Authors: Chris Cade, Marten Folkertsma, Jordi Weggemans

Published on: July 20, 2022

Impact Score: 8.22

Arxiv code: Arxiv:2207.10097

Summary

• What is new: The paper extends the hardness of the guided local Hamiltonian problem to 2-local Hamiltonians, allows for a larger overlap between the guiding and target states, and expands the problem to include excited states.
• Why this is important: Prior research showed the guided local Hamiltonian problem was BQP-complete for $k \\geq 6$ local Hamiltonians. This paper aims to investigate whether the problem remains hard for simpler, 2-local Hamiltonians and under conditions of larger overlaps between the guiding and target states.
• What the research proposes: The researchers demonstrate that the problem is indeed BQP-complete for 2-local Hamiltonians and even when the overlap between the guiding and target states is nearly total. They also show that the problem’s scope can be expanded to estimating energies of excited states.
• Results: The findings indicate that the guided local Hamiltonian problem retains its computational complexity even under significantly relaxed constraints, broadening the types of quantum systems and states it can be applied to.

Technical Details

Technological frameworks used: BQP-completeness framework, polynomial hardness proofs

Models used: Quantum computational models, eigenvalue estimation techniques

Data used: Theoretical constructs, no empirical data

Potential Impact

Quantum computing, specifically companies focused on quantum algorithms for solving Hamiltonian problems, and those developing new quantum computational models might both be impacted. This research could inform the design of more efficient quantum algorithms, affecting sectors reliant on quantum simulation, such as pharmaceuticals, materials science, and cryptography.

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