The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear efficiency gains in numerous quantum circuits as well as for entire algorithms such as Shor's factoring algorithm and quantum simulations. In cases such as full adders and multiple-control Toffoli gates, parallelism can provide an exponential improvement in overall execution time. More importantly, quantum gate parallelism is essential for the practical fault-tolerant error correction of qubits that suffer from idle errors. The implementation of parallel quantum gates is complicated by potential crosstalk, especially between qubits fully connected by a common-mode bus, such as in Coulomb-coupled trapped atomic ions or cavity-coupled superconducting transmons. Here, we present the first experimental results for parallel 2-qubit entangling gates in an array of fully-connected trapped ion qubits. We demonstrate an application of this capability by performing a 1-bit full addition operation on a quantum computer using a depth-4 quantum circuit. These results exploit the power of highly connected qubit systems through classical control techniques, and provide an advance toward speeding up quantum circuits and achieving fault tolerance with trapped ion quantum computers.

1 aFiggatt, C.1 aOstrander, A.1 aLinke, N., M.1 aLandsman, K., A.1 aZhu, D.1 aMaslov, D.1 aMonroe, C. uhttps://arxiv.org/abs/1810.1194802065nas a2200169 4500008004100000245007000041210006900111260001500180520154900195100001601744700001901760700002101779700001801800700001601818700002401834856003701858 2017 eng d00aComplete 3-Qubit Grover Search on a Programmable Quantum Computer0 aComplete 3Qubit Grover Search on a Programmable Quantum Computer c2017/03/303 aSearching 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.

1 aFiggatt, C.1 aMaslov, Dmitri1 aLandsman, K., A.1 aLinke, N., M.1 aDebnath, S.1 aMonroe, Christopher uhttps://arxiv.org/abs/1703.1053501709nas a2200229 4500008004100000245006700041210006700108250000700175260001500182300001400197490000800211520106700219100001601286700001901302700002201321700001601343700001601359700002101375700001501396700002401411856004401435 2017 eng d00aExperimental Comparison of Two Quantum Computing Architectures0 aExperimental Comparison of Two Quantum Computing Architectures a13 c2017/03/21 a3305-33100 v1143 aWe 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.

1 aLinke, N.M.1 aMaslov, Dmitri1 aRoetteler, Martin1 aDebnath, S.1 aFiggatt, C.1 aLandsman, K., A.1 aWright, K.1 aMonroe, Christopher uhttp://www.pnas.org/content/114/13/330502040nas a2200193 4500008004100000245007800041210006900119260001500188300001000203490000800213520145000221100001601671700001801687700001601705700002101721700001501742700001501757856007401772 2016 eng d00aDemonstration of a small programmable quantum computer with atomic qubits0 aDemonstration of a small programmable quantum computer with atom c2016/08/04 a63-660 v5363 aQuantum 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.

1 aDebnath, S.1 aLinke, N., M.1 aFiggatt, C.1 aLandsman, K., A.1 aWright, K.1 aMonroe, C. uhttp://www.nature.com/nature/journal/v536/n7614/full/nature18648.html01724nas a2200181 4500008004100000245005800041210005800099260001500157520121100172100001801383700001801401700002101419700001601440700001601456700001801472700001501490856003701505 2016 eng d00aExperimental demonstration of quantum fault tolerance0 aExperimental demonstration of quantum fault tolerance c2016/11/213 aQuantum 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.

1 aLinke, N., M.1 aGutierrez, M.1 aLandsman, K., A.1 aFiggatt, C.1 aDebnath, S.1 aBrown, K., R.1 aMonroe, C. uhttps://arxiv.org/abs/1611.06946