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Generalising quantum imaginary time evolution to solve linear partial differential equations
Swagat Kumar1, Colin Michael Wilmott2
1Department of Physics and Mathematics, Nottingham Trent University, Nottingham, NG11 8NS, UK. swagat.kumar02@ntu.ac.uk.
Scientific Reports
|August 30, 2024
Summary
Quantum imaginary time evolution (QITE) offers a new quantum numerical solver for linear partial differential equations. This method tracks state vector scale to solve differential equations, demonstrating success with the heat equation.
Area of Science:
- Quantum Computing
- Numerical Analysis
- Computational Physics
Background:
- Quantum imaginary time evolution (QITE) addresses non-unitarity in quantum computing.
- QITE has been utilized for approximating ground states of physical systems.
Purpose of the Study:
- To demonstrate a practical application of QITE as a quantum numerical solver for linear partial differential equations.
- To adapt QITE's state vector tracking for solving differential equations.
Main Methods:
- Algorithm inspired by QITE, maintaining normalized trajectory.
- Key innovation: tracking the scale of the quantum state vector over time.
- Demonstrated using numerical simulations on quantum systems.
Main Results:
- Successfully applied the QITE-inspired methodology to solve linear partial differential equations.
- Solved the one-dimensional heat equation using six qubits.
- Solved the two-dimensional heat equation using ten qubits.
Conclusions:
- The QITE methodology can be practically applied as a quantum numerical solver for differential equations.
- Tracking state vector scale is crucial for solving differential equations with this quantum approach.
- The method shows promise for tackling complex computational problems on quantum computers.
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