aiqbench analysis
This paper proposes "quantum folding," a way to seed Chebyshev-based quantum subspace diagonalization with a product of subsystem ground states instead of a naive product state, which the authors argue sidesteps the exponentially small overlaps that otherwise undermine convergence and noise robustness. The reported gains (fewer Krylov dimensions and lower noisy-simulation error on Heisenberg chains) are from exact simulations on small spin models, so they show promise for fault-tolerant ground-state methods but not yet practical advantage on hardware. Readers should watch whether the error bounds and the recursive preparation claim hold up at larger system sizes and under realistic noise.
Quantum Folding in Chebyshev-Based Quantum Subspace Diagonalization
arXiv:2610.19922v1 Announce Type: new Abstract: Quantum subspace diagonalization (QSD) with a Krylov space spanned by Chebyshev polynomials of the Hamiltonian is a natural ground-state method for fault-tolerant quantum computers, but every guarantee it offers---convergence rate, noise floor, and the cost of turning its classical output back into a physical state---is controlled by the overlap of the reference state with the true ground state, which decays exponentially with system size for any product state and non-trivial Hamiltonian. We propose quantum folding: for a system governed by a local Hamiltonian, seed the QSD with the product of the ground states of its subsystems, which differs from the target only through the interface terms. We prove a nonasymptotic error bound for the Chebyshev QSD that is linear in the measurement noise, by transplanting Kirby's effective-Hamiltonian analysis to the Chebyshev--Krylov basis, and identify the block-encoding rescaling of the Hamiltonian as a parameter of the guarantee. Exact simulations of antiferromagnetic Heisenberg chains show that the folded reference state reduces the Krylov dimension for a given accuracy severalfold and lowers the error under noise by two to five orders of magnitude relative to the N\'eel state. We show how the Ritz vector is prepared as a physical state and that the ground-state generation probability obeys a tight ceiling set by the overlap, so that recursive folding prepares ground states at polynomial cost. Taken together, these results allow for a scalable QSD framework that avoids the exponentially small ground-state overlaps associated with conventional product-state initialization. Finally we compute the fold fidelity itself: a slow power law for the gapless spin-1/2 chain, a size-independent constant for the gapped spin-$1$ chain, and an exact closed form converging to 1/4 for the AKLT chain.
Abstract:Quantum subspace diagonalization (QSD) with a Krylov space spanned by Chebyshev polynomials of the Hamiltonian is a natural ground-state method for fault-tolerant quantum computers, but every guarantee it offers---convergence rate, noise floor, and the cost of turning its classical output back into a physical state---is controlled by the overlap of the reference state with the true ground state, which decays exponentially with system size for any product state and non-trivial Hamiltonian. We propose quantum folding: for a system governed by a local Hamiltonian, seed the QSD with the product of the ground states of its subsystems, which differs from the target only through the interface terms. We prove a nonasymptotic error bound for the Chebyshev QSD that is linear in the measurement noise, by transplanting Kirby's effective-Hamiltonian analysis to the Chebyshev--Krylov basis, and identify the block-encoding rescaling of the Hamiltonian as a parameter of the guarantee. Exact simulations of antiferromagnetic Heisenberg chains show that the folded reference state reduces the Krylov dimension for a given accuracy severalfold and lowers the error under noise by two to five orders of magnitude relative to the Néel state. We show how the Ritz vector is prepared as a physical state and that the ground-state generation probability obeys a tight ceiling set by the overlap, so that recursive folding prepares ground states at polynomial cost. Taken together, these results allow for a scalable QSD framework that avoids the exponentially small ground-state overlaps associated with conventional product-state initialization. Finally we compute the fold fidelity itself: a slow power law for the gapless spin-1/2 chain, a size-independent constant for the gapped spin-$1$ chain, and an exact closed form converging to 1/4 for the AKLT chain.
arXiv:2610.19922 [quant-ph]
(or arXiv:2610.19922v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.19922 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 370 words
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