1
|
Monz T, Nigg D, Martinez EA, Brandl MF, Schindler P, Rines R, Wang SX, Chuang IL, Blatt R. Realization of a scalable Shor algorithm. Science 2016; 351:1068-70. [DOI: 10.1126/science.aad9480] [Citation(s) in RCA: 223] [Impact Index Per Article: 27.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
|
2
|
Lamata L, Leibrandt DR, Chuang IL, Cirac JI, Lukin MD, Vuletić V, Yelin SF. Ion crystal transducer for strong coupling between single ions and single photons. Phys Rev Lett 2011; 107:030501. [PMID: 21838337 DOI: 10.1103/physrevlett.107.030501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2011] [Indexed: 05/31/2023]
Abstract
A new approach for the realization of a quantum interface between single photons and single ions in an ion crystal is proposed and analyzed. In our approach the coupling between a single photon and a single ion is enhanced via the collective degrees of freedom of the ion crystal. Applications including single-photon generation, a memory for a quantum repeater, and a deterministic photon-photon, photon-phonon, or photon-ion entangler are discussed.
Collapse
Affiliation(s)
- L Lamata
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany.
| | | | | | | | | | | | | |
Collapse
|
3
|
Antohi PB, Schuster D, Akselrod GM, Labaziewicz J, Ge Y, Lin Z, Bakr WS, Chuang IL. Cryogenic ion trapping systems with surface-electrode traps. Rev Sci Instrum 2009; 80:013103. [PMID: 19191425 DOI: 10.1063/1.3058605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We present two simple cryogenic rf ion trap systems in which cryogenic temperatures and ultra high vacuum pressures can be reached in as little as 12 h. The ion traps are operated either in a liquid helium bath cryostat or in a low vibration closed cycle cryostat. The fast turn around time and availability of buffer gas cooling made the systems ideal for testing surface-electrode ion traps. The vibration amplitude of the closed cycled cryostat was found to be below 106 nm. We evaluated the systems by loading surface-electrode ion traps with (88)Sr(+) ions using laser ablation, which is compatible with the cryogenic environment. Using Doppler cooling we observed small ion crystals in which optically resolved ions have a trapped lifetime over 2500 min.
Collapse
Affiliation(s)
- P B Antohi
- Department of Physics, Center for Ultracold Atoms, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
| | | | | | | | | | | | | | | |
Collapse
|
4
|
Heersche HB, de Groot Z, Folk JA, Kouwenhoven LP, van der Zant HSJ, Houck AA, Labaziewicz J, Chuang IL. Kondo effect in the presence of magnetic impurities. Phys Rev Lett 2006; 96:017205. [PMID: 16486511 DOI: 10.1103/physrevlett.96.017205] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2005] [Indexed: 05/06/2023]
Abstract
We measure transport through gold grain quantum dots fabricated using electromigration, with magnetic impurities in the leads. A Kondo interaction is observed between dot and leads, but the presence of magnetic impurities results in a gate-dependent zero-bias conductance peak that is split due to a RKKY interaction between the spin of the dot and the static spins of the impurities. A magnetic field restores the single Kondo peak in the case of an antiferromagnetic RKKY interaction. This system provides a new platform to study Kondo and RKKY interactions in metals at the level of a single spin.
Collapse
Affiliation(s)
- H B Heersche
- Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands.
| | | | | | | | | | | | | | | |
Collapse
|
5
|
Abstract
We present gate-dependent transport measurements of Kondo impurities in bare gold break junctions, generated with high yield using an electromigration process that is actively controlled. Thirty percent of measured devices show zero-bias conductance peaks. Temperature dependence suggests Kondo temperatures approximately 7 K. The peak splitting in magnetic field is consistent with theoretical predictions for g = 2, though in many devices the splitting is offset from 2g mu(B)B by a fixed energy. The Kondo resonances observed here may be due to atomic-scale metallic grains formed during electromigration.
Collapse
Affiliation(s)
- A A Houck
- Center for Bits and Atoms and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | | | | | | | | |
Collapse
|
6
|
Gulde S, Häffner H, Riebe M, Lancaster G, Becher C, Eschner J, Schmidt-Kaler F, Chuang IL, Blatt R. Quantum information processing with trapped Ca(+) ions. Philos Trans A Math Phys Eng Sci 2003; 361:1363-1374. [PMID: 12869313 DOI: 10.1098/rsta.2003.1206] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Quantum information processing is performed with single trapped Ca(+) ions, stored in a linear Paul trap and laser-cooled to the ground state of their harmonic quantum motion. Composite laser-pulse sequences were used to implement SWAP gate, phase gate and controlled-NOT gate operations. Stark shifts on the quantum-bit transitions were precisely measured and compensated. For a demonstration of quantum information processing, a Deutsch-Jozsa algorithm has been implemented using two quantum bits encoded on a single ion.
Collapse
Affiliation(s)
- S Gulde
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
| | | | | | | | | | | | | | | | | |
Collapse
|
7
|
Vandersypen LM, Steffen M, Breyta G, Yannoni CS, Sherwood MH, Chuang IL. Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance. Nature 2001; 414:883-7. [PMID: 11780055 DOI: 10.1038/414883a] [Citation(s) in RCA: 228] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
The number of steps any classical computer requires in order to find the prime factors of an l-digit integer N increases exponentially with l, at least using algorithms known at present. Factoring large integers is therefore conjectured to be intractable classically, an observation underlying the security of widely used cryptographic codes. Quantum computers, however, could factor integers in only polynomial time, using Shor's quantum factoring algorithm. Although important for the study of quantum computers, experimental demonstration of this algorithm has proved elusive. Here we report an implementation of the simplest instance of Shor's algorithm: factorization of N = 15 (whose prime factors are 3 and 5). We use seven spin-1/2 nuclei in a molecule as quantum bits, which can be manipulated with room temperature liquid-state nuclear magnetic resonance techniques. This method of using nuclei to store quantum information is in principle scalable to systems containing many quantum bits, but such scalability is not implied by the present work. The significance of our work lies in the demonstration of experimental and theoretical techniques for precise control and modelling of complex quantum computers. In particular, we present a simple, parameter-free but predictive model of decoherence effects in our system.
Collapse
Affiliation(s)
- L M Vandersypen
- IBM Almaden Research Center, San Jose, California 95120, USA
| | | | | | | | | | | |
Collapse
|
8
|
Vandersypen LM, Steffen M, Breyta G, Yannoni CS, Cleve R, Chuang IL. Experimental realization of an order-finding algorithm with an NMR quantum computer. Phys Rev Lett 2000; 85:5452-5455. [PMID: 11136019 DOI: 10.1103/physrevlett.85.5452] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2000] [Indexed: 05/23/2023]
Abstract
We report the realization of a nuclear magnetic resonance quantum computer which combines the quantum Fourier transform with exponentiated permutations, demonstrating a quantum algorithm for order finding. This algorithm has the same structure as Shor's algorithm and its speed-up over classical algorithms scales exponentially. The implementation uses a particularly well-suited five quantum bit molecule and was made possible by a new state initialization procedure and several quantum control techniques.
Collapse
Affiliation(s)
- L M Vandersypen
- Solid State and Photonics Laboratory, Stanford University, Stanford, California 94305-4075, USA.
| | | | | | | | | | | |
Collapse
|
9
|
Abstract
The rotation of a spin subject to an on-resonance soft pulse and simultaneously to a soft pulse at a nearby frequency may strongly deviate from the desired rotation expected for a single on-resonance pulse. The deviation is the result of transient frequency shifts of the spin caused by the off-resonance irradiation. We show that the resulting error can be corrected by shifting the frequency of the on-resonance pulse in such a way that it tracks the shift of the spin frequency. Experimentally, the effectiveness of this simple and intuitive method is demonstrated for simultaneous inversions at nearby frequencies in the case of both coupled and uncoupled spins. Simulations predict that the correction technique is effective for arbitrary pulse shapes and tip angles and is particularly useful when the frequency window of the shaped pulse is two to eight times the frequency separation between the chemical shifts of the two spins. Copyright 2000 Academic Press.
Collapse
Affiliation(s)
- M Steffen
- Solid State and Photonics Laboratory, Stanford University, Stanford, California, 94305-4075, USA
| | | | | |
Collapse
|
10
|
Abstract
The clock synchronization problem is to determine the time difference Delta between two spatially separated clocks. When message delivery times between the two clocks are uncertain, O(2(2n)) classical messages must be exchanged between the clocks to determine n digits of Delta. On the other hand, as we show, there exists a quantum algorithm to obtain n digits of Delta while communicating only O(n) quantum messages.
Collapse
Affiliation(s)
- IL Chuang
- IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, USA
| |
Collapse
|
11
|
Chuang IL, Gershenfeld N, Kubinec MG, Leung DW. Bulk quantum computation with nuclear magnetic resonance: theory and experiment. Proc Math Phys Eng Sci 1998. [DOI: 10.1098/rspa.1998.0170] [Citation(s) in RCA: 240] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Affiliation(s)
- I. L. Chuang
- Los Alamos National Laboratory, Theoretical Astrophysics T‐6, Mail Stop B288, Los Alamos, NM 87545, USA
| | - N. Gershenfeld
- Physics and Media Group, MIT Media Laboratory, 20 Ames Street, Cambridge, MA 02139, USA
| | - M. G. Kubinec
- College of Chemistry, D7 Latimer Hall, University of California Berkeley, Berkeley, CA 94720-1460, USA
| | - D. W. Leung
- ERATO Quantum Fluctuation Project, Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| |
Collapse
|
12
|
Abstract
Quantum computation remains an enormously appealing but elusive goal. It is appealing because of its potential to perform superfast algorithms, such as finding prime factors in polynomial time, but also elusive because of the difficulty of simultaneously manipulating quantum degrees of freedom while preventing environmentally induced decoherence. A new approach to quantum computing is introduced based on the use of multiple-pulse resonance techniques to manipulate the small deviation from equilibrium of the density matrix of a macroscopic ensemble so that it appears to be the density matrix of a much lower dimensional pure state. A complete prescription for quantum computing is given for such a system.
Collapse
Affiliation(s)
- NA Gershenfeld
- N. A. Gershenfeld is at the Physics and Media Group, MIT Media Lab, Cambridge, MA 02139, USA. I. L. Chuang is with the Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA. E-mail:
| | | |
Collapse
|
13
|
|
14
|
Affiliation(s)
- I. L. Chuang
- I. L. Chuang, Edward L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - R. Laflamme
- R. Laflamme and W. H. Zurek, Theoretical Astrophysics, T-6, MS B288, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| | - P. W. Shor
- P. W. Shor, AT&T Bell Labs, 600 Mountain Avenue, Murray Hill, NJ 07974, USA
| | - W. H. Zurek
- R. Laflamme and W. H. Zurek, Theoretical Astrophysics, T-6, MS B288, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| |
Collapse
|
15
|
|