Avoiding Exponentially Large Groups with Open Quantum System Technology
Abstract
We propose a novel approach to state preparation by embracing the full power of open quantum systems. Instead of working with the whole unitary group in n qubits, we identify a small Lie group G in (n+3) qubits. The dimension of its Lie algebra is poly(n). Every state can be approximated starting from any fixed input state by repeatedly using partial trace and state preparation in the environment alongside group operations. Moreover, we also identify a single (open system magic) interaction Hamiltonian whose unitary group can be combined with open system quantum technology mentioned above to achieve transitivity on the space of all densities. Similarly, we show that all channels on n qubits can be approximated by using a larger environment, achieving channel universality. The interesting small groups we identify are derived from Lie algebras of local Pauli strings and lead to a new landscape of cheap and expensive states, densities, and channels.
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BibTeX
@misc{cai2026avoiding,
title = {{Avoiding Exponentially Large Groups with Open Quantum System Technology}},
author = {Jihong Cai and Advith Govindarajan and Marius Junge},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01932},
eprint = {2610.01932},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01932},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Avoiding Exponentially Large Groups with Open Quantum System Technology
AU - Jihong Cai
AU - Advith Govindarajan
AU - Marius Junge
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01932
UR - https://arxiv.org/abs/2610.01932
AB - We propose a novel approach to state preparation by embracing the full power of open quantum systems. Instead of working with the whole unitary group in n qubits, we identify a small Lie group G in (n+3) qubits. The dimension of its Lie algebra is poly(n). Every state can be approximated starting from any fixed input state by repeatedly using partial trace and state preparation in the environment alongside group operations. Moreover, we also identify a single (open system magic) interaction Hamiltonian whose unitary group can be combined with open system quantum technology mentioned above to achieve transitivity on the space of all densities. Similarly, we show that all channels on n qubits can be approximated by using a larger environment, achieving channel universality. The interesting small groups we identify are derived from Lie algebras of local Pauli strings and lead to a new landscape of cheap and expensive states, densities, and channels.
ER -