Quantum Folding in Chebyshev-Based Quantum Subspace Diagonalization
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.
Related
- Mirror subspace diagonalization: a real-time quantum Krylov algorithm with near-optimal sampling cost
- Sample-based Quantum Diagonalization via Density Matrix Renormalization Group
- A scalable sample-based quantum diagonalization solver for general Pauli-sum Hamiltonians
- Code-space recovery for sample-based quantum diagonalization beyond native symmetry constraints
- Green's Functions from Sample-based Krylov Quantum Diagonalization: An Impurity Solver for Dynamical Mean-Field Theory
BibTeX
@misc{park2026quantum,
title = {{Quantum Folding in Chebyshev-Based Quantum Subspace Diagonalization}},
author = {Seung Park and Dongni Chen and Stefano Chesi and Kyunghyun Baek and Mahn-Soo Choi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19922},
eprint = {2610.19922},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19922},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Folding in Chebyshev-Based Quantum Subspace Diagonalization
AU - Seung Park
AU - Dongni Chen
AU - Stefano Chesi
AU - Kyunghyun Baek
AU - Mahn-Soo Choi
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19922
UR - https://arxiv.org/abs/2610.19922
AB - 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.
ER -