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Related Experiment Video

Updated: Jun 29, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Approximate locality for quantum systems on graphs.

Tobias J Osborne¹

¹Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom. Tobias.Osborne@rhul.ac.uk

Physical Review Letters

|October 15, 2008

Summary

This summary is machine-generated.

Researchers show that sparse unitary operators with spectral gaps can be converted into sparse logarithmic Hamiltonians. This advances quantum computing by enabling transformations between continuous-time and discrete-time quantum processes.

Related Experiment Videos

Last Updated: Jun 29, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Area of Science:

Quantum Information Theory
Theoretical Computer Science
Quantum Computing

Background:

Aaronson and Ambainis posed a long-standing problem regarding sparse unitary operators.
Understanding the relationship between continuous-time and discrete-time quantum processes is crucial for quantum computation.

Purpose of the Study:

To address the open problem concerning the existence of approximate logarithms for sparse unitary operators.
To establish a method for converting between local continuous-time and discrete-time quantum processes.

Main Methods:

The study focuses on theoretical analysis of sparse unitary operators.
It involves constructing an approximate logarithmic Hamiltonian (H) from a sparse unitary operator (U).
The density of the sparsity pattern of H is analyzed in relation to the spectral gap (Delta) of U.

Main Results:

It is proven that a sparse unitary operator U with a spectral gap Delta admits a sparse approximate logarithm H.
The sparsity of H increases as the spectral gap (1/Delta) increases.
A practical example demonstrates the conversion of a discrete-time coined quantum walk from a continuous-time quantum walk.

Conclusions:

The findings provide a significant theoretical advancement in quantum information science.
The results offer a novel approach for simulating discrete quantum systems using continuous-time dynamics.
This work bridges the gap between different models of quantum computation, enhancing the flexibility of quantum algorithms.