Zero- Versus Infinite-Temperature Damping in Variational Quantum Circuits: Feature Scale, Sampling Cost, and Frame Gauge
Abstract
The Pauli twirl of amplitude damping (AD) is generalized amplitude damping at infinite temperature: it keeps the contraction of AD and removes its non-unital term, so comparing the two in variational circuits isolates the zero-temperature bias, which acts mainly through the scale of the features. For random parameters, features under AD settle on a floor, which at strong damping is set by the last layer, has a closed form, and at fixed T1 falls with temperature as tanh(ℏω/2kBT); under the twirls they shrink by a constant factor per layer, up to eight qubits. A trainable output scale removes most of the resulting accuracy differences, leaving AD ahead of its twirls by at most about three percentage points in our simulations; what it removes reappears as a cost in measurement shots: trained and tested with 103 shots per image, a four-qubit classifier under AD at p=0.3 stays within 1.5 points of noiseless accuracy, while the twirled classifiers lose up to 33. At weaker damping the separation depth grows roughly as (np)−1ln(1/p). The damping direction is a gauge when the damping follows complete entangling layers and the circuit boundaries are trainable; in an eigensolver it becomes physical inside a decomposed two-qubit gate.
Related
- BAHAMAS: A Control Plane for Optimization and Execution of Variational Quantum Circuits
- Quantum Hierarchical Reinforcement Learning via Variational Quantum Circuits
- Subspace Controllability in Variational Quantum Circuits: Maximising Expressivity and Increasing Search Efficiency with Dynamical Lie Algebras
- Operator Learning with Variational Quantum Circuits
- A quantum representation of π fragmentation functions through variational quantum circuits
BibTeX
@misc{nguyen2026zero,
title = {{Zero- Versus Infinite-Temperature Damping in Variational Quantum Circuits: Feature Scale, Sampling Cost, and Frame Gauge}},
author = {Vu-Quoc-Minh Nguyen and Tuan-Vu Truong and Hoang-Long Nguyen and Trung-Khanh Le},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01466},
eprint = {2610.01466},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01466},
}
RIS
TY - UNPB
TI - Zero- Versus Infinite-Temperature Damping in Variational Quantum Circuits: Feature Scale, Sampling Cost, and Frame Gauge
AU - Vu-Quoc-Minh Nguyen
AU - Tuan-Vu Truong
AU - Hoang-Long Nguyen
AU - Trung-Khanh Le
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01466
UR - https://arxiv.org/abs/2610.01466
AB - The Pauli twirl of amplitude damping (AD) is generalized amplitude damping at infinite temperature: it keeps the contraction of AD and removes its non-unital term, so comparing the two in variational circuits isolates the zero-temperature bias, which acts mainly through the scale of the features. For random parameters, features under AD settle on a floor, which at strong damping is set by the last layer, has a closed form, and at fixed T_1 falls with temperature as tanh(ℏω/2k_BT); under the twirls they shrink by a constant factor per layer, up to eight qubits. A trainable output scale removes most of the resulting accuracy differences, leaving AD ahead of its twirls by at most about three percentage points in our simulations; what it removes reappears as a cost in measurement shots: trained and tested with 10^3 shots per image, a four-qubit classifier under AD at p=0.3 stays within 1.5 points of noiseless accuracy, while the twirled classifiers lose up to 33. At weaker damping the separation depth grows roughly as (np)^−1ln(1/p). The damping direction is a gauge when the damping follows complete entangling layers and the circuit boundaries are trainable; in an eigensolver it becomes physical inside a decomposed two-qubit gate.
ER -