Constructing Fermionic Hamiltonians with Non-Gaussianic low-energy states

• URL: http://arxiv.org/abs/2502.15368v1
• Date: Fri, 21 Feb 2025 10:34:07 GMT
• Title: Constructing Fermionic Hamiltonians with Non-Gaussianic low-energy states
• Authors: Kartik Anand,
• Abstract summary: Quantum PCP conjecture is one of the most influential open problems in quantum complexity theory.<n>We construct a class of fermionic Hamilltonians for which energy of Gaussian states, a subclass of sampleable fermionic states, is bounded below by a constant.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum PCP conjecture is one of the most influential open problems in quantum complexity theory, which states that approximating the ground state energy for a sparse local Hamiltonian upto a constant is QMA-complete. However, even though the problem remains unsolved, weaker versions of it-such as the NLTS [FH13, ABN22] and NLSS [GG22] conjectures-have surfaced in the hope of providing evidence for QPCP. While the NLTS hamiltonians were first constructed in[ABN22], NLSS conjecture still remains unsolved. Weaker versions of the NLSS conjecture were addressed in [CCNN23, CCNN24], demonstrating that Clifford and almost-Clifford states-a subclass of sampleable states-have a lower energy bound on Hamiltonians prepared by conjugating the NLTS Hamiltonians from [ABN22]. In similar spirit, we construct a class of fermionic Hamilltonians for which energy of Gaussian states, a subclass of sampleable fermionic states, is bounded below by a constant. We adapt the technique used in [CCNN23] to our context.

Related papers

• Hamiltonians whose low-energy states require $Ω(n)$ T gates [0.22499166814992438]
  We prove a relationship between the number of T gates preparing a state and the number of terms at which the state is pseudo-stabilizer. This result represents a significant improvement over [CCNN23] where we used a different technique to give an energy bound.
  arXiv  Detail & Related papers  (2023-10-02T17:09:52Z)
• Comment on "Can Neural Quantum States Learn Volume-Law Ground States?" [44.99833362998488]
  We show that suitably chosen NQS can learn ground states with volume-law entanglement both for spin and fermionic problems. We argue that the setup utilized in the aforementioned letter reveals the inefficiency of non-fermionic NQS to learn fermionic states.
  arXiv  Detail & Related papers  (2023-09-20T14:44:04Z)
• Fermionic Hamiltonians without trivial low-energy states [12.961180148172197]
  We construct local fermionic Hamiltonians with no low-energy trivial states (NLTS) Distinctly from the qubit case, we define trivial states via finite-depth $textitfermionic$ quantum circuits. We define a fermionic analogue of the class quantum PCP and discuss its relation with the qubit version.
  arXiv  Detail & Related papers  (2023-07-25T18:00:02Z)
• Local Hamiltonians with no low-energy stabilizer states [0.4588028371034407]
  A family of local Hamiltonians with low-enough constant energy do not have succinct representations allowing perfect sampling access. We describe families that exhibit this requisite property via a simple alteration to local Hamiltonians corresponding to CSS codes. Our method can also be applied to the recent NLTS Hamiltonians of Anshu, Breuckmann, and Nirkhe [ABN22], resulting in a family of local Hamiltonians whose low-energy space contains neither stabilizer states nor trivial states.
  arXiv  Detail & Related papers  (2023-02-28T16:55:05Z)
• Sparse random Hamiltonians are quantumly easy [105.6788971265845]
  A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
  arXiv  Detail & Related papers  (2023-02-07T10:57:36Z)
• NLTS Hamiltonians from good quantum codes [14.00987234726578]
  The NLTS (No Low-Energy Trivial State) conjecture posits that there exist families of Hamiltonians with all low energy states of non-trivial complexity.<n>We prove this conjecture by showing that the recently discovered families of constant-rate and linear-distance QLDPC codes correspond to NLTS local Hamiltonians.
  arXiv  Detail & Related papers  (2022-06-27T12:22:56Z)
• A construction of Combinatorial NLTS [22.539300644593936]
  NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of high complexity. Here, we prove a weaker version called the NLTS, where a quantum circuit lower bound is shown against states that violate a (small) constant fraction of local terms.
  arXiv  Detail & Related papers  (2022-06-06T16:55:34Z)
• Average-case Speedup for Product Formulas [69.68937033275746]
  Product formulas, or Trotterization, are the oldest and still remain an appealing method to simulate quantum systems. We prove that the Trotter error exhibits a qualitatively better scaling for the vast majority of input states. Our results open doors to the study of quantum algorithms in the average case.
  arXiv  Detail & Related papers  (2021-11-09T18:49:48Z)
• 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)
• Mesoscopic quantum superposition states of weakly-coupled matter-wave solitons [58.720142291102135]
  We establish quantum features of an atomic soliton Josephson junction (SJJ) device. We show that the SJJ-model in quantum domain exhibits unusual features due to its effective nonlinear strength proportional to the square of total particle number. We have shown that the obtained quantum state is more resistant to few particle losses from the condensates if tiny components of entangled Fock states are present.
  arXiv  Detail & Related papers  (2020-11-26T09:26:19Z)
• 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)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)

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.