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.
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.
Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982)
Aspuru-Guzik, A., Dutoi, A. D., Love, P. J. & Head-Gordon, M. Simulated quantum computation of molecular energies. Science 309, 1704–1707 (2005)
Farhi, E., Goldstone, J., Gutmann, S. & Sipser, M. Quantum computation by adiabatic evolution. Preprint at http://arxiv.org/abs/quant-ph/0001106 (2000)
Farhi, E. et al. A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292, 472–475 (2001)
Nishimori, H. Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford Univ. Press, 2001)
Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996)
Bravyi, S. B. & Kitaev, A. Yu. Quantum codes on a lattice with boundary. Preprint at http://arxiv.org/abs/quant-ph/9811052 (1998)
Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012)
Steffen, M. et al. Experimental implementation of an adiabatic quantum optimization algorithm. Phys. Rev. Lett. 90, 067903 (2003)
Lanyon, B. P. et al. Universal digital quantum simulation with trapped ions. Science 334, 57–61 (2011)
Barends, R. et al. Digital quantum simulation of fermionic models with a superconducting circuit. Nat. Commun. 6, 7654 (2015)
Salathé, Y. et al. Digital quantum simulation of spin models with circuit quantum electrodynamics. Phys. Rev. X 5, 021027 (2015)
Bravyi, S., DiVincenzo, D. P., Oliveira, R. I. & Terhal, B. M. The complexity of stoquastic local Hamiltonian problems. Quantum Inf. Comput. 8, 361–385 (2008)
Aharonov, D. et al. Adiabatic quantum computation is equivalent to standard quantum computation. SIAM Rev. 50, 755–787 (2008)
Lloyd, S. & Terhal, B. M. Adiabatic and Hamiltonian computing on a 2D lattice with simple two-qubit interactions. New J. Phys. 18, 023042 (2016)
Crosson, E., Farhi, E., Lin, C. Y.-Y., Lin, H.-H. & Shor, P. Different strategies for optimization using the quantum adiabatic algorithm. Preprint at http://arxiv.org/abs/1401.7320 (2014)
Babbush, R., Love, P. J. & Aspuru-Guzik, A. Adiabatic quantum simulation of quantum chemistry. Sci. Rep. 4, 6603 (2014)
Troyer, M. & Wiese, U.-J. Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations. Phys. Rev. Lett. 94, 170201 (2005)
Boixo, S. et al. Computational multiqubit tunnelling in programmable quantum annealers. Nat. Commun. 7, 10327 (2016)
Bravyi, S. B. & Kitaev, A. Yu. Fermionic quantum computation. Ann. Phys. 298, 210–226 (2002)
Seeley, J. T., Richard, M. J. & Love, P. J. The Bravyi–Kitaev transformation for quantum computation of electronic structure. J. Chem. Phys. 137, 224109 (2012)
Barends, R. et al. Coherent Josephson qubit suitable for scalable quantum integrated circuits. Phys. Rev. Lett. 111, 080502 (2013)
Kelly, J. et al. State preservation by repetitive error detection in a superconducting quantum circuit. Nature 519, 66–69 (2015)
Suzuki, M. Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations. Phys. Lett. A 146, 319–323 (1990)
Barends, R. et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014)
Kibble, T. W. B. Some implications of a cosmological phase transition. Phys. Rep. 67, 183–199 (1980)
Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985)
Wiebe, N., Berry, D., Hoyer, P. & Sanders, B. C. Higher order decompositions of ordered operator exponentials. J. Phys. A 43, 065203 (2010)
Berry, D., Childs, A. M., Cleve, R., Kothari, R. & Somma, R. D. Simulating Hamiltonian dynamics with a truncated Taylor series. Phys. Rev. Lett. 114, 090502 (2015)
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.
The authors declare no competing financial interests.
About this article
Cite this article
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
Physical Review Letters (2020)
Reports on Progress in Physics (2020)
New Journal of Physics (2020)
Topological phase transitions, Majorana modes, and quantum simulation of the Su–Schrieffer–Heeger model with nearest-neighbor interactions
Physical Review B (2020)
Physical Review A (2020)