Experimental Quantum Computing without Entanglement

Abstract

Entanglement is widely believed to lie at the heart of the advantages offered by a quantum computer. This belief is supported by the discovery that a noiseless (pure) state quantum computer must generate a large amount of entanglement in order to offer any speed up over a classical computer. However, deterministic quantum computation with one pure qubit (DQC1), which employs noisy (mixed) states, is an efficient model that generates at most a marginal amount of entanglement. Although this model cannot implement any arbitrary algorithm it can efficiently solve a range of problems of significant importance to the scientific community. Here we experimentally implement a first-order case of a key DQC1 algorithm and explicitly characterise the non-classical correlations generated. Our results show that while there is no entanglement the algorithm does give rise to other non-classical correlations, which we quantify using the quantum discord-a stronger measure of nonclassical correlations that includes entanglement as a subset. Our results suggest that discord could replace entanglement as a necessary resource for a quantum computational speed-up. Furthermore, DQC1 is far less resource intensive than universal quantum computing and our implementation in a scalable architecture highlights the model as a practical short-term goal.In contrast to the highly pure multi-qubit states required for the conventional models of quantum computing [1, 2], DQC1 employs only a single qubit in a pure state, alongside a register of qubits in the fully mixed state [3]. While this model is strictly less powerful than a universal quantum computer (where one can implement any arbitrary algorithm) it can still efficiently solve important problems that are thought to be classically intractable. The application originally identified was the efficient simulation of some quantum systems [3]. Since then exponential speed-ups 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]. Recently it has been shown that DQC1 also affords efficient parameter estimation at the quantum metrology limit [7]. Furthermore, attempts to find an efficient way of classically simulating DQC1 have failed [8]. These results provide strong evidence that a device capable of implenting scalable DQC1 algorithms would be an extremely useful tool.Besides the practical applications, DQC1 is also fascinating from a fundamental perspective. For example, it is straightforward to show that a model employing only fully mixed qubits offers no advantage over a classical computer. It is therefore surprising that the addition of only a single pure qubit offers such a dramatic increase in computational power. Furthermore, an important quantum information result is that a pure state quantum computer can only offer an advantage over a classical approach if it generates an amount of entanglement that grows with the size of the problem being tackled [9,10]. This support...

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