Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries over classical computers. It is an optimal search algorithm for a quantum computer, and has further applications as a subroutine for other quantum algorithms. Searches with two qubits have been demonstrated on a variety of platforms and proposed for others, but larger search spaces have only been demonstrated on a non-scalable NMR system. Here, we report results for a complete three-qubit Grover search algorithm using the scalable quantum computing technology of trapped atomic ions, with better-than-classical performance. The algorithm is performed for all 8 possible single-result oracles and all 28 possible two-result oracles. Two methods of state marking are used for the oracles: a phase-flip method employed by other experimental demonstrations, and a Boolean method requiring an ancilla qubit that is directly equivalent to the state-marking scheme required to perform a classical search. All quantum solutions are shown to outperform their classical counterparts. We also report the first implementation of a Toffoli-4 gate, which is used along with Toffoli-3 gates to construct the algorithms; these gates have process fidelities of 70.5% and 89.6%, respectively.

%B Nature Communications, accepted %8 2017/03/30 %G eng %U https://arxiv.org/abs/1703.10535 %0 Conference Proceedings %B Proceedings of the National Academy of Sciences %D 2017 %T Experimental Comparison of Two Quantum Computing Architectures %A N.M. Linke %A Dmitri Maslov %A Martin Roetteler %A S. Debnath %A C. Figgatt %A K. A. Landsman %A K. Wright %A Christopher Monroe %XWe run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device [1] with limited connectivity, and the other is a fully connected trapped-ion system [2]. Even though the two systems have different native quantum interactions, both can be programmed in a way that is blind to the underlying hardware, thus allowing the first comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that employ more connectivity clearly benefit from a better connected system of qubits. While the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that co-designing particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future.

%B Proceedings of the National Academy of Sciences %7 13 %V 114 %P 3305-3310 %8 2017/03/21 %G eng %U http://www.pnas.org/content/114/13/3305 %R 10.1073/pnas.1618020114 %0 Journal Article %J Nature %D 2016 %T Demonstration of a small programmable quantum computer with atomic qubits %A S. Debnath %A N. M. Linke %A C. Figgatt %A K. A. Landsman %A K. Wright %A C. Monroe %XQuantum 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 paths. 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 %. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa (DJ) and Bernstein-Vazirani (BV) algorithms with average success rates of 95 % and 90 %, respectively. We also perform a coherent quantum Fourier transform (QFT) on five trappedion qubits for phase estimation and period finding with average fidelities of 62 % and 84 %, 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 shuttling or photonic quantum channels.

%B Nature %V 536 %P 63-66 %8 2016/08/04 %G eng %U http://www.nature.com/nature/journal/v536/n7614/full/nature18648.html %N 7614 %R 10.1038/nature18648 %0 Journal Article %D 2016 %T Experimental demonstration of quantum fault tolerance %A N. M. Linke %A M. Gutierrez %A K. A. Landsman %A C. Figgatt %A S. Debnath %A K. R. Brown %A C. Monroe %XQuantum computers will eventually reach a size at which quantum error correction (QEC) becomes imperative. In order to make quantum information robust to errors introduced by qubit imperfections and flawed control operations, QEC protocols encode a logical qubit in multiple physical qubits. This redundancy allows the extraction of error syndromes and the subsequent correction or detection of errors without destroying the logical state itself through direct measurement. While several experiments have shown a reduction of high intrinsic or artificially introduced errors in logical qubits, fault-tolerant encoding of a logical qubit has never been demonstrated. Here we show the encoding and syndrome measurement of a fault-tolerant logical qubit via an error detection protocol on four physical qubits, represented by trapped atomic ions. This demonstrates for the first time the robustness of a fault-tolerant qubit to imperfections in the very operations used to encode it. This advantage persists in the face of large added error rates and experimental calibration errors.

%8 2016/11/21 %G eng %U https://arxiv.org/abs/1611.06946