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Ballance CJ, Schäfer VM, Home JP, Szwer DJ, Webster SC, Allcock DTC, Linke NM, Harty TP, Aude Craik DPL, Stacey DN, Steane AM, Lucas DM. Hybrid quantum logic and a test of Bell's inequality using two different atomic isotopes. Nature 2016; 528:384-6. [PMID: 26672554 DOI: 10.1038/nature16184] [Citation(s) in RCA: 71] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2015] [Accepted: 10/26/2015] [Indexed: 11/09/2022]
Abstract
Entanglement is one of the most fundamental properties of quantum mechanics, and is the key resource for quantum information processing (QIP). Bipartite entangled states of identical particles have been generated and studied in several experiments, and post-selected or heralded entangled states involving pairs of photons, single photons and single atoms, or different nuclei in the solid state, have also been produced. Here we use a deterministic quantum logic gate to generate a 'hybrid' entangled state of two trapped-ion qubits held in different isotopes of calcium, perform full tomography of the state produced, and make a test of Bell's inequality with non-identical atoms. We use a laser-driven two-qubit gate, whose mechanism is insensitive to the qubits' energy splittings, to produce a maximally entangled state of one (40)Ca(+) qubit and one (43)Ca(+) qubit, held 3.5 micrometres apart in the same ion trap, with 99.8 ± 0.6 per cent fidelity. We test the CHSH (Clauser-Horne-Shimony-Holt) version of Bell's inequality for this novel entangled state and find that it is violated by 15 standard deviations; in this test, we close the detection loophole but not the locality loophole. Mixed-species quantum logic is a powerful technique for the construction of a quantum computer based on trapped ions, as it allows protection of memory qubits while other qubits undergo logic operations or are used as photonic interfaces to other processing units. The entangling gate mechanism used here can also be applied to qubits stored in different atomic elements; this would allow both memory and logic gate errors caused by photon scattering to be reduced below the levels required for fault-tolerant quantum error correction, which is an essential prerequisite for general-purpose quantum computing.
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Affiliation(s)
- C J Ballance
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - V M Schäfer
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - J P Home
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - D J Szwer
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - S C Webster
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - D T C Allcock
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - N M Linke
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - T P Harty
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - D P L Aude Craik
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - D N Stacey
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - A M Steane
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - D M Lucas
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
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Harty TP, Allcock DTC, Ballance CJ, Guidoni L, Janacek HA, Linke NM, Stacey DN, Lucas DM. High-Fidelity Preparation, Gates, Memory, and Readout of a Trapped-Ion Quantum Bit. Phys Rev Lett 2014; 113:220501. [PMID: 25494060 DOI: 10.1103/physrevlett.113.220501] [Citation(s) in RCA: 57] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2014] [Indexed: 06/04/2023]
Abstract
We implement all single-qubit operations with fidelities significantly above the minimum threshold required for fault-tolerant quantum computing, using a trapped-ion qubit stored in hyperfine "atomic clock" states of ^{43}Ca^{+}. We measure a combined qubit state preparation and single-shot readout fidelity of 99.93%, a memory coherence time of T_{2}^{*}=50 sec, and an average single-qubit gate fidelity of 99.9999%. These results are achieved in a room-temperature microfabricated surface trap, without the use of magnetic field shielding or dynamic decoupling techniques to overcome technical noise.
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Affiliation(s)
- T P Harty
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - D T C Allcock
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - C J Ballance
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - L Guidoni
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom and Laboratoire Matériaux et Phénomènes Quantiques, University of Paris Diderot, UMR 7162 CNRS, F-75205 Paris, France
| | - H A Janacek
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - N M Linke
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - D N Stacey
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - D M Lucas
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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Myerson AH, Szwer DJ, Webster SC, Allcock DTC, Curtis MJ, Imreh G, Sherman JA, Stacey DN, Steane AM, Lucas DM. High-fidelity readout of trapped-ion qubits. Phys Rev Lett 2008; 100:200502. [PMID: 18518518 DOI: 10.1103/physrevlett.100.200502] [Citation(s) in RCA: 70] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2008] [Indexed: 05/26/2023]
Abstract
We demonstrate single-shot qubit readout with a fidelity sufficient for fault-tolerant quantum computation. For an optical qubit stored in 40Ca+ we achieve 99.991(1)% average readout fidelity in 10(6) trials, using time-resolved photon counting. An adaptive measurement technique allows 99.99% fidelity to be reached in 145 micros average detection time. For 43Ca+, we propose and implement an optical pumping scheme to transfer a long-lived hyperfine qubit to the optical qubit, capable of a theoretical fidelity of 99.95% in 10 micros. We achieve 99.87(4)% transfer fidelity and 99.77(3)% net readout fidelity.
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Affiliation(s)
- A H Myerson
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
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McDonnell MJ, Home JP, Lucas DM, Imreh G, Keitch BC, Szwer DJ, Thomas NR, Webster SC, Stacey DN, Steane AM. Long-lived mesoscopic entanglement outside the Lamb-Dicke regime. Phys Rev Lett 2007; 98:063603. [PMID: 17358940 DOI: 10.1103/physrevlett.98.063603] [Citation(s) in RCA: 6] [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: 05/15/2006] [Indexed: 05/14/2023]
Abstract
We create entangled states of the spin and motion of a single 40Ca+ ion in a linear ion trap. We theoretically study and experimentally observe the behavior outside the Lamb-Dicke regime, where the trajectory in phase space is modified and the motional coherent states become squeezed. We directly observe the modification of the return time of the trajectory, and infer the squeezing. The mesoscopic entanglement is observed up to Deltaalpha=5.1 with coherence time 170 micros and mean phonon excitation n = 16.
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Affiliation(s)
- M J McDonnell
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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McDonnell MJ, Stacey JP, Webster SC, Home JP, Ramos A, Lucas DM, Stacey DN, Steane AM. High-efficiency detection of a single quantum of angular momentum by suppression of optical pumping. Phys Rev Lett 2004; 93:153601. [PMID: 15524877 DOI: 10.1103/physrevlett.93.153601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2003] [Indexed: 05/24/2023]
Abstract
We propose and demonstrate experimentally the discrimination between two spin states of an atom purely on the basis of their angular momentum. The discrimination relies on angular momentum selection rules and does not require magnetic effects such as a magnetic dipole moment of the atom or an applied magnetic field. The central ingredient is to prevent by coherent population trapping an optical pumping process which would otherwise relax the spin state before a detectable signal could be obtained. We detected the presence or absence of a single quantum (h) of angular momentum in a trapped calcium ion in a single observation with success probability 0.86. As a practical technique, the method can be applied to read out some types of quantum computer.
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Affiliation(s)
- M J McDonnell
- Centre for Quantum Computation, Department of Atomic and Laser Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, England
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Lucas DM, Donald CJS, Home JP, McDonnell MJ, Ramos A, Stacey DN, Stacey JP, Steane AM, Webster SC. Oxford ion-trap quantum computing project. Philos Trans A Math Phys Eng Sci 2003; 361:1401-1408. [PMID: 12869316 DOI: 10.1098/rsta.2003.1209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [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
We describe recent progress in the development of an ion-trap quantum information processor. We discuss the choice of ion species and describe recent experiments on read-out for a ground-state qubit and photoionization trap loading.
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Affiliation(s)
- D M Lucas
- Centre for Quantum Computation, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
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Carrington CG, Stacey DN, Cooper J. Multipole relaxation and transfer rates in the impact approximation: application to the resonance interaction. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0022-3700/6/3/009] [Citation(s) in RCA: 84] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Palmer CWP, Baird PEG, Blundell SA, Brandenberger JR, Foot CJ, Stacey DN, Woodgate GK. Laser spectroscopy of calcium isotopes. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0022-3700/17/11/014] [Citation(s) in RCA: 54] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Roberts GJ, Baird PEG, Brimicombe MWSM, Sandars PGH, Selby DR, Stacey DN. The Faraday effect and magnetic circular dichroism in atomic bismuth. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0022-3700/13/7/014] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Blundell SA, Baird PEG, Botham CP, Palmer CWP, Stacey DN, Woodgate GK. Isotope shift and hyperfine structure for a valence s electron. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0022-3700/17/1/011] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Lawrence SJ, Stacey DN, Bell IM, Burnett K. Ultraviolet spectroscopy of HgAr in a supersonic jet: A new determination of the A 30+ state potential. J Chem Phys 1996. [DOI: 10.1063/1.471503] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Bourzeix S, Nez F, Plimmer MD, Julien L, Biraben F, Stacey DN. High resolution spectroscopy of the hydrogen atom: Determination of the 1S Lamb shift. Phys Rev Lett 1996; 76:384-387. [PMID: 10061443 DOI: 10.1103/physrevlett.76.384] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Macpherson MJ, Zetie KP, Warrington RB, Stacey DN, Hoare JP. Precise measurement of parity nonconserving optical rotation at 876 nm in atomic bismuth. Phys Rev Lett 1991; 67:2784-2787. [PMID: 10044554 DOI: 10.1103/physrevlett.67.2784] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Boshier MG, Baird PE, Foot CJ, Hinds EA, Plimmer MD, Stacey DN, Swan JB, Tate DA, Warrington DM, Woodgate GK. Laser spectroscopy of the 1S-2S transition in hydrogen and deuterium: Determination of the 1S Lamb shift and the Rydberg constant. Phys Rev A Gen Phys 1989; 40:6169-6184. [PMID: 9902003 DOI: 10.1103/physreva.40.6169] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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