Finite temperature quantum algorithm and majorization

Debabrata Ghoshal; Richard Gomez; Marco Lanzagorta; Jeffrey Uhlmann

doi:10.1117/12.777461

27 March 2008 Finite temperature quantum algorithm and majorization

Debabrata Ghoshal, Richard Gomez, Marco Lanzagorta, Jeffrey Uhlmann

Proceedings Volume 6976, Quantum Information and Computation VI; 69760V (2008) https://doi.org/10.1117/12.777461
Event: SPIE Defense and Security Symposium, 2008, Orlando, Florida, United States

Abstract

It is often believed that quantum entanglement plays an important role in the speed-up of quantum algorithms. In addition, a few research groups have found that Majorization behavior may also play an important role in some quantum algorithms. In some of our previous work we showed that for a simple spin 1/2 system, consisting of two or three qubits, the value of a Groverian entanglement (a rather useful measure of entanglement) varies inversely with the temperature. In practical terms this means that more iterations of the Grover's algorithm may be needed when a quantum computer is working at finite temperature. That is, the performance of a quantum algorithm suffers due to temperature-dependent changes on the density matrix of the system. Most recently, we have been interested in the behavior of Majorization for the same types of quantum system, and we are trying to determine the relationship between Groverian entanglement and Majorization at finite temperature. As Majorization entails the probability distribution arising out of the evolving quantum state from the probabilities of the final outcomes, our study will reveal how Majorization affects the evolution of Grover's algorithm at finite temperature.

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Debabrata Ghoshal, Richard Gomez, Marco Lanzagorta, and Jeffrey Uhlmann "Finite temperature quantum algorithm and majorization", Proc. SPIE 6976, Quantum Information and Computation VI, 69760V (27 March 2008); https://doi.org/10.1117/12.777461

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KEYWORDS

Quantum communications

Quantum computing

Error analysis

Chemical elements

Quantum information

Temperature metrology

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