aiqbench analysis
This study proposes a variational quantum algorithm that leverages classical shadow tomography to efficiently estimate ground state correlations for local spin Hamiltonians. By optimizing an ensemble of randomized measurement snapshots, the method accurately predicts energy and other observables while enforcing physical constraints like reduced density matrix positivity. The approach demonstrates robust performance on extended systems (up to L=64) with improved optimization techniques and theoretical justification for the shadow ansatz.
Learning shadows to predict quantum ground state correlations
arXiv:2508.00052v2 Announce Type: replace Abstract: We introduce a variational scheme inspired by classical shadow tomography to compute ground state correlations of quantum spin Hamiltonians. Shadow tomography allows for efficient reconstruction of expectation values of arbitrary observables from a bag of repeated, randomized measurements, called snapshots, on copies of the state $\rho$. The prescription allows one to infer expectation values of $M$ $k-$local observables to accuracy $\epsilon$ using just $N \sim 3^k \text{log}M /\epsilon^2$ snapshots when measurements are performed in locally random bases. Turning this around, a bag of snapshots can be considered an efficient representation of the state $\rho$, particularly for estimating low-weight observables, such as terms in a local Hamiltonian needed to estimate the energy. Inspired by this, we consider a variational scheme wherein a bag of $N$ parametrized snapshots is used to represent the putative ground state of a desired local spin Hamiltonian and optimized to lower the energy with respect to it. Additional constraints in the form of positivity of reduced density matrices, motivated by work in quantum chemistry, are employed to ensure compatibility of the predicted correlations with the underlying Hilbert space. Despite the limited set of imposed constraints, we show that the optimized ensemble of snapshots yields fairly accurate estimates of the ground state energy and other correlations, including those that do not appear in the set of constraints used in optimization.
Abstract:We introduce a variational scheme inspired by classical shadow tomography to compute ground state correlations of quantum spin Hamiltonians. Shadow tomography allows for efficient reconstruction of expectation values of arbitrary observables from a bag of repeated, randomized measurements, called snapshots, on copies of the state $\rho$. The prescription allows one to infer expectation values of $M$ $k-$local observables to accuracy $\epsilon$ using just $N \sim 3^k \text{log}M /\epsilon^2$ snapshots when measurements are performed in locally random bases. Turning this around, a bag of snapshots can be considered an efficient representation of the state $\rho$, particularly for estimating low-weight observables, such as terms in a local Hamiltonian needed to estimate the energy. Inspired by this, we consider a variational scheme wherein a bag of $N$ parametrized snapshots is used to represent the putative ground state of a desired local spin Hamiltonian and optimized to lower the energy with respect to it. Additional constraints in the form of positivity of reduced density matrices, motivated by work in quantum chemistry, are employed to ensure compatibility of the predicted correlations with the underlying Hilbert space. Despite the limited set of imposed constraints, we show that the optimized ensemble of snapshots yields fairly accurate estimates of the ground state energy and other correlations, including those that do not appear in the set of constraints used in optimization.
17 pages (including supplementary material), 6 figures, 2 tables. Improved optimization and clarified the cost function; extended simulations to (L=64); restricted positivity constraints to finite range; removed the post-processing correction factor; broadened the models studied; and added theoretical justification for the shadow ansatz and inversion constant
Quantum Physics (quant-ph); Computational Physics (physics.comp-ph)
arXiv:2508.00052 [quant-ph]
(or arXiv:2508.00052v2 [quant-ph] for this version)
Full text under the publisher's open licence · 282 words
Related coverage
Game Design Creativity evals
LessWrong · Oct 12, 2026
Synthesis Superintelligence: from Semiconductors to Superconductors — Periodic Labs’ Liam Fedus and Ekin Dogus Cubuk
Latent Space · Oct 8, 2026
Learning ground state observables from quantum computing experiments
arXiv · Jun 16, 2026
Interview with Matthias Troyer, Vice President & Technical Fellow at Microsoft
Quantum Computing Report · Sep 23, 2026