Representation of the Fermionic Boundary Operator
| Autor: | Ismail Yunus Akhalwaya, Yang-Hui He, Lior Horesh, Vishnu Jejjala, William Kirby, Kugendran Naidoo, Shashanka Ubaru |
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| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
High Energy Physics - Theory
Quantum Physics Condensed Matter - Strongly Correlated Electrons Strongly Correlated Electrons (cond-mat.str-el) High Energy Physics - Theory (hep-th) Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) FOS: Physical sciences Numerical Analysis (math.NA) Mathematics - Numerical Analysis Quantum Physics (quant-ph) |
| Popis: | The boundary operator is a linear operator that acts on a collection of high-dimensional binary points (simplices) and maps them to their boundaries. This boundary map is one of the key components in numerous applications, including differential equations, machine learning, computational geometry, machine vision and control systems. We consider the problem of representing the full boundary operator on a quantum computer. We first prove that the boundary operator has a special structure in the form of a complete sum of fermionic creation and annihilation operators. We then use the fact that these operators pairwise anticommute to produce an $O(n)$-depth circuit that exactly implements the boundary operator without any Trotterization or Taylor series approximation errors. Having fewer errors reduces the number of shots required to obtain desired accuracies. 16 pages |
| Databáze: | OpenAIRE |
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