A quantum information processor with trapped ions

Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a small-scale quantum information processor based on a string of 40Ca+ ions confined in a macroscopic linear Paul trap. We review our set of operations which includes non-coherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate of the available operations which is only possible if the physics of the noise processes is well understood. We identify the dominant noise sources in our system and discuss their effects on different algorithms. Finally we demonstrate how our entire set of operations can be used to facilitate the implementation of algorithms by examples of the quantum Fourier transform and the quantum order finding algorithm.

[1]  Isaac L. Chuang,et al.  Prescription for experimental determination of the dynamics of a quantum black box , 1997 .

[2]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[3]  K. Mølmer,et al.  Wave-function approach to dissipative processes in quantum optics. , 1992, Physical review letters.

[4]  David J. Wineland,et al.  Minimization of ion micromotion in a Paul trap , 1998 .

[5]  T. Monz,et al.  14-Qubit entanglement: creation and coherence. , 2010, Physical review letters.

[6]  F. Schmidt-Kaler,et al.  Precision measurement and compensation of optical stark shifts for an ion-trap quantum processor. , 2002, Physical review letters.

[7]  T. Monz,et al.  Realization of universal ion-trap quantum computation with decoherence-free qubits. , 2009, Physical review letters.

[8]  Steane,et al.  Error Correcting Codes in Quantum Theory. , 1996, Physical review letters.

[9]  C. F. Roos,et al.  Nonlinear coupling of continuous variables at the single quantum level , 2008 .

[10]  D. M. Lucas,et al.  Scalable simultaneous multiqubit readout with 99.99% single-shot fidelity , 2009, 0906.3304.

[11]  C. Schwemmer,et al.  Permutationally invariant quantum tomography. , 2010, Physical review letters.

[12]  I. Bloch Quantum coherence and entanglement with ultracold atoms in optical lattices , 2008, Nature.

[13]  Klaus Molmer,et al.  Entanglement and quantum computation with ions in thermal motion , 2000 .

[14]  Daniel Nigg,et al.  Undoing a quantum measurement. , 2013, Physical review letters.

[15]  C. Monroe,et al.  Architecture for a large-scale ion-trap quantum computer , 2002, Nature.

[16]  Nir Davidson,et al.  Process tomography of dynamical decoupling in a dense cold atomic ensemble. , 2010, Physical review letters.

[17]  Moore,et al.  Quantum projection noise: Population fluctuations in two-level systems. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[18]  Andrew M. Steane,et al.  Keeping a single qubit alive by experimental dynamic decoupling , 2010, 1009.6189.

[19]  F. Schmidt-Kaler,et al.  Interaction of a laser with a qubit in thermal motion and its application to robust and efficient readout , 2011 .

[20]  F. Schmidt-Kaler,et al.  Quantum State Engineering on an Optical Transition and Decoherence in a Paul Trap , 1999 .

[21]  J. Clarke,et al.  Superconducting quantum bits , 2008, Nature.

[22]  R. Blatt,et al.  Quantum simulation of dynamical maps with trapped ions , 2012, Nature Physics.

[23]  T. Hänsch,et al.  Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities , 2008, 0801.4199.

[24]  C. F. Roos,et al.  Quantum teleportation with atoms: quantum process tomography , 2007, 0704.2027.

[25]  M D Barrett,et al.  Implementation of the Semiclassical Quantum Fourier Transform in a Scalable System , 2005, Science.

[26]  Klaus Mølmer,et al.  A Monte Carlo wave function method in quantum optics , 1993, Optical Society of America Annual Meeting.

[27]  R. Blatt,et al.  Towards fault-tolerant quantum computing with trapped ions , 2008, 0803.2798.

[28]  Anna Keselman,et al.  Single-ion quantum lock-in amplifier , 2011, Nature.

[29]  Hiroshi Tanaka,et al.  Angular correlation between Auger electrons successively emitted from photoexcited resonances in Kr and Xe , 2003 .

[30]  C. F. Roos,et al.  ‘Designer atoms’ for quantum metrology , 2006, Nature.

[31]  D. Cory,et al.  Noise spectroscopy through dynamical decoupling with a superconducting flux qubit , 2011 .

[32]  D. M. Lucas,et al.  Precision Measurement of the Lifetime of the 3d 2 D 5/2 state in 40 Ca + , 2000 .

[33]  Shannon X. Wang Quantum gates, sensors, and systems with trapped ions , 2012 .

[34]  Daniel Nigg,et al.  Experimental Repetitive Quantum Error Correction , 2011, Science.

[35]  R Hanson,et al.  Universal Dynamical Decoupling of a Single Solid-State Spin from a Spin Bath , 2010, Science.

[36]  C. F. Roos,et al.  Sympathetic ground-state cooling and coherent manipulation with two-ion crystals , 2000, quant-ph/0009031.

[37]  Timo O. Reiss,et al.  Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. , 2005, Journal of magnetic resonance.

[38]  G. Revalde,et al.  The $\mathsf{g_{\scriptscriptstyle J}}$-factor in the ground state of Ca $^\mathsf{+}$ , 2003 .

[39]  Masoud Mohseni,et al.  Experimental characterization of quantum dynamics through many-body interactions. , 2012, Physical review letters.

[40]  X-Q Zhou,et al.  Experimental realization of Shor's quantum factoring algorithm using qubit recycling , 2011, Nature Photonics.

[41]  A. Gossard,et al.  Interlaced dynamical decoupling and coherent operation of a singlet-triplet qubit. , 2010, Physical review letters.

[42]  C. F. Roos,et al.  Optimal control of entangling operations for trapped-ion quantum computing , 2008, 0809.1414.

[43]  Germany,et al.  Quantum states and phases in driven open quantum systems with cold atoms , 2008, 0803.1482.

[44]  H. Häffner,et al.  Robust entanglement , 2005 .

[45]  Griffiths,et al.  Semiclassical Fourier transform for quantum computation. , 1995, Physical review letters.

[46]  R. Blatt,et al.  Entangled states of trapped atomic ions , 2008, Nature.

[47]  Shor,et al.  Good quantum error-correcting codes exist. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[48]  K. Mølmer,et al.  QUANTUM COMPUTATION WITH IONS IN THERMAL MOTION , 1998, quant-ph/9810039.

[49]  Christoph Becher,et al.  The coherence of qubits based on single Ca+ions , 2003 .

[50]  J. Cirac,et al.  Quantum Computations with Cold Trapped Ions. , 1995, Physical review letters.

[51]  C. F. Roos,et al.  Simulating open quantum systems: from many-body interactions to stabilizer pumping , 2011, 1104.2507.

[52]  M. Abgrall,et al.  Absolute Frequency Measurement of the 40Ca+ 4s 2S1/2 -3d2D5/2 Clock Transition , 2008, 0806.1414.

[53]  Michael J. Biercuk,et al.  Optimized dynamical decoupling in a model quantum memory , 2008, Nature.

[54]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[55]  Blatt,et al.  Laser cooling of trapped three-level ions: Designing two-level systems for sideband cooling. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[56]  C. Fuchs Distinguishability and Accessible Information in Quantum Theory , 1996, quant-ph/9601020.

[57]  C. F. Roos,et al.  Deterministic entanglement of ions in thermal states of motion , 2008, 0810.0670.

[58]  Giovanna Morigi,et al.  Laser Cooling of Trapped Ions , 2003 .

[59]  Lorenza Viola,et al.  Engineering quantum dynamics , 2001 .

[60]  F. Verstraete,et al.  Quantum computation and quantum-state engineering driven by dissipation , 2009 .

[61]  Paul Tân Thế Phạm A general-purpose pulse sequencer for quantum computing , 2005 .

[62]  O. Gühne,et al.  Experimental multiparticle entanglement dynamics induced by decoherence , 2010, 1005.1965.

[63]  D. Cory,et al.  Robust decoupling techniques to extend quantum coherence in diamond. , 2010, Physical review letters.

[64]  T. Monz,et al.  An open-system quantum simulator with trapped ions , 2011, Nature.

[65]  Giacomo Baggio,et al.  Quantum state preparation by controlled dissipation in finite time: From classical to quantum controllers , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[66]  Michael Chwalla,et al.  Precision spectroscopy with 40 Ca + ions in a Paul trap , 2009 .

[67]  Xing Rong,et al.  Preserving electron spin coherence in solids by optimal dynamical decoupling , 2009, Nature.