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Revisiting the simulation of quantum Turing machines by quantum circuits
1Institute for Quantum Computing and School of Computer Science, University of Waterloo, Waterloo, Canada.
Proceedings. Mathematical, Physical, and Engineering Sciences
|July 12, 2019
Summary
This study enhances quantum Turing machine simulations using quantum circuits. We show linear-depth circuits can simulate quantum Turing machines, improving upon previous quadratic-depth models for quantum computation.
Area of Science:
- Quantum Computing
- Theoretical Computer Science
Background:
- Quantum Turing machines and quantum circuits are polynomially equivalent computational models.
- Yao's 1995 work established a quadratic simulation of quantum Turing machines by quantum circuits.
Purpose of the Study:
- To revisit and improve the simulation of quantum Turing machines using uniformly generated quantum circuits.
- To present a novel analysis of quantum circuit simulation methods.
Main Methods:
- Extension of the Arright, Nesme, and Werner (2011) method for localizing causal unitary evolutions.
- Analysis of simulation complexity focusing on circuit depth.
Main Results:
- Demonstration that quantum Turing machines can be simulated by quantum circuits with linear depth.
- The simulation method is adaptable to variants of quantum Turing machines, including multi-dimensional tape models.
Conclusions:
- The simulation of quantum Turing machines by quantum circuits can be achieved with improved depth complexity.
- This research offers a more efficient method for understanding the relationship between quantum Turing machines and quantum circuits.
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