When is a bosonic operator a Hamiltonian?
Abstract
Hermitian polynomials in the quadrature operators x and p are the basic ingredients of continuous-variable quantum information, and increasingly exotic ones are now routinely engineered in superconducting circuits and trapped ions. However, such a polynomial need not define unique quantum dynamics: it may define exactly one, none, or an infinite family of physically distinct ones. Such obstructions are invisible to algebraic arguments and can compromise finite-dimensional truncations, which may fail to converge or silently converge to the wrong dynamics. We develop a method, implemented as an algorithm, which decides which case occurs, and how large the family is, from the coefficients alone, with no functional-analytic input from the user. For Gaussian operators the answer is always one; for non-Gaussian ones, a regime continuous-variable quantum computing cannot do without, the other outcomes occur already for simple and physically natural Hamiltonians. We apply the algorithm to operators drawn from the recent literature.
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BibTeX
@misc{fischer2026when,
title = {{When is a bosonic operator a Hamiltonian?}},
author = {Felix Fischer and Hermann Schulz-Baldes and Daniel Burgarth and Davide Lonigro},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33545},
eprint = {2610.33545},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33545},
}
RIS
TY - UNPB
TI - When is a bosonic operator a Hamiltonian?
AU - Felix Fischer
AU - Hermann Schulz-Baldes
AU - Daniel Burgarth
AU - Davide Lonigro
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33545
UR - https://arxiv.org/abs/2610.33545
AB - Hermitian polynomials in the quadrature operators x and p are the basic ingredients of continuous-variable quantum information, and increasingly exotic ones are now routinely engineered in superconducting circuits and trapped ions. However, such a polynomial need not define unique quantum dynamics: it may define exactly one, none, or an infinite family of physically distinct ones. Such obstructions are invisible to algebraic arguments and can compromise finite-dimensional truncations, which may fail to converge or silently converge to the wrong dynamics. We develop a method, implemented as an algorithm, which decides which case occurs, and how large the family is, from the coefficients alone, with no functional-analytic input from the user. For Gaussian operators the answer is always one; for non-Gaussian ones, a regime continuous-variable quantum computing cannot do without, the other outcomes occur already for simple and physically natural Hamiltonians. We apply the algorithm to operators drawn from the recent literature.
ER -