arXiv subjects

Mitchell Chiew

Publications and source records attributed to Mitchell Chiew.

4 recordsLinked to original sources

arXiv2025

Optimal fermion-qubit mappings via quadratic assignment

Simulation of fermionic systems is one of the most promising applications of quantum computers. It spans problems in quantum chemistry, high-energy physics and condensed matter. Underpinning the core steps of any quantum simulation algorithm, fermion-qubit mappings translate the fermionic interactions to the operators and states of quantum computers. This translation is highly non-trivial: a burgeoning supply of fermion-qubit mappings has arisen over the past twenty years to address the limited resources of early quantum technology. Previous literature has presented a dichotomy between ancilla-free fermion-qubit mappings, which minimise qubit count, and local encodings, which minimise gate complexity. We present two computational approaches to the construction of general mappings while working with a limited number of qubits, striking a balance between the low-qubit and low-gate demands of present quantum technology. The first method frames the order of fermionic labels as an instance of the quadratic assignment problem to minimize the total and maximum Pauli weights in a problem Hamiltonian. We compare the order-optimized performance of several common ancilla-free mappings on systems of size up to 225 fermionic modes. The second method is a computational approach to incrementally add ancilla qubits to Jordan--Wigner transformations and further reduce the Pauli weights. By adding up to 10 ancilla qubits, we were able to reduce the total Pauli weight by as much as 67% in Jordan--Wigner transformations of fermionic systems with up to 64 modes, outperforming the previous state-of-the-art ancilla-free mappings. Reproducibility: source code and data are available at https://github.com/cameton/QCE_QubitAssignment

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arXiv2024

Ternary tree transformations are equivalent to linear encodings of the Fock basis

We consider two approaches to designing fermion-qubit mappings: (1) ternary tree transformations, which use Pauli representations of the Majorana operators that correspond to root-to-leaf paths of a tree graph and (2) linear encodings of the Fock basis, such as the Jordan-Wigner and Bravyi-Kitaev transformations, which store linear binary transformations of the fermionic occupation number vectors in the computational basis of qubits. These approaches have emerged as distinct concepts, with little notational consistency between them. In this paper we propose a universal description of fermion-qubit mappings, which reveals the relationship between ternary tree transformations and linear encodings. Using our notation, we show that every product-preserving ternary tree transformation is equivalent to a linear encoding of the Fock basis.

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arXiv2024

A Sierpinski Triangle Fermion-to-Qubit Transform

In order to simulate a system of fermions on a quantum computer, it is necessary to represent the fermionic states and operators on qubits. This can be accomplished in multiple ways, including the well-known Jordan-Wigner transform, as well as the parity, Bravyi-Kitaev, and ternary tree encodings. Notably, the Bravyi-Kitaev encoding can be described in terms of a classical data structure, the Fenwick tree. Here we establish a correspondence between a class of classical data structures similar to the Fenwick tree, and a class of one-to-one fermion-to-qubit transforms. We present a novel fermion-to-qubit encoding based on the recently discovered "Sierpinski tree" data structure, which matches the operator locality of the ternary tree encoding, and has the additional benefit of encoding the fermionic states as computational basis states. This is analogous to the formulation of the Bravyi-Kitaev encoding in terms of the Fenwick tree.

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arXiv2021

Discovering optimal fermion-qubit mappings through algorithmic enumeration

Simulating fermionic systems on a quantum computer requires a high-performing mapping of fermionic states to qubits. A characteristic of an efficient mapping is its ability to translate local fermionic interactions into local qubit interactions, leading to easy-to-simulate qubit Hamiltonians. All fermion-qubit mappings must use a numbering scheme for the fermionic modes in order for translation to qubit operations. We make a distinction between the unordered labelling of fermions and the ordered labelling of the qubits. This separation shines light on a new way to design fermion-qubit mappings by making use of the enumeration scheme for the fermionic modes. The purpose of this paper is to demonstrate that this concept permits notions of fermion-qubit mappings that are optimal with regard to any cost function one might choose. Our main example is the minimisation of the average number of Pauli matrices in the Jordan-Wigner transformations of Hamiltonians for fermions interacting in square lattice arrangements. In choosing the best ordering of fermionic modes for the Jordan-Wigner transformation, and unlike other popular modifications, our prescription does not cost additional resources such as ancilla qubits. We demonstrate how Mitchison and Durbin's enumeration pattern minimises the average Pauli weight of Jordan-Wigner transformations of systems interacting in square lattices. This leads to qubit Hamiltonians consisting of terms with average Pauli weights 13.9% shorter than previously known. By adding only two ancilla qubits we introduce a new class of fermion-qubit mappings, and reduce the average Pauli weight of Hamiltonian terms by 37.9% compared to previous methods. For $n$-mode fermionic systems in cellular arrangements, we find enumeration patterns which result in $n^{1/4}$ improvement in average Pauli weight over na\"ive schemes.

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