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2010•Theory of ComputingOpen access

Untitled research work

Andris Ambainis

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Abstract

We present a new method for proving lower bounds on quantum query algorithms. The new method is an extension of the adversary method, by analyzing the eigenspace structure of the problem. Using the new method, we prove a strong direct product theorem for quantum search. This result was previously proved by Klauck, Špalek, and de Wolf (FOCS’04) using the polynomials method. No proof using the adversary method was known before.

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We present a new method for proving lower bounds on quantum query algorithms. The new method is an extension of the adversary method, by analyzing the eigenspace structure of the problem. Using the new method, we prove a strong direct product theorem for quantum search. This result was previously proved by Klauck, Špalek, and de Wolf (FOCS’04) using the polynomials method. No proof using the adversary method was known before.

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Available abstract

We present a new method for proving lower bounds on quantum query algorithms. The new method is an extension of the adversary method, by analyzing the eigenspace structure of the problem. Using the new method, we prove a strong direct product theorem for quantum search. This result was previously proved by Klauck, Špalek, and de Wolf (FOCS’04) using the polynomials method. No proof using the adversary method was known before.

Key concepts: Extension (predicate logic), Mathematics, Product (mathematics), Adversary, Quantum, Discrete mathematics, Computer science, Quantum mechanics

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