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.
Your institute does not have access to this article
Open Access articles citing this article.
Frontiers of Optoelectronics Open Access 04 August 2022
npj Quantum Information Open Access 27 June 2022
Scientific Reports Open Access 03 May 2022
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.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
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)
Vandersypen, L. M. K. et al. Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883–887 (2001)
Gulde, S. et al. Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer. Nature 421, 48–50 (2003)
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)
Chiaverini, J. et al. Implementation of the semiclassical quantum Fourier transform in a scalable system. Science 308, 997–1000 (2005)
Brickman, K.-A. et al. Implementation of Grover’s quantum search algorithm in a scalable system. Phys. Rev. A 72, 050306(R) (2005)
DiCarlo, L. et al. Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature 460, 240–244 (2009)
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)
Martín-López, E. et al. Experimental realization of Shor’s quantum factoring algorithm using qubit recycling. Nat. Photon. 6, 773–776 (2012)
Monz, T. et al. Realization of a scalable Shor algorithm. Science 351, 1068–1070 (2016)
Deutsch, D. & Jozsa, R. Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553–558 (1992)
Bernstein, E. & Vazirani, U. Quantum complexity theory. SIAM J. Comput. 26, 1411–1473 (1997)
Shor, P. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)
Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information 1st edn (Cambridge Univ. Press, 2002)
Kielpinski, D., Monroe, C. & Wineland, D. J. Architecture for a large-scale ion-trap quantum computer. Nature 417, 709–711 (2002)
Monroe, C. et al. Large scale modular quantum computer architecture with atomic memory and photonic interconnects. Phys. Rev. A 89, 022317 (2014)
Cirac, J. I. & Zoller, P. Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995)
Mølmer, K. & Sørensen, A. Multipartite entanglement of hot trapped ions. Phys. Rev. Lett. 82, 1835–1838 (1999)
Barends, R. et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014)
Hill, C. D. et al. A surface code quantum computer in silicon. Sci. Adv. 1, e1500707 (2015)
Gottesman, D. Fault-tolerant quantum computation with local gates. J. Mod. Opt. 47, 333–345 (2000)
Green, T. J. & Biercuk, M. J. Phase-modulated decoupling and error suppression in qubit-oscillator systems. Phys. Rev. Lett. 114, 120502 (2015)
Ballance, C. J. et al. Laser-driven quantum logic gates with precision beyond the fault-tolerant threshold. Preprint at http://arxiv.org/abs/1512.04600 (2016)
True Merrill, J. et al. Demonstration of integrated microscale optics in surface-electrode ion traps. New J. Phys. 13, 103005 (2011)
Gaebler, J. P. et al. High-fidelity universal gate set for 9Be+ ion qubits. Preprint at http://arxiv.org/abs/1604.00032 (2016)
Choi, T. et al. Optimal quantum control of multimode couplings between trapped ion qubits for scalable entanglement. Phys. Rev. Lett. 112, 190502 (2014)
Olmschenk, S. et al. Manipulation and detection of a trapped Yb+ hyperfine qubit. Phys. Rev. A 76, 052314 (2007)
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)
Hayes, D. et al. Entanglement of atomic qubits using an optical frequency comb. Phys. Rev. Lett. 104, 140501 (2010)
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)
Johnson, K. G. et al. Active stabilization of ion trap radiofrequency potentials. Rev. Sci. Instrum. 87, 053110 (2016)
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)
Schiffer, J. P. Phase transitions in anisotropically confined ionic crystals. Phys. Rev. Lett. 70, 818–821 (1993)
Zhu, S.-L., Monroe, C. & Duan, L.-M. Trapped ion quantum computation with transverse phonon modes. Phys. Rev. Lett. 97, 050505 (2006)
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)
Milburn, G. J., Schneider, S. & James, D. F. V. Ion trap quantum computing with warm ions. Fortschr. Phys. 48, 801–810 (2000)
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.
C.M. is a founding scientist of ionQ, Inc.
Reviewer Information Nature thanks S. Bartlett and T. Northup for their contribution to the peer review of this work.
Extended data figures and tables
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.
About this article
Cite this article
Debnath, S., Linke, N., Figgatt, C. et al. Demonstration of a small programmable quantum computer with atomic qubits. Nature 536, 63–66 (2016). https://doi.org/10.1038/nature18648
Scientific Reports (2022)
Dynamic compensation of stray electric fields in an ion trap using machine learning and adaptive algorithm
Scientific Reports (2022)
npj Quantum Information (2022)
Scientific Reports (2022)
Nature Communications (2022)