Quantum Effects in Algorithms

TL;DR

This paper explores paradoxical quantum effects in information processing, highlighting how entanglement and measurement can lead to computational advantages without traditional computation.

Contribution

It introduces novel quantum phenomena related to 'doing nothing' and measurement, explaining their roles in quantum algorithm speedup and decision problems.

Findings

'Doing nothing' on entangled systems is crucial for quantum speedup.

Quantum measurement effects enable answer retrieval without running the algorithm.

Potential for new quantum computational paradigms.

Abstract

We discuss some seemingly paradoxical yet valid effects of quantum physics in information processing. Firstly, we argue that the act of ``doing nothing'' on part of an entangled quantum system is a highly non-trivial operation and that it is the essential ingredient underlying the computational speedup in the known quantum algorithms. Secondly, we show that the watched pot effect of quantum measurement theory gives the following novel computational possibility: suppose that we have a quantum computer with an on/off switch, programmed ready to solve a decision problem. Then (in certain circumstances) the mere fact that the computer would have given the answer if it were run, is enough for us to learn the answer, even though the computer is in fact not run.