Abstract

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: https://quantum-journal.org/papers/q-2023-10-18-1145/