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Quantum Computation as Gravity
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Quantum Computation as Gravity
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We formulate Nielsen's geometric approach to complexity in the context of two dimensional conformal field theories, where series of conformal transformations are interpreted as unitary circuits. We show that the complexity functional can be written as the Polyakov action of two dimensional gravity or, equivalently, as the geometric action on the coadjoint orbits of the Virasoro group. This way, we argue that gravity sets the rules for optimal quantum computation in conformal field theories.
Forward citations
Cited by 4 Pith papers
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The Geometry of Quantum Complexity in Open Systems
Nielsen complexity for Lindbladian open systems induces a sub-Finslerian geometry on mixed states whose flag curvature depends on control penalty factors.
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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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The Normalised Wigner Negativity Rate as a Second-Moment Probe of Infall in AdS$_3$
Normalized Krylov-Wigner negativity rate matches Krylov variance growth and equals tidal stretch rate R ∝ C P_ρ if and only if Δ=1 in AdS3.
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The Normalised Wigner Negativity Rate as a Second-Moment Probe of Infall in AdS$_3$
A rescaled Wigner negativity in Krylov space grows as sinh^{4Δ} and, at Δ=1, its rate matches the tidal momentum of infalling geodesics in AdS3.
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