Quantum simulation beyond Hamiltonian paradigm: categorical quantum
simulation
- URL: http://arxiv.org/abs/2203.17252v1
- Date: Tue, 29 Mar 2022 14:36:01 GMT
- Title: Quantum simulation beyond Hamiltonian paradigm: categorical quantum
simulation
- Authors: Yuanye Zhu
- Abstract summary: We propose a new dynamic simulation method,categorical quantum simulation.
In our paradigm quantum simulation is no longer based on the structure of the group theory, but based on the structure of the tensor category.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: With the development of topological field theory, the mathematical tool of
the tensor category was also introduced into physics. Traditional group theory
corresponds to a special category,group category. Tensor categories can
describe higher-order interactions and symmetric relations, while group theory
can only describe first-order interactions. In fact, the quantum circuit itself
constitutes a category. However, at present, the field of quantum computing
mainly uses group theory as a mathematical tool. If category theory is
introduced into the field of quantum simulation, the application scope of
quantum computers can be greatly expanded. This paper propose a new dynamic
simulation method,categorical quantum simulation. In our paradigm quantum
simulation is no longer based on the structure of the group theory, but based
on the structure of the tensor category. This could enable many systems that
could not be efficiently quantum simulated before.In this article we give an
concrete example of the categorical simulation of $SU(3)$ Yang-Mills theory. It
shows that categorical quantum simulation provides a new encoding
method,emergenism encoding, which saves more qubits resources than reductionism
quantum encoding. In addition, many domains can be described in the language of
category theory, which allows quantum circuits to directly encode and simulate
these domains.
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