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Demonstration of a small programmable quantum computer with atomic qubits


Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths1,2,3,4,5,6,7,8,9,10. Here we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully connected set of gate operations that are native to the hardware and have a mean fidelity of 98 per cent. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch–Jozsa11 and Bernstein–Vazirani12 algorithms with average success rates of 95 and 90 per cent, respectively. We also perform a coherent quantum Fourier transform13,14 on five trapped-ion qubits for phase estimation and period finding with average fidelities of 62 and 84 per cent, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling15 or photonic quantum channels16.

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Figure 1: Computation architecture.
Figure 2: Two-qubit modular gates.
Figure 3: Quantum algorithms.
Figure 4: Quantum Fourier transform protocol.

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  1. Linden, N., Barjat, H. & Freeman, R. An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR quantum computer. Chem. Phys. Lett. 296, 61–67 (1998)

    Article  CAS  ADS  Google Scholar 

  2. Vandersypen, L. M. K. et al. Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883–887 (2001)

    Article  CAS  ADS  Google Scholar 

  3. Gulde, S. et al. Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer. Nature 421, 48–50 (2003)

    Article  CAS  ADS  Google Scholar 

  4. Brainis, E. et al. Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits. Phys. Rev. Lett. 90, 157902 (2003)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  5. Chiaverini, J. et al. Implementation of the semiclassical quantum Fourier transform in a scalable system. Science 308, 997–1000 (2005)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  6. Brickman, K.-A. et al. Implementation of Grover’s quantum search algorithm in a scalable system. Phys. Rev. A 72, 050306(R) (2005)

    Article  ADS  Google Scholar 

  7. DiCarlo, L. et al. Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature 460, 240–244 (2009)

    Article  CAS  ADS  Google Scholar 

  8. Shi, F. et al. Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond. Phys. Rev. Lett. 105, 040504 (2010)

    Article  ADS  Google Scholar 

  9. Martín-López, E. et al. Experimental realization of Shor’s quantum factoring algorithm using qubit recycling. Nat. Photon. 6, 773–776 (2012)

    Article  ADS  Google Scholar 

  10. Monz, T. et al. Realization of a scalable Shor algorithm. Science 351, 1068–1070 (2016)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  11. Deutsch, D. & Jozsa, R. Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553–558 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  12. Bernstein, E. & Vazirani, U. Quantum complexity theory. SIAM J. Comput. 26, 1411–1473 (1997)

    Article  MathSciNet  Google Scholar 

  13. Shor, P. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)

    Article  MathSciNet  Google Scholar 

  14. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information 1st edn (Cambridge Univ. Press, 2002)

  15. Kielpinski, D., Monroe, C. & Wineland, D. J. Architecture for a large-scale ion-trap quantum computer. Nature 417, 709–711 (2002)

    Article  CAS  ADS  Google Scholar 

  16. Monroe, C. et al. Large scale modular quantum computer architecture with atomic memory and photonic interconnects. Phys. Rev. A 89, 022317 (2014)

    Article  ADS  Google Scholar 

  17. Cirac, J. I. & Zoller, P. Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995)

    Article  CAS  ADS  Google Scholar 

  18. Mølmer, K. & Sørensen, A. Multipartite entanglement of hot trapped ions. Phys. Rev. Lett. 82, 1835–1838 (1999)

    Article  ADS  Google Scholar 

  19. Barends, R. et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014)

    Article  CAS  ADS  Google Scholar 

  20. Hill, C. D. et al. A surface code quantum computer in silicon. Sci. Adv. 1, e1500707 (2015)

    Article  ADS  Google Scholar 

  21. Gottesman, D. Fault-tolerant quantum computation with local gates. J. Mod. Opt. 47, 333–345 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  22. Green, T. J. & Biercuk, M. J. Phase-modulated decoupling and error suppression in qubit-oscillator systems. Phys. Rev. Lett. 114, 120502 (2015)

    Article  ADS  Google Scholar 

  23. Ballance, C. J. et al. Laser-driven quantum logic gates with precision beyond the fault-tolerant threshold. Preprint at (2016)

  24. True Merrill, J. et al. Demonstration of integrated microscale optics in surface-electrode ion traps. New J. Phys. 13, 103005 (2011)

    Article  ADS  Google Scholar 

  25. Gaebler, J. P. et al. High-fidelity universal gate set for 9Be+ ion qubits. Preprint at (2016)

  26. Choi, T. et al. Optimal quantum control of multimode couplings between trapped ion qubits for scalable entanglement. Phys. Rev. Lett. 112, 190502 (2014)

    Article  CAS  ADS  Google Scholar 

  27. Olmschenk, S. et al. Manipulation and detection of a trapped Yb+ hyperfine qubit. Phys. Rev. A 76, 052314 (2007)

    Article  ADS  Google Scholar 

  28. Fisk, P. T. H., Sellars, M. J., Lawn, M. A. & Coles, C. Accurate measurement of the 12.6GHz “clock” transition in trapped 171Yb+ ions. IEEE Trans. Ultrasonics Ferroelectrics Frequency 44, 344–354 (1997)

    Article  CAS  Google Scholar 

  29. Hayes, D. et al. Entanglement of atomic qubits using an optical frequency comb. Phys. Rev. Lett. 104, 140501 (2010)

    Article  CAS  ADS  Google Scholar 

  30. Higgins, B. L., Berry, D. W., Bartlett, S. D., Wiseman, H. M. & Pryde, G. J. Entanglement-free Heisenberg-limited phase estimation. Nature 450, 393–396 (2007)

    Article  CAS  ADS  Google Scholar 

  31. Johnson, K. G. et al. Active stabilization of ion trap radiofrequency potentials. Rev. Sci. Instrum. 87, 053110 (2016)

    Article  CAS  ADS  Google Scholar 

  32. Crain, S., Mount, E., Baek, S. & Kim, J. Individual addressing of trapped 171Yb+ ion qubits using a microelectromechanical systems-based beam steering system. Appl. Phys. Lett. 105, 181115 (2014)

    Article  ADS  Google Scholar 

  33. Schiffer, J. P. Phase transitions in anisotropically confined ionic crystals. Phys. Rev. Lett. 70, 818–821 (1993)

    Article  CAS  ADS  Google Scholar 

  34. Zhu, S.-L., Monroe, C. & Duan, L.-M. Trapped ion quantum computation with transverse phonon modes. Phys. Rev. Lett. 97, 050505 (2006)

    Article  ADS  Google Scholar 

  35. Solano, E., de Matos Filho, R. L. & Zagury, N. Deterministic Bell states and measurement of the motional state of two trapped ions. Phys. Rev. A 59, R2539–R2543 (1999)

    Article  CAS  ADS  Google Scholar 

  36. Milburn, G. J., Schneider, S. & James, D. F. V. Ion trap quantum computing with warm ions. Fortschr. Phys. 48, 801–810 (2000)

    Article  CAS  Google Scholar 

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We thank K. R. Brown, J. Kim, T. Choi, Z.-X. Gong, T. A. Manning, D. Maslov and C. Volin for discussions. This work was supported by the US Army Research Office with funds from the IARPA MQCO and LogiQ Programs, the Air Force Office of Scientific Research MURI on Quantum Measurement and Verification, and the National Science Foundation Physics Frontier Center at JQI.

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Authors and Affiliations



S.D., N.M.L, C.F., K.A.L., K.W. and C.M. all contributed to the experimental design, construction, data collection and analysis of this experiment. All authors contributed to this manuscript.

Corresponding author

Correspondence to S. Debnath.

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Competing interests

C.M. is a founding scientist of ionQ, Inc.

Additional information

Reviewer Information Nature thanks S. Bartlett and T. Northup for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Figure 1 Controlled-phase gate.

Shown is the performance of the controlled-phase (CP) gate between control (red) and target (blue) qubit for different qubit-pairs. The control qubit is prepared in the state |1〉 which remains unchanged during the gate. Solid blue lines indicate the theoretical probability of measuring the target qubit in |1〉 whereas the data points show experimental data. Error bars are statistical, indicating a 95% confidence interval for 2,000 experimental repetitions.

Extended Data Table 1 Controlled-NOT gate fidelities
Extended Data Table 2 Controlled-phase gate fidelities
Extended Data Table 3 Input states in QFT-period finding

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Debnath, S., Linke, N., Figgatt, C. et al. Demonstration of a small programmable quantum computer with atomic qubits. Nature 536, 63–66 (2016).

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