Experimental Quantum Computing without Entanglement

Experimental Quantum Computing without Entanglement　2008-11-25 18:44

B. P. Lanyon,* M. Barbieri,? M. P. Almeida, and A. G. White
Department of Physics and Centre for Quantum Computer Technology, University of Queensland, Brisbane 4072, Australia
(Received 15 August 2008; published 13 November 2008)
Deterministic quantum computation with one pure qubit (DQC1) is an efficient model of computation
that uses highly mixed states. Unlike pure-state models, its power is not derived from the generation of a
large amount of entanglement. Instead it has been proposed that other nonclassical correlations are
responsible for the computational speedup, and that these can be captured by the quantum discord. In this
Letter we implement DQC1 in an all-optical architecture, and experimentally observe the generated
correlations. We find no entanglement, but large amounts of quantum discord—except in three cases
where an efficient classical simulation is always possible. Our results show that even fully separable,
highly mixed, states can contain intrinsically quantum mechanical correlations and that these could offer a
valuable resource for quantum information technologies.
DOI: 10.1103/PhysRevLett.101.200501 PACS numbers: 03.67.Lx, 03.67.Ac



While a great deal of work has been done on the conventional pure-state models of quantum computing [1,2], relatively little is known about computing with mixed states. Deterministic quantum computation with one pure
qubit (DQC1) is a model of computation that employs only a single qubit in a pure state, alongside a register of qubits in the fully mixed state [3]. While this model is not universal—it cannot implement any arbitrary algorithm—
it can still efficiently solve important problems that are thought to be classically intractable. One of the original
applications identified was the simulation of quantum systems [3]. Since then exponential speedups have been identified in estimating the average fidelity decay under quantum maps [4], quadratically signed weight enumerators[5], and the Jones Polynomial in knot theory [6]. DQC1 also affords efficient parameter estimation at the quantum metrology limit [7]. That such a useful tool could be built with only a single pure quantum bit is particularly appealing given the current state of experimental quantum computing, where decoherence is a significant obstacle in the path to large-scale implementations. Besides its practical applications, DQC1 is also fascinating from a fundamental perspective. Its power is thought to lie somewhere between universal classical and quantum computing—it is strictly less powerful than a universal quantum computer [3] and no efficient classical simulation has been found or thought likely to exist [8,9]. Furthermore its power is thought not to come from the generation of entanglement, which is at most marginally present in DQC1 [9]. This is surprising, as entanglement is widely believed to lie at the heart of the advantages offered by a quantum computer—a belief supported by the discovery that a universal pure-state quantum computer must generate a large amount of entanglement in order to offer any speedup over a classical computer [10,11]. However, no such proof exists for mixed-state models. Instead it has been proposed that DQC1 generates other types of nonclassical correlations and that these are responsible for the computational advantage [8,12–14].
In this Letter we present a small-scale implementation of DQC1 in a linear-optic architecture [15]. We observe and fully characterize the predicted nonclassical correlations. Our results show that while there is no entanglement, other intrinsically quantum mechanical correlations are generated, except in the cases where an efficient classical simulation is always possible. Furthermore, we demonstrate that a small fraction of a single pure quantum bit is enough to implement DQC1 efficiently [9]. This represents the first implementation of DQC1 outside of a liquid-state NMR architecture, in which the question of nonclassical correlations was not addressed [16]. Unlike liquid-state NMR, there are several known paths to scalable linear-optic quantum computing [2,17,18], and there is active development of the necessary technology [19–21].

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*Corresponding author.
lanyon@physics.uq.edu.au
?Present address: Laboratoire C. Fabry, Institut d’Optique,
France.
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