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

Logical Majorana Fermions for Fault-Tolerant Quantum Simulation.

Benjamin Morrison, Andrew J. Landahl

Published Oct 1, 2022• 4 citations
Publisher

Abstract

▶︎ Simplified architecture stack without logical qubit layer.▶︎ Quadratic gate depth reduction for Trotter-Suzuki simulation [5] of 2D Hubbard model by exploring locality for parallelism.▶︎ T-count reduction of 20% to leading order over [4] for qubitized simulation of 2D Hubbard model using Majorana-inspired techniques also compatible with logical qubit architectures.

DOI
10.2172/2005519

Related papers

Logical fermions for fault-tolerant quantum simulation

Andrew J. Landahl, Benjamin Morrison

We show how to absorb fermionic quantum simulation's expensive fermion-to-qubit mapping overhead into the overhead already incurred by surface-code-based fault-tolerant quantum computing. The key idea is to process information in surface-code twist defects, which behave like logical Majorana fermions. Our approach encodes Dirac fermions, a key data type for simulation applications, directly into logical Majorana fermions rather than atop a logical qubit layer in the architecture. Using quantum simulation of the $N$-fermion 2D Fermi-Hubbard model as an exemplar, we demonstrate two immediate algorithmic improvements. First, by preserving the model's locality at the logical level, we reduce the asymptotic Trotter-Suzuki quantum circuit depth from $\mathcal{O}(\sqrt{N})$ in a typical Jordan-Wigner encoding to $\mathcal{O}(1)$ in our encoding. Second, by exploiting optimizations manifest for logical fermions but less obvious for logical qubits, we reduce the $T$-count of the block-encoding \textsc{select} oracle by 20\% over standard implementations, even when realized by logical qubits and not logical fermions.

arXiv:2110.10280•Oct 19, 2021•4 citations

Fault-tolerant fermionic quantum computation based on color code

Ying Li

An important approach to fault-tolerant quantum computation is protecting logical information using quantum error correction. Usually, logical information is in the form of logical qubits, which are encoded in physical qubits using quantum error correction codes. Compared with qubit quantum computation, fermionic quantum computation has advantages in quantum simulations of fermionic systems, e.g., molecules. In this paper, we show that fermionic quantum computation can be universal and fault tolerant if we encode logical Majorana fermions in physical Majorana fermions. We take a color code as an example to demonstrate the universal set of fault-tolerant operations on logical Majorana fermions, and we numerically find that the fault-tolerance threshold is about $0.8%$.

arXiv:1709.06245•Physical Review A•Jul 31, 2018•18 citations

Practical gates by Majorana fermion motion

Yuri D. Lensky, Bryce Kobrin, Kostyantyn Kechedzhi +1 more

Quantum error correction protocols protect against local errors by storing logical information non-locally. This poses a challenge: how to design efficient logical gates on the non-local ``hidden'' logical information, and how to implement these gates using the local physical operations. We develop a general description of planar Pauli stabilizer codes and protocols for logical operations in terms of point-like particles called Majorana fermions. Information is stored in the pairwise fermion parities of spatially separated Majorana fermions. The description in terms of Majorana fermions captures not only large distance asymptotics, but also all scales down to the lattice constants. We exploit this locality to densely pack logical information in spacetime. The simplest application is to a static case: dense memory. More importantly, we implement fault-tolerant Majorana motion and leverage this primitive to design braiding-based logical gates. This approach reduces space overhead of logical operations resulting in an improved logical error rate given fixed number of physical qubits. We illustrate a practical use of our approach by designing and benchmarking of 2-qubit Clifford gates. We find numerically that our protocol outperforms lattice surgery in this setting for near-term error rates and realistic device constraints. More generally, introduction of compact motion of Majorana fermions as an efficient computational primitive opens a promising new route for the design of low overhead error correction protocols.

quant-pharXiv:2606.03916•Jun 3, 2026•0 citations

Quantum gates and architecture for the quantum simulation of the Fermi-Hubbard model

Pierre-Luc Dallaire-Demers, Frank K. Wilhelm

Quantum computers are the ideal platform for quantum simulations. Given enough coherent operations and qubits, such machines can be leveraged to simulate strongly correlated materials, where intricate quantum effects give rise to counterintuitive macroscopic phenomena such as high-temperature superconductivity. In this paper, we provide a gate decomposition and an architecture for a quantum simulator used to simulate the Fermi-Hubbard model in a hybrid variational quantum-classical algorithm. We propose a simple planar implementation-independent layout of qubits that can also be used to simulate more general fermionic systems. By working through a concrete application, we show the gate decomposition used to simulate the Hamiltonian of a cluster of the Fermi-Hubbard model. We briefly analyze the Trotter-Suzuki errors and estimate the scaling properties of the algorithm for more complex applications.

arXiv:1606.00208•Physical Review A•Dec 5, 2016•34 citations

Fault-Tolerant Quantum Simulation of Generalized Hubbard Models

Andreas Juul Bay-Smidt, Frederik Ravn Klausen, Christoph Sünderhauf +3 more

Quantum simulations of strongly interacting fermionic systems, such as those described by the Hubbard model, are promising candidates for useful early fault-tolerant quantum computing applications. This paper presents tile Trotterization, a generalization of plaquette Trotterization, which uses a set of tiles to construct Trotter decompositions of arbitrary lattice Hubbard models. The tile Trotterization scheme also enables the simulation of more complex models, including the extended Hubbard model. We improve previous Hubbard-model commutator bounds, further provide tight commutator bounds for periodic extended Hubbard models, and demonstrate the use of tensor network methods for this task. We consider applications of tile Trotterization to simulate hexagonal lattice Hubbard models and compare the resource requirements of tile Trotterization for performing quantum phase estimation to a qubitization-based approach, demonstrating that tile Trotterization scales more efficiently with system size. These advancements significantly broaden the potential applications of early fault-tolerant quantum computers to models of practical interest in materials research and organic chemistry.

arXiv:2501.10314•PRX Quantum•Jul 30, 2025•2 citations

Quantum simulation of Fermi-Hubbard model based on transmon qudit interaction

Arian Vezvaee, Nathan Earnest, Khadijeh Najafi

The Fermi-Hubbard model, a fundamental framework for studying strongly correlated phenomena could significantly benefit from quantum simulations when exploring non-trivial settings. However, simulating this problem requires twice as many qubits as the physical sites, in addition to complicated on-chip connectivities and swap gates required to simulate the physical interactions. In this work, we introduce a novel quantum simulation approach utilizing qudits to overcome such complexities. Leveraging on the symmetries of the Fermi-Hubbard model and their intrinsic relation to Clifford algebras, we first demonstrate a Qudit Fermionic Mapping (QFM) that reduces the encoding cost associated with the qubit-based approach. We then describe the unitary evolution of the mapped Hamiltonian by interpreting the resulting Majorana operators in terms of physical single- and two-qudit gates. While the QFM can be used for any quantum hardware with four accessible energy levels, we demonstrate the specific reduction in overhead resulting from utilizing the native Controlled-SUM gate (equivalent to qubit CNOT) for a fixed-frequency ququart transmon. We further transpile the resulting two transmon-qudit gates by demonstrating a qudit operator Schmidt decomposition using the Controlled-SUM gate. Finally, we demonstrate the efficacy of our proposal by numerical simulation of local observables such as the filling factor and Green's function for various Trotter steps. The compatibility of our approach with different qudit platforms paves the path for achieving quantum advantage in simulating non-trivial quantum many-body systems.

arXiv:2402.01243•Feb 2, 2024•0 citations
▶︎ Simplified architecture stack without logical qubit layer.▶︎ Quadratic gate depth reduction for Trotter-Suzuki simulation [5] of 2D Hubbard model by exploring locality for parallelism.▶︎ T-count reduction of 20% to leading order over [4] for qubitized simulation of 2D Hubbard model using Majorana-inspired techniques also compatible with logical qubit architectures.
We show how to absorb fermionic quantum simulation's expensive fermion-to-qubit mapping overhead into the overhead already incurred by surface-code-based fault-tolerant quantum computing. The key idea is to process information in surface-code twist defects, which behave like logical Majorana fermions. Our approach encodes Dirac fermions, a key data type for simulation applications, directly into logical Majorana fermions rather than atop a logical qubit layer in the architecture. Using quantum simulation of the NNN-fermion 2D Fermi-Hubbard model as an exemplar, we demonstrate two immediate algorithmic improvements. First, by preserving the model's locality at the logical level, we reduce the asymptotic Trotter-Suzuki quantum circuit depth from O(N)\mathcal{O}(\sqrt{N})O(N​) in a typical Jordan-Wigner encoding to O(1)\mathcal{O}(1)O(1) in our encoding. Second, by exploiting optimizations manifest for logical fermions but less obvious for logical qubits, we reduce the TTT-count of the block-encoding \textsc{select} oracle by 20\% over standard implementations, even when realized by logical qubits and not logical fermions.
An important approach to fault-tolerant quantum computation is protecting logical information using quantum error correction. Usually, logical information is in the form of logical qubits, which are encoded in physical qubits using quantum error correction codes. Compared with qubit quantum computation, fermionic quantum computation has advantages in quantum simulations of fermionic systems, e.g., molecules. In this paper, we show that fermionic quantum computation can be universal and fault tolerant if we encode logical Majorana fermions in physical Majorana fermions. We take a color code as an example to demonstrate the universal set of fault-tolerant operations on logical Majorana fermions, and we numerically find that the fault-tolerance threshold is about 0.80.8%0.8.
Quantum error correction protocols protect against local errors by storing logical information non-locally. This poses a challenge: how to design efficient logical gates on the non-local ``hidden'' logical information, and how to implement these gates using the local physical operations. We develop a general description of planar Pauli stabilizer codes and protocols for logical operations in terms of point-like particles called Majorana fermions. Information is stored in the pairwise fermion parities of spatially separated Majorana fermions. The description in terms of Majorana fermions captures not only large distance asymptotics, but also all scales down to the lattice constants. We exploit this locality to densely pack logical information in spacetime. The simplest application is to a static case: dense memory. More importantly, we implement fault-tolerant Majorana motion and leverage this primitive to design braiding-based logical gates. This approach reduces space overhead of logical operations resulting in an improved logical error rate given fixed number of physical qubits. We illustrate a practical use of our approach by designing and benchmarking of 2-qubit Clifford gates. We find numerically that our protocol outperforms lattice surgery in this setting for near-term error rates and realistic device constraints. More generally, introduction of compact motion of Majorana fermions as an efficient computational primitive opens a promising new route for the design of low overhead error correction protocols.
Quantum computers are the ideal platform for quantum simulations. Given enough coherent operations and qubits, such machines can be leveraged to simulate strongly correlated materials, where intricate quantum effects give rise to counterintuitive macroscopic phenomena such as high-temperature superconductivity. In this paper, we provide a gate decomposition and an architecture for a quantum simulator used to simulate the Fermi-Hubbard model in a hybrid variational quantum-classical algorithm. We propose a simple planar implementation-independent layout of qubits that can also be used to simulate more general fermionic systems. By working through a concrete application, we show the gate decomposition used to simulate the Hamiltonian of a cluster of the Fermi-Hubbard model. We briefly analyze the Trotter-Suzuki errors and estimate the scaling properties of the algorithm for more complex applications.
Quantum simulations of strongly interacting fermionic systems, such as those described by the Hubbard model, are promising candidates for useful early fault-tolerant quantum computing applications. This paper presents tile Trotterization, a generalization of plaquette Trotterization, which uses a set of tiles to construct Trotter decompositions of arbitrary lattice Hubbard models. The tile Trotterization scheme also enables the simulation of more complex models, including the extended Hubbard model. We improve previous Hubbard-model commutator bounds, further provide tight commutator bounds for periodic extended Hubbard models, and demonstrate the use of tensor network methods for this task. We consider applications of tile Trotterization to simulate hexagonal lattice Hubbard models and compare the resource requirements of tile Trotterization for performing quantum phase estimation to a qubitization-based approach, demonstrating that tile Trotterization scales more efficiently with system size. These advancements significantly broaden the potential applications of early fault-tolerant quantum computers to models of practical interest in materials research and organic chemistry.
The Fermi-Hubbard model, a fundamental framework for studying strongly correlated phenomena could significantly benefit from quantum simulations when exploring non-trivial settings. However, simulating this problem requires twice as many qubits as the physical sites, in addition to complicated on-chip connectivities and swap gates required to simulate the physical interactions. In this work, we introduce a novel quantum simulation approach utilizing qudits to overcome such complexities. Leveraging on the symmetries of the Fermi-Hubbard model and their intrinsic relation to Clifford algebras, we first demonstrate a Qudit Fermionic Mapping (QFM) that reduces the encoding cost associated with the qubit-based approach. We then describe the unitary evolution of the mapped Hamiltonian by interpreting the resulting Majorana operators in terms of physical single- and two-qudit gates. While the QFM can be used for any quantum hardware with four accessible energy levels, we demonstrate the specific reduction in overhead resulting from utilizing the native Controlled-SUM gate (equivalent to qubit CNOT) for a fixed-frequency ququart transmon. We further transpile the resulting two transmon-qudit gates by demonstrating a qudit operator Schmidt decomposition using the Controlled-SUM gate. Finally, we demonstrate the efficacy of our proposal by numerical simulation of local observables such as the filling factor and Green's function for various Trotter steps. The compatibility of our approach with different qudit platforms paves the path for achieving quantum advantage in simulating non-trivial quantum many-body systems.