Local fermion-to-qudit mappings

• URL: http://arxiv.org/abs/2412.05616v2
• Date: Sat, 14 Dec 2024 12:09:01 GMT
• Title: Local fermion-to-qudit mappings
• Authors: Rodolfo Carobene, Stefano Barison, Andrea Giachero, Jannes Nys,
• Abstract summary: We present a new set of local fermion-to-qudit mappings for simulating fermionic lattice systems. We show that these mappings enable more efficient quantum simulations in terms of two-qudit gates.
• Score: 0.0
• License:
• Abstract: 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.

Related papers

• Gradient projection method for constrained quantum control [50.24983453990065]
  We adopt the Gradient Projection Method (GPM) to problems of quantum control. The main advantage of the method is that it allows to exactly satisfy the bounds. We apply the GPM to several examples including generation of one- and two-qubit gates and two-qubit Bell and Werner states.
  arXiv  Detail & Related papers  (2024-11-29T11:56:55Z)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model [0.0]
  We provide a step-by-step recipe for simulating the paradigmatic two-dimensional Fermi-Hubbard model on a quantum computer using only local operations. We provide a detailed recipe for an end-to-end simulation including embedding on a physical device.
  arXiv  Detail & Related papers  (2024-08-26T18:00:07Z)
• Quantum simulation of Fermi-Hubbard model based on transmon qudit interaction [0.0]
  We introduce a novel quantum simulation approach utilizing qudits to overcome such complexities. 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.
  arXiv  Detail & Related papers  (2024-02-02T09:10:40Z)
• Quantum Computation and Simulation using Fermion-Pair Registers [0.0]
  We propose and analyze an approach to realize quantum computation and simulation using fermionic particles under quantum gas microscopes. We describe how to engineer the SWAP gate and high-fidelity controlled-phase gates. We show that 2D quantum Ising Hamiltonians with transverse and longitudinal fields can be efficient simulated by modulating Feshbach interaction strengths.
  arXiv  Detail & Related papers  (2023-06-06T17:59:08Z)
• Fermionic quantum processing with programmable neutral atom arrays [0.539215791790606]
  Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics. We present a fermionic quantum processor, where fermionic models are encoded in a fermionic register and simulated in a hardware-efficient manner using fermionic gates.
  arXiv  Detail & Related papers  (2023-03-13T10:35:48Z)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)
• A Compact Fermion to Qubit Mapping [0.4061135251278187]
  We present a novel fermion to qubit mapping which outperforms all previous local mappings in both the qubit to mode ratio, and the locality of mapped operators.
  arXiv  Detail & Related papers  (2020-03-15T22:23:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.