Role of entanglement and correlations in mixed-state quantum computation

By Animesh Datta, Guifré Vidal. 2006

219 citations recorded by the source corpus.

In a quantum computation with pure states, the generation of large amounts of entanglement is known to be necessary for a speedup with respect to classical computations. However, examples of quantum computations with mixed states are known, such as the deterministic computation with one quantum qubit (DQC1) model [Knill and Laflamme, Phys. Rev. Lett. 81, 5672 (1998)], in which entanglement is at most marginally present, and yet a computational speedup is believed to occur. Correlations, and not entanglement, have been identified as a necessary ingredient for mixed-state quantum computation speedups. Here we show that correlations, as measured through the operator Schmidt rank, are indeed present in large amounts in the DQC1 circuit. This provides evidence for the preclusion of efficient classical simulation of DQC1 by means of a whole class of classical simulation algorithms, thereby reinforcing the conjecture that DQC1 leads to a genuine quantum computational speedup.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/ce3a314c933b0ba0a2eaa5648fe2335a9df4e897

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

The classical-quantum boundary for correlations: Discord and related measures (2011, methodology): “(Datta and Vidal, 2007) show that standard methods for classically simulating quantum processes are inefficient for simulating the trace estimation algorithm.”
Observing the operational significance of discord consumption (2012, background): “[2] Datta, A.”