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The Complexity Geometry of a Single Qubit
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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.
Forward citations
Cited by 3 Pith papers
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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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A submersion-based method turns weighted generator costs into state-complexity metrics for CFTs, giving analytic formulas in simple limits and constraints on which weight choices are viable.
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Probing the Black Hole Interior with Holographic Entanglement Entropy and the Role of AdS/BCFT Correspondence
The paper's central claim, that a Horndeski-gravity residual entropy -ξ/6 identifies smooth-interior microstates and firewalls, is an unsupported interpretation of previously derived formulas.
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