Extendibility of fermionic states and rigorous ground state approximations of interacting fermionic systems

• URL: http://arxiv.org/abs/2410.08322v1
• Date: Thu, 10 Oct 2024 19:19:35 GMT
• Title: Extendibility of fermionic states and rigorous ground state approximations of interacting fermionic systems
• Authors: Christian Krumnow, Zoltán Zimborás, Jens Eisert,
• Abstract summary: We provide rigorous guarantees on how well fermionic Gaussian product states can approximate the true ground state. Our result can be on the one hand seen as a extendibility result of fermionic quantum states. On the other hand, this is a non-symmetric de-Finetti theorem for fermions, as the direct fermionic analog of a theorem due to Brandao and Harrow.
• Score: 0.3277163122167433
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Solving interacting fermionic quantum many-body problems as they are ubiquitous in quantum chemistry and materials science is a central task of theoretical and numerical physics, a task that can commonly only be addressed in the sense of providing approximations of ground states. For this reason, it is important to have tools at hand to assess how well simple ansatzes would fare. In this work, we provide rigorous guarantees on how well fermionic Gaussian product states can approximate the true ground state, given a weighted interaction graph capturing the interaction pattern of the systems. Our result can be on the one hand seen as a extendibility result of fermionic quantum states: It says in what ways fermionic correlations can be distributed. On the other hand, this is a non-symmetric de-Finetti theorem for fermions, as the direct fermionic analog of a theorem due to Brandao and Harrow. We compare the findings with the distinctly different situation of distinguishable finite-dimensional quantum systems, comment on the approximation of ground states with Gaussian states and elaborate on the connection to the no low-energy trivial state conjecture.

Related papers

• Resolving nonclassical magnon composition of a magnetic ground state via a qubit [44.99833362998488]
  We show that a direct dispersive coupling between a qubit and a noneigenmode magnon enables detecting the magnonic number states' quantum superposition. This unique coupling is found to enable control over the equilibrium magnon squeezing and a deterministic generation of squeezed even Fock states.
  arXiv  Detail & Related papers  (2023-06-08T09:30:04Z)
• Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective [39.58317527488534]
  We develop a framework to characterize the separability of a specific type of one-dimensional quasiparticle known as a fermionic anyon. We map this notion of fermionic-anyon separability to the free resources of matchgate circuits. We also identify how entanglement between two qubits encoded in a dual-rail manner, as standard for matchgate circuits, corresponds to the notion of entanglement between fermionic anyons.
  arXiv  Detail & Related papers  (2023-06-01T15:25:19Z)
• Schr\"odinger cat states of a 16-microgram mechanical oscillator [54.35850218188371]
  The superposition principle is one of the most fundamental principles of quantum mechanics. Here we demonstrate the preparation of a mechanical resonator with an effective mass of 16.2 micrograms in Schr"odinger cat states of motion. We show control over the size and phase of the superposition and investigate the decoherence dynamics of these states.
  arXiv  Detail & Related papers  (2022-11-01T13:29:44Z)
• Entanglement Spectroscopy and probing the Li-Haldane Conjecture in Topological Quantum Matter [0.0]
  Topological phases are characterized by their entanglement properties. We propose to leverage the power of synthetic quantum systems for measuring entanglement via the Entanglement Hamiltonian.
  arXiv  Detail & Related papers  (2021-10-08T06:13:51Z)
• Experimental proposal to probe the extended Pauli principle [2.1839191255085995]
  We propose an experiment in a system of multiple quantum dots capable of producing highly entangled fermionic states. The type and strength of the required multi-fermion entanglement provides barriers to reaching deep into this regime.
  arXiv  Detail & Related papers  (2021-07-13T10:05:54Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Quantum Operations in an Information Theory for Fermions [0.0]
  We introduce the physically allowed quantum operations, in congruence with the parity super-selection rule, that map the set of allowed fermionic states onto itself. We explicitly show the equivalence between these three representations of fermionic quantum operations.
  arXiv  Detail & Related papers  (2021-02-17T23:41:05Z)
• Semiclassical limit for almost fermionic anyons [0.0]
  Quasi-particles obeying quantum statistics can be described as bosons and fermions with magnetic interactions. We prove that the ground state of a gas of anyons is described to leading order by a semi-classical, Vlasov-like, energy functional.
  arXiv  Detail & Related papers  (2021-01-12T13:03:17Z)
• Bose-Einstein condensate soliton qubit states for metrological applications [58.720142291102135]
  We propose novel quantum metrology applications with two soliton qubit states. Phase space analysis, in terms of population imbalance - phase difference variables, is also performed to demonstrate macroscopic quantum self-trapping regimes.
  arXiv  Detail & Related papers  (2020-11-26T09:05:06Z)
• Direct estimation of the energy gap between the ground state and excited state with quantum annealing [0.0]
  We propose a direct estimation of the energy gap between the ground state and excited state of the target Hamiltonian. Based on typical parameters of superconducting qubits, we numerically investigate the performance of our scheme. Our results pave a new way to estimate the energy gap of the Hamiltonian for quantum chemistry.
  arXiv  Detail & Related papers  (2020-07-21T02:03:42Z)
• From communication complexity to an entanglement spread area law in the ground state of gapped local Hamiltonians [16.951941479979716]
  We make a connection between two seemingly different problems. The first problem involves characterizing the properties of entanglement in the ground state of gapped local Hamiltonians. The second problem is on the quantum communication complexity of testing bipartite states with EPR assistance.
  arXiv  Detail & Related papers  (2020-04-30T17:54:22Z)

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.