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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 1 Pith paper
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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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