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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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.
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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). https://doi.org/10.1038/nature18648
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