Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2208.07192

Quantum circuits for solving local fermion-to-qubit mappings

Jannes Nys, Giuseppe Carleo

Published Aug 15, 2022• 5 citations
arXivHTMLPDF

Abstract

Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining the locality of the operators comes at the expense of increasing the Hilbert space with auxiliary degrees of freedom. In order to retrieve the lower-dimensional physical Hilbert space that represents fermionic degrees of freedom, one must satisfy a set of constraints. In this work, we introduce quantum circuits that exactly satisfy these stringent constraints. We demonstrate how maintaining locality allows one to carry out a Trotterized time-evolution with constant circuit depth per time step. Our construction is particularly advantageous to simulate the time evolution operator of fermionic systems in d>1 dimensions. We also discuss how these families of circuits can be used as variational quantum states, focusing on two approaches: a first one based on general constant-fermion-number gates, and a second one based on the Hamiltonian variational ansatz where the eigenstates are represented by parametrized time-evolution operators. We apply our methods to the problem of finding the ground state and time-evolved states of the $t$-$V$ model.

DOI
10.48550/arxiv.2208.07192

Related papers

Variational solutions to fermion-to-qubit mappings in two spatial dimensions

Jannes Nys, Giuseppe Carleo

Through the introduction of auxiliary fermions, or an enlarged spin space, one can map local fermion Hamiltonians onto local spin Hamiltonians, at the expense of introducing a set of additional constraints. We present a variational Monte-Carlo framework to study fermionic systems through higher-dimensional ( > 1D) Jordan-Wigner transformations. We provide exact solutions to the parity and Gauss-law constraints that are encountered in bosonization procedures. We study the t - V model in 2D and demonstrate how both the ground state and the low-energy excitation spectra can be retrieved in combination with neural network quantum state ansatze.

arXiv:2205.00733•Quantum•Oct 13, 2022•17 citations

Investigating Interacting Fermionic Models with Locality-Preserving Qubit Encodings

Ashutosh P. Tripathi, Debasish Banerjee, Sandip Maiti +1 more

We investigate the utility of the locality-preserving Derby-Klassen (DK) fermion-to-qubit mapping [arXiv:2003.06939] for variational quantum simulation of two-dimensional $t$-$V$ and Fermi-Hubbard models. The DK mapping preserves the locality of fermionic interactions with an enlarged Hilbert space, thereby requiring additional constraints that define the physical sector. We incorporate these constraints directly into a Hamiltonian Variational Ansätz (HVA) through Clifford-gate state preparation and use the Variational Quantum Eigensolver (VQE) to show that the low-energy properties of the resulting qubit Hamiltonian are accurately reproduced. We further exploit particle-number conservation inherent in the ansätz to resolve distinct symmetry sectors and reliably access degenerate states. Consequently, we benchmark the DK-HVA against Jordan-Wigner-based variational circuits at nonzero chemical potential, where particle-hole symmetry and the associated half-filled sign-free condition are absent. Finally, we demonstrate the advantage of locality-preserving mappings in higher-dimensional fermionic systems, where the conventional Jordan-Wigner (JW) transformation generates increasingly long Pauli strings and corresponding circuit overheads. We further extend the framework to the spinful Fermi-Hubbard model and identify a tradeoff between fermionic-mode placement and the locality of hopping and on-site interaction terms. These results establish a practical framework combining locality-preserving fermion-to-qubit mappings, constraint-preserving Clifford state preparation, and symmetry-preserving variational circuits, that trades auxiliary-qubit and stabilizer-preparation overhead for reduced operator nonlocality, providing a practical route toward resource-efficient quantum simulation of higher-dimensional interacting fermionic systems.

quant-pharXiv:2609.16142•Sep 16, 2026•0 citations

Efficient Simulation of Sparse, Non-Local Fermion Models

Reinis Irmejs, J. Ignacio Cirac

Efficient simulation of interacting fermionic systems is a key application of near-term quantum computers, but is hindered by the overhead required to encode fermionic operators on qubit hardware. Here, we consider models with $N$ fermionic modes in which each participates in at most a constant number $d$ of interactions and study the circuit depth required to implement the Trotterized time evolution on qubit hardware with all-to-all connectivity. We introduce an encoding that augments each physical fermionic mode with a small number of auxiliary fermions, enabling the removal of Jordan--Wigner strings. Although the preparation of the auxiliary fermion state incurs an initial overhead, this state remains invariant under time evolution. As a result, long-time evolution can be implemented with asymptotically optimal circuit depth, reducing a previously multiplicative $O(\log N)$ overhead to an additive overhead. Our results thus establish that the simulation of sparse fermionic models on qubit hardware matches the performance achievable on ideal fermionic hardware up to constant factors and $O(dN)$ ancillary qubits.

quant-pharXiv:2512.15843•Dec 18, 2025•0 citations

Local fermion-to-qudit mappings: A practical recipe for four-level systems

Rodolfo Carobene, Andrea Giachero, Stefano Barison +1 more

In this paper, we present a new set of local fermion-to-qudit mappings for simulating fermionic lattice systems. We focus on the use of multi-level qudits, specifically ququarts. Traditional mappings, such as the Jordan-Wigner transformation (JWT), while useful, often result in non-local operators that scale unfavorably with system size. To address these challenges, we introduce mappings that efficiently localize fermionic operators on qudits, reducing the non-locality and operator weights associated with JWT. We propose one mapping for spinless fermions and two mappings for spinful fermions, comparing their performance in terms of qudit-weight, circuit depth, and gate complexity. By leveraging the extended local Hilbert space of qudits, we show that these mappings enable more efficient quantum simulations in terms of two-qudit gates, reducing hardware requirements without increasing computational complexity. We validate our approach by simulating prototypical models such as the spinless t-V model and the Fermi-Hubbard model in two dimensions, using Trotterized time evolution. Our results highlight the potential of qudit-based quantum simulations in achieving scalability and efficiency for fermionic systems on near-term quantum devices.

arXiv:2412.05616•Physical Review A•Sep 2, 2025•1 citation

Lowering qubit requirements for quantum simulations of fermionic systems

Mark Steudtner, Stephanie Wehner

The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in chemistry and physics, quantum simulation is one of the great promises of the coming age of quantum computers. One challenge in realizing simulations on near-term quantum devices is the large number of qubits required by such mappings. In this work, we develop methods that allow us to trade-off qubit requirements against the complexity of the resulting quantum circuit. We first show that any classical code used to map the state of a fermionic Fock space to qubits gives rise to a mapping of fermionic models to quantum gates. As an illustrative example, we present a mapping based on a non-linear classical error correcting code, which leads to significant qubit savings albeit at the expense of additional quantum gates. We proceed to use this framework to present a number of simpler mappings that lead to qubit savings with only a very modest increase in gate difficulty. We discuss the role of symmetries such as particle conservation, and savings that could be obtained if an experimental platform could easily realize multi-controlled gates.

arXiv:1712.07067•Bulletin of the American Physical Society•Dec 19, 2017•18 citations

Optimal compression of constrained quantum time evolution

Maurits S. J. Tepaske, David J. Luitz, Dominik Hahn

The time evolution of quantum many-body systems is one of the most promising applications for near-term quantum computers. However, the utility of current quantum devices is strongly hampered by the proliferation of hardware errors. The minimization of the circuit depth for a given quantum algorithm is therefore highly desirable, since shallow circuits generally are less vulnerable to decoherence. Recently, it was shown that variational circuits are a promising approach to outperform current state-of-the-art methods such as Trotter decomposition, although the optimal choice of parameters is a computationally demanding task. In this work, we demonstrate a simplification of the variational optimization of circuits implementing the time evolution operator of local Hamiltonians by directly encoding constraints of the physical system under consideration. We study the expressibility of such constrained variational circuits for different models and constraints. Our results show that the encoding of constraints allows a reduction of optimization cost by more than one order of magnitude and scalability to arbitrary large system sizes, without loosing accuracy in most systems. Furthermore, we discuss the exceptions in locally constrained systems and provide an explanation by means of an restricted lightcone width after incorporating the constraints into the circuits.

arXiv:2311.06347•Physical review. B./Physical review. B•May 15, 2024•3 citations
Local Hamiltonians of fermionic systems on a lattice can be mapped onto local qubit Hamiltonians. Maintaining the locality of the operators comes at the expense of increasing the Hilbert space with auxiliary degrees of freedom. In order to retrieve the lower-dimensional physical Hilbert space that represents fermionic degrees of freedom, one must satisfy a set of constraints. In this work, we introduce quantum circuits that exactly satisfy these stringent constraints. We demonstrate how maintaining locality allows one to carry out a Trotterized time-evolution with constant circuit depth per time step. Our construction is particularly advantageous to simulate the time evolution operator of fermionic systems in d>1 dimensions. We also discuss how these families of circuits can be used as variational quantum states, focusing on two approaches: a first one based on general constant-fermion-number gates, and a second one based on the Hamiltonian variational ansatz where the eigenstates are represented by parametrized time-evolution operators. We apply our methods to the problem of finding the ground state and time-evolved states of the ttt-VVV model.
Through the introduction of auxiliary fermions, or an enlarged spin space, one can map local fermion Hamiltonians onto local spin Hamiltonians, at the expense of introducing a set of additional constraints. We present a variational Monte-Carlo framework to study fermionic systems through higher-dimensional ( > 1D) Jordan-Wigner transformations. We provide exact solutions to the parity and Gauss-law constraints that are encountered in bosonization procedures. We study the t - V model in 2D and demonstrate how both the ground state and the low-energy excitation spectra can be retrieved in combination with neural network quantum state ansatze.
We investigate the utility of the locality-preserving Derby-Klassen (DK) fermion-to-qubit mapping [arXiv:2003.06939] for variational quantum simulation of two-dimensional ttt-VVV and Fermi-Hubbard models. The DK mapping preserves the locality of fermionic interactions with an enlarged Hilbert space, thereby requiring additional constraints that define the physical sector. We incorporate these constraints directly into a Hamiltonian Variational Ansätz (HVA) through Clifford-gate state preparation and use the Variational Quantum Eigensolver (VQE) to show that the low-energy properties of the resulting qubit Hamiltonian are accurately reproduced. We further exploit particle-number conservation inherent in the ansätz to resolve distinct symmetry sectors and reliably access degenerate states. Consequently, we benchmark the DK-HVA against Jordan-Wigner-based variational circuits at nonzero chemical potential, where particle-hole symmetry and the associated half-filled sign-free condition are absent. Finally, we demonstrate the advantage of locality-preserving mappings in higher-dimensional fermionic systems, where the conventional Jordan-Wigner (JW) transformation generates increasingly long Pauli strings and corresponding circuit overheads. We further extend the framework to the spinful Fermi-Hubbard model and identify a tradeoff between fermionic-mode placement and the locality of hopping and on-site interaction terms. These results establish a practical framework combining locality-preserving fermion-to-qubit mappings, constraint-preserving Clifford state preparation, and symmetry-preserving variational circuits, that trades auxiliary-qubit and stabilizer-preparation overhead for reduced operator nonlocality, providing a practical route toward resource-efficient quantum simulation of higher-dimensional interacting fermionic systems.
Efficient simulation of interacting fermionic systems is a key application of near-term quantum computers, but is hindered by the overhead required to encode fermionic operators on qubit hardware. Here, we consider models with NNN fermionic modes in which each participates in at most a constant number ddd of interactions and study the circuit depth required to implement the Trotterized time evolution on qubit hardware with all-to-all connectivity. We introduce an encoding that augments each physical fermionic mode with a small number of auxiliary fermions, enabling the removal of Jordan--Wigner strings. Although the preparation of the auxiliary fermion state incurs an initial overhead, this state remains invariant under time evolution. As a result, long-time evolution can be implemented with asymptotically optimal circuit depth, reducing a previously multiplicative O(log⁡N)O(\log N)O(logN) overhead to an additive overhead. Our results thus establish that the simulation of sparse fermionic models on qubit hardware matches the performance achievable on ideal fermionic hardware up to constant factors and O(dN)O(dN)O(dN) ancillary qubits.
In this paper, we present a new set of local fermion-to-qudit mappings for simulating fermionic lattice systems. We focus on the use of multi-level qudits, specifically ququarts. Traditional mappings, such as the Jordan-Wigner transformation (JWT), while useful, often result in non-local operators that scale unfavorably with system size. To address these challenges, we introduce mappings that efficiently localize fermionic operators on qudits, reducing the non-locality and operator weights associated with JWT. We propose one mapping for spinless fermions and two mappings for spinful fermions, comparing their performance in terms of qudit-weight, circuit depth, and gate complexity. By leveraging the extended local Hilbert space of qudits, we show that these mappings enable more efficient quantum simulations in terms of two-qudit gates, reducing hardware requirements without increasing computational complexity. We validate our approach by simulating prototypical models such as the spinless t-V model and the Fermi-Hubbard model in two dimensions, using Trotterized time evolution. Our results highlight the potential of qudit-based quantum simulations in achieving scalability and efficiency for fermionic systems on near-term quantum devices.
The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in chemistry and physics, quantum simulation is one of the great promises of the coming age of quantum computers. One challenge in realizing simulations on near-term quantum devices is the large number of qubits required by such mappings. In this work, we develop methods that allow us to trade-off qubit requirements against the complexity of the resulting quantum circuit. We first show that any classical code used to map the state of a fermionic Fock space to qubits gives rise to a mapping of fermionic models to quantum gates. As an illustrative example, we present a mapping based on a non-linear classical error correcting code, which leads to significant qubit savings albeit at the expense of additional quantum gates. We proceed to use this framework to present a number of simpler mappings that lead to qubit savings with only a very modest increase in gate difficulty. We discuss the role of symmetries such as particle conservation, and savings that could be obtained if an experimental platform could easily realize multi-controlled gates.
The time evolution of quantum many-body systems is one of the most promising applications for near-term quantum computers. However, the utility of current quantum devices is strongly hampered by the proliferation of hardware errors. The minimization of the circuit depth for a given quantum algorithm is therefore highly desirable, since shallow circuits generally are less vulnerable to decoherence. Recently, it was shown that variational circuits are a promising approach to outperform current state-of-the-art methods such as Trotter decomposition, although the optimal choice of parameters is a computationally demanding task. In this work, we demonstrate a simplification of the variational optimization of circuits implementing the time evolution operator of local Hamiltonians by directly encoding constraints of the physical system under consideration. We study the expressibility of such constrained variational circuits for different models and constraints. Our results show that the encoding of constraints allows a reduction of optimization cost by more than one order of magnitude and scalability to arbitrary large system sizes, without loosing accuracy in most systems. Furthermore, we discuss the exceptions in locally constrained systems and provide an explanation by means of an restricted lightcone width after incorporating the constraints into the circuits.