[Paper Review] Phase Information in Quantum Oracle Computing

Jonathan Machta|ArXiv.org|May 7, 1998

Quantum Computing Algorithms and Architecture5 references8 citations

TL;DR

This paper demonstrates that quantum oracles can transmit phase information inaccessible to classical computers, enabling quantum computers to solve undecidable problems when such phase data is available. The key contribution is showing that useful quantum-classical complexity separations must exclude phase information transmission, as it leads to relativized separations that are not meaningful for practical complexity theory.

ABSTRACT

Computational devices may be supplied with external sources of information (oracles). Quantum oracles may transmit phase information which is available to a quantum computer but not a classical computer. One consequence of this observation is that there is an oracle which is of no assistance to a classical computer but which allows a quantum computer to solve undecidable problems. Thus useful relativized separations between quantum and classical complexity classes must exclude the transmission of phase information from oracle to computer.

Motivation & Objective

• To investigate the role of phase information in quantum oracle computing and its implications for computational power.
• To examine whether phase data transmitted by oracles can grant quantum computers capabilities beyond classical computers.
• To analyze the consequences of phase information for relativized complexity classes and the validity of quantum-classical separations.
• To establish criteria for meaningful complexity class separations by identifying phase information as a source of artificial advantage.
• To clarify the conditions under which quantum oracles provide genuine computational speedups versus artificial advantages from phase data.

Proposed method

• Analyzes the computational model of quantum oracles that transmit phase information to quantum computers.
• Compares the information access of quantum versus classical computers when interacting with oracles that encode phase data.
• Uses relativized complexity theory to evaluate the impact of phase information on decidability and complexity class separations.
• Constructs a theoretical oracle that is ineffective for classical computers but enables quantum computers to solve undecidable problems due to phase access.
• Applies results from quantum query complexity and oracle-based computation to demonstrate the power of phase information.
• Argues that any valid quantum-classical complexity separation must exclude phase information to avoid trivial or misleading separations.

Experimental results

Research questions

• RQ1 Can quantum oracles transmit phase information that classical computers cannot access?
• RQ2 What computational advantages arise from phase information in quantum oracle models?
• RQ3 Does the transmission of phase information allow quantum computers to solve undecidable problems?
• RQ4 How does phase information affect the validity of relativized quantum-classical complexity separations?
• RQ5 What conditions must be imposed on oracles to ensure meaningful complexity class distinctions between quantum and classical computation?

Key findings

• Quantum oracles can transmit phase information that is inaccessible to classical computers.
• A quantum computer with access to phase information from an oracle can solve undecidable problems, while a classical computer cannot.
• This implies that any relativized complexity separation between quantum and classical computation must explicitly exclude phase information to be meaningful.
• The presence of phase information in oracles leads to artificial separations that do not reflect genuine computational advantages.
• The result establishes a fundamental limitation on how oracle-based complexity results should be formulated in quantum computing.
• Phase information must be excluded from oracle models when seeking to establish valid, non-trivial separations between quantum and classical complexity classes.