Generating random unitaries by products of conjugated Hamiltonian evolutions
Abstract
Random unitary operations are a fundamental resource for quantum information processing, yet provably generating them with experimentally available controls remains challenging. Existing approaches often require calculating higher-order operator expectation values, relying on statistical assumptions about the experimental Hamiltonian's spectrum to make these calculations tractable. We show how to implement random unitaries by a sequence of evolutions generated by a fixed Hamiltonian conjugated by a global control operator. We give a geometric argument that establishes exponential convergence to the uniform random (Haar) measure on the accessible unitary group under uniform parameter sampling, beyond a finite sequence-length threshold that we bound. We show this holds when the connected Lie subgroup generated by the conjugated Hamiltonians is closed. Native dynamics and global control thus provide a constructive route to uniform randomness, with applications to many experimental platforms including Rydberg atoms, bosons and fermions in optical lattices, transmons, and trapped ions.
Related
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- Unitary designs from perturbed time evolutions of a chaotic Hamiltonian
- Near-Optimal Ground-State Preparation without Controlled Hamiltonian Evolutions
- The Hidden Subgroup Problem in Semidirect Products and Quasi-Hamiltonian Groups
- Fully global numerical evolutions of the linearised spin-2 equation
BibTeX
@misc{scholin2026generating,
title = {{Generating random unitaries by products of conjugated Hamiltonian evolutions}},
author = {Oscar Scholin and Apollonas S. Matsoukas-Roubeas and Sathyawageeswar Subramanian},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38738},
eprint = {2609.38738},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38738},
}
RIS
TY - UNPB
TI - Generating random unitaries by products of conjugated Hamiltonian evolutions
AU - Oscar Scholin
AU - Apollonas S. Matsoukas-Roubeas
AU - Sathyawageeswar Subramanian
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.38738
UR - https://arxiv.org/abs/2609.38738
AB - Random unitary operations are a fundamental resource for quantum information processing, yet provably generating them with experimentally available controls remains challenging. Existing approaches often require calculating higher-order operator expectation values, relying on statistical assumptions about the experimental Hamiltonian's spectrum to make these calculations tractable. We show how to implement random unitaries by a sequence of evolutions generated by a fixed Hamiltonian conjugated by a global control operator. We give a geometric argument that establishes exponential convergence to the uniform random (Haar) measure on the accessible unitary group under uniform parameter sampling, beyond a finite sequence-length threshold that we bound. We show this holds when the connected Lie subgroup generated by the conjugated Hamiltonians is closed. Native dynamics and global control thus provide a constructive route to uniform randomness, with applications to many experimental platforms including Rydberg atoms, bosons and fermions in optical lattices, transmons, and trapped ions.
ER -