Hamiltonian simulation for time-evolving partial differential equation
by scalable quantum circuits
- URL: http://arxiv.org/abs/2402.18398v1
- Date: Wed, 28 Feb 2024 15:17:41 GMT
- Title: Hamiltonian simulation for time-evolving partial differential equation
by scalable quantum circuits
- Authors: Yuki Sato, Ruho Kondo, Ikko Hamamura, Tamiya Onodera, Naoki Yamamoto
- Abstract summary: Hamiltonian simulation is a potential and promising approach to achieve this purpose.
This paper presents a method that enables us to explicitly implement the quantum circuit for Hamiltonian simulation.
We show that the space and time complexity of the constructed circuit is exponentially smaller than that of all classical algorithms.
- Score: 1.7453899104963828
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Solving partial differential equations for extremely large-scale systems
within a feasible computation time serves in accelerating engineering
developments. Quantum computing algorithm, particularly the Hamiltonian
simulation, is a potential and promising approach to achieve this purpose.
Actually there are several proposals of Hamiltonian simulation with potential
quantum speedup, but their detailed implementation and accordingly the detailed
computational complexity are all somewhat unclear. This paper presents a method
that enables us to explicitly implement the quantum circuit for Hamiltonian
simulation; the key technique is the explicit gate construction of differential
operators contained in the target partial differential equation. Moreover, we
show that the space and time complexity of the constructed circuit is
exponentially smaller than that of all classical algorithms. We also provide
numerical experiments and an experiment on a real device for the wave equation
to demonstrate the validity of our proposed method.
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