A. H. Myerson, D. J. Szwer, S. C. Webster, D. T. C. Allcock,M. J. Curtis, G. Imreh, J. A. Sherman, D. N. Stacey,A. M. Steane and D. M. Lucas
The very precise state measurements necessary to build a quantum computer (QC) have recently been achieved in the lab at Oxford [1]. If built, a QC could exploit the quantum phenomena of superposition and entanglement to solve certain problems which are intractable on any conceivable conventional machine. Building such a computer is a difficult challenge; nevertheless much progress has been made over the last few years. At the most basic level, a QC requires qubits that can be prepared accurately and made to interact through high-quality logic gates. High fidelity state measurement is also required both during the computation and also at the end to read out the final state of the QC. However, can we still hope to realise an error-free computation even if we cannot perform these operations perfectly with 100% fidelity? Fortunately the answer is yes-- a small level of error can indeed be tolerated through the use of fault tolerant quantum error-correction (QEC) schemes. Even so, there remains a minimum fidelity threshold for each process that must be met in order to successfully perform a computation.
QEC schemes involve extra "ancilla" qubits and in general there is a trade-off between the error rate permitted and the number of extra qubits required to achieve fault-tolerant operation. With every additional qubit there is then a corresponding increase in the number of high fidelity measurements required in the computation. In general, QEC schemes require more gate operations than measurement operations, so gate error is the more critical parameter. However, very precise readout can be used to compensate for gate error [2]. Typical studies require measurement errors to be below ~10^(-3) for realistic implementations [2,3]. Speed is also an important issue for fault-tolerance as QEC schemes must be implemented fast enough to overcome the effects of decoherence. Therefore it is important that state measurements and gates are fast as several must be performed for each readout.
Trapped ions are widely recognised as currently one of the most promising systems with which to build a quantum computer. Trapped-ion QC approaches use a qubit encoded in two energy states of the ion. State preparation is achieved by optical pumping and measurement of the qubit state is performed by using a laser to excite fluorescence from only one of the qubit levels. By exciting a cycling transition involving only one of the qubit states, many photons can be emitted by an ion in the "bright" state before some off-resonant process or decay occurs which transfers an ion from the "dark" to the "bright" state (or vice versa). This means high readout fidelities can be achieved despite low detection efficiencies (typically less than ~1%). Ion trap readout fidelities compare favourably with those achieved in other QC implementations.
In our recent paper [1], we report the direct single-shot measurement of an "optical" qubit stored in the (4S_1/2, 3D_5/2) levels of 40Ca+ with a fidelity of 99.991(1)%. We employ an optimum time-resolved maximum likelihood method based on that in [4] to discriminate between the two qubits states based on photon-counting information. This method is efficient even in the presence of a dark to bright transfer mechanism (the ~1s lifetime of the 3D_5/2 qubit state). An adaptive method allows 99.99% fidelity to be reached in only 145us average detection time. This speed is comparable to current gate speeds in the same ion [5]. Because the bright to dark transfer rate is so low, the bright state can be detected faster and with higher fidelity, a fact which could be exploited in QEC. The time-resolved analysis method used is also in principle applicable to state inference in qubits in other systems, for example solid state qubits [6].
The ~1s lifetime of the 3D_5/2 qubit state limits the lifetime of the optical qubit in 40Ca+. For QC applications it is advantageous to have a longer lived qubit, such as one stored in the ground-state hyperfine levels of 43Ca+. Hyperfine qubits exhibit some of the longest coherence times ever measured [7,8].
To read out this hyperfine qubit, the qubit is first mapped onto an optical qubit by moving population from one of the qubit levels to a metastable "shelf" level not addressed by the readout lasers. Readout then proceeds by driving a cycling transition to collect photons, as for the optical qubit in 40Ca+. The technique of "shelving" enables a cycling transition to be driven on one qubit state which has a much lower probability of off-resonantly exciting the other qubit state than an alternate transition that attempts to selectively address one of the ground state qubit levels.
In [1], we propose and implement a simple and robust pumping scheme to transfer the hyperfine qubit to the optical qubit, capable of a theoretical fidelity of 99.95% in 10us. Experimentally, 99.77(3)% net readout fidelity is achieved, of which a fidelity of at least 99.87(4)% is inferred for the transfer operation.
In summary, the fast, direct, single-shot readout methods demonstrated in this paper provide a fidelity comparable with that required for a fault-tolerant QC and compare very favourably with other reported high fidelity measurements. Measurements with such a high fidelity could be exploited as the driving force for computation in a "measurement based" QC architecture. In this scheme, the qubits are initially prepared in a massively entangled state and then the computation proceeds with each computing step being realised as a quantum measurement.
REFERENCES:
[1] A.H. Myerson, D.J. Szwer, S.C. Webster, D.T.C. Allcock, M.J. Curtis, G. Imreh, J. Sherman, D.N. Stacey, A.M. Steane, and D.M. Lucas.
High-fidelity readout of trapped-ion qubits.
Physical Review Letters, 100:200502, May 2008.
[2] A.M. Steane.
How to build a 300 bit, 1 giga-operation quantum computer. Quantum Information & Computation, 7(3):171-183, March 2007.
[3] E. Knill.
Quantum computing with realistically noisy devices.
Nature, 434(7029):39-44, March 2005.
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PhD thesis, University of Colorado, Boulder, 2006.
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[6] Jay Gambetta, W.A. Braff, A. Wallraff, S.M. Girvin, and R.J. Schoelkopf.
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[7] C. Langer, R. Ozeri, J.D. Jost, J. Chiaverini, B. DeMarco, A. Ben-Kish, R.B. Blakestad, J. Britton, D.B. Hume, W.M. Itano, D. Leibfried, R. Reichle, T. Rosenband, T. Schaetz, P.O. Schmidt, and D.J. Wineland.
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[8] D.M. Lucas, B.C. Keitch, J.P. Home, G. Imreh, M.J. McDonnell, D.N. Stacey, D.J. Szwer, and A.M. Steane.
A long-lived memory qubit on a low-decoherence quantum bus.
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