A hardware-efficient variational ansatz with an exact diagonal metric for real- and imaginary-time evolution and Haar sampling
Abstract
Variational quantum algorithms depend on the geometry of their parametrised circuits: metric-aware optimisation and time evolution require the Fubini--Study metric, which has hitherto demanded costly auxiliary measurements and ill-conditioned inversions. This work introduces a hardware-efficient n-qubit ansatz, which parametrises states by a binary tree and whose Hilbert-space pullback metric is diagonal in closed form. Quantum natural gradient on the tree parameters, variational imaginary- and real-time evolution, and exact unitary-invariant (Haar) sampling on a symmetry sector run with no auxiliary metric circuits or matrix inversion. When the target state is supported on a subspace of k computational-basis states, the redundant tree parameters carry a gauge freedom a pruning compiler converts into circuits whose two-qubit count provably grows linearly in k; a variant reaches near-optimal O(nk/log n) scaling with the closed-form metric intact. On electronic-structure calculations for small molecules and half-filled Hubbard quench dynamics, the method reaches reference-level accuracy with one to three orders of magnitude fewer two-qubit gates than leading alternatives. Interchangeable constructions (a Schur-transform dressing or internal reparameterisations) make the ansatz exactly spin-adapted, with fixed total spin at every parameter and no penalty terms. The bare ansatz is an exactly controllable, well-conditioned and barren-plateau-free primitive for preparing and sampling sector states: on its own, it is classically simulable in k (a boundary proved for a general class of sector-sparse ansätze); composed with a classically hard dressing, it yields molecular ground states, sector-Haar benchmarking, thermal correlators, and exact effective Hamiltonians trained from energy measurements alone, with the composed circuit carrying the potential for quantum advantage.
Related
- Hardware-Efficient Ground-State Preparation using Variational Imaginary-Time Majorana Evolution
- Probabilistic imaginary-time evolution via compiled diagonal representations
- svPITE: A Python package for the state-vector-based probabilistic imaginary-time evolution algorithm
- Hardware-Efficient Error Mitigation and Shot-Efficient Sampling on IBM Quantum Hardware
- svPITE: A Python package for the state-vector-based probabilistic imaginary-time evolution algorithm
BibTeX
@misc{picozzi2026hardwareefficient,
title = {{A hardware-efficient variational ansatz with an exact diagonal metric for real- and imaginary-time evolution and Haar sampling}},
author = {Dario Picozzi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.07942},
eprint = {2607.07942},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.07942},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A hardware-efficient variational ansatz with an exact diagonal metric for real- and imaginary-time evolution and Haar sampling
AU - Dario Picozzi
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2607.07942
UR - https://arxiv.org/abs/2607.07942
AB - Variational quantum algorithms depend on the geometry of their parametrised circuits: metric-aware optimisation and time evolution require the Fubini--Study metric, which has hitherto demanded costly auxiliary measurements and ill-conditioned inversions. This work introduces a hardware-efficient n-qubit ansatz, which parametrises states by a binary tree and whose Hilbert-space pullback metric is diagonal in closed form. Quantum natural gradient on the tree parameters, variational imaginary- and real-time evolution, and exact unitary-invariant (Haar) sampling on a symmetry sector run with no auxiliary metric circuits or matrix inversion. When the target state is supported on a subspace of k computational-basis states, the redundant tree parameters carry a gauge freedom a pruning compiler converts into circuits whose two-qubit count provably grows linearly in k; a variant reaches near-optimal O(nk/log n) scaling with the closed-form metric intact. On electronic-structure calculations for small molecules and half-filled Hubbard quench dynamics, the method reaches reference-level accuracy with one to three orders of magnitude fewer two-qubit gates than leading alternatives. Interchangeable constructions (a Schur-transform dressing or internal reparameterisations) make the ansatz exactly spin-adapted, with fixed total spin at every parameter and no penalty terms. The bare ansatz is an exactly controllable, well-conditioned and barren-plateau-free primitive for preparing and sampling sector states: on its own, it is classically simulable in k (a boundary proved for a general class of sector-sparse ansätze); composed with a classically hard dressing, it yields molecular ground states, sector-Haar benchmarking, thermal correlators, and exact effective Hamiltonians trained from energy measurements alone, with the composed circuit carrying the potential for quantum advantage.
ER -