Open-system quantum complexity is governed by a sub-Finslerian geometry whose curvature depends on the cost penalties for unitary and dissipative controls.
The Complexity Geometry of a Single Qubit
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we demonstrate many of the attractive features of complexity geometry using the example of a single qubit, which turns out to be rich enough to be illustrative but simple enough to be illuminating.
fields
quant-ph 2years
2026 2representative citing papers
Generalizes Nielsen complexity to multiple cost factors, derives modified Euler-Arnold and Jacobi equations, and examines effects on conjugate points in single-qubit and SYK systems.
citing papers explorer
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The Geometry of Quantum Complexity in Open Systems
Open-system quantum complexity is governed by a sub-Finslerian geometry whose curvature depends on the cost penalties for unitary and dissipative controls.
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Nielsen complexity with multiple cost factors
Generalizes Nielsen complexity to multiple cost factors, derives modified Euler-Arnold and Jacobi equations, and examines effects on conjugate points in single-qubit and SYK systems.