A guide to one-to-one fermion-qubit mappings: Mitchell Chiew

Mitchell Chiew (Faculty of Mathematics, University of Cambridge)
A guide to one-to-one fermion-qubit mappings
2nd May 2024
talks.cam.ac.u...
Quantum Computing for Quantum Chemistry Seminar Series
www.ch.cam.ac....
Yusuf Hamied Department of Chemistry, University of Cambridge
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Even on a quantum computer, simulating fermionic dynamics via the second quantisation approach can be exponentially difficult. One of the most important ingredients in any successful attempt is the judicious choice of a fermion-qubit mapping: the qubit representation, as matrices, of the fermionic creation and annihilation operators. For decades, the Jordan-Wigner transformation has been the quantum scientist’s fermion-qubit mapping of choice due to its elegance and simplicity. In more recent years, contenders such as the Bravyi-Kitaev and ternary tree transformations have risen to challenge Jordan-Wigner, claiming exponential improvements at the cost of technical difficulty and a lack of physical intuition. These are all examples of one-to-one fermion-qubit mappings.
In this presentation, we will go over our recent and upcoming work in revealing the true nature of one-to-one fermion-qubit mappings. In doing so, we establish a universal description for a mapping - a set of 2n anticommuting Pauli operators - and derive all known fermion-qubit mappings as a result, while also discovering new mappings which outperform the existing ones in metrics of real-world interest. ​
The talk is based on this work: quantum-journa...