for universal quantum computation using bosonic modes.
Access optionsAccess options
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
The data that support the findings of this study are available from the corresponding authors on reasonable request.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
We thank R. Filip for helpful discussions; N. Frattini, K. Sliwa, M. J. Hatridge and A. Narla for providing the Josephson parametric converters; and N. Ofek and P. Reinhold for providing the logic and control interface for the field programmable gate array used in this experiment. This research was supported by the US Army Research Office (W911NF-14-1-0011 and W911NF-16-10349). Y.Y.G. was supported by an A∗STAR NSS Fellowship; B.J.L. was supported by a Yale QIMP Fellowship; S.M.G. was supported by the National Science Foundation (DMR-1609326); and L.J. was supported by the Alfred P. Sloan Foundation (BR 2013-049) and the Packard Foundation (2013-39273). Facilities use was supported by the Yale Institute for Nanoscience and Quantum Engineering (YINQE), the Yale SEAS cleanroom, and the National Science Foundation (MRSECDMR-1119826).
Nature thanks Kero Lau and Gheorghe Paraoanu for their contribution to the peer review of this work.