Digitized adiabatic quantum computing with a superconducting circuit

Abstract

Quantum mechanics can help to solve complex problems in physics1 and chemistry2, provided they can be programmed in a physical device. In adiabatic quantum computing3,4,5, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing6, which enables the construction of arbitrary interactions and is compatible with error correction7,8, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation9,10,11,12 of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.

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Figure 1: Spin-chain problem and device.
Figure 2: Quantum state tomography of the digital evolution into a Greenberger–Horne–Zeilinger state.
Figure 3: Kink errors, residual energy and scaling with system size.
Figure 4: Digital evolutions of random stoquastic and non-stoquastic problems.

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Acknowledgements

We acknowledge support from Spanish MINECO FIS2012-36673-C03-02; Ramón y Cajal grant RYC-2012-11391; UPV/EHU UFI 11/55 and EHUA14/04; Basque Government IT472-10; a UPV/EHU PhD grant; and PROMISCE and SCALEQIT EU projects. Devices were made at the UC Santa Barbara Nanofabrication Facility, a part of the NSF-funded National Nanotechnology Infrastructure Network, and at the NanoStructures Cleanroom Facility.

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R. Barends, A.S. and L.L. designed the experiment, with E.S., H.N. and J.M.M. providing supervision and A. Mezzacapo, U.L.H. and R. Babbush providing additional theoretical support. R. Barends, A.S., L.L. and R. Babbush co-wrote the manuscript with E.S., H.N. and J.M.M. R. Barends, A.S. and L.L. performed the experiment and analysed the data. The device was designed by R. Barends and J.K. All authors contributed to the fabrication process, experimental set-up and manuscript preparation.

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Correspondence to R. Barends or A. Shabani.

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The authors declare no competing financial interests.

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Barends, R., Shabani, A., Lamata, L. et al. Digitized adiabatic quantum computing with a superconducting circuit. Nature 534, 222–226 (2016). https://doi.org/10.1038/nature17658

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