Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for complexity inequalities.
Quantum Computation as Geometry
9 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms, or to prove limitations on the power of quantum computers.
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Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
Open-system quantum complexity is governed by a sub-Finslerian geometry whose curvature depends on the cost penalties for unitary and dissipative controls.
Krylov complexity equals Fubini-Study volume for closed and open two-mode squeezed states, providing analytic support for the generalized CV conjecture via information geometry.
Studies holographic complexity in the Klebanov-Strassler background, reporting common scaling with confinement scale across functionals and more complex UV divergences than in AdS.
Holographic complexity of CFTs in global dS_d is computed via volume and action prescriptions in AdS foliation and brane setups, then compared to results from static and Poincare patches.
Post-selection probability and fidelity of bidirectional teleportation are expressed via the Loschmidt echo, revealing initial-state dependence of fidelity and stability of probability in integrable models.
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.
Time-dependent holographic entanglement entropy and complexity are computed perturbatively for braneworld FLRW universes with radiation, matter, and exotic matter by using time-dependent brane positions in black brane bulk geometries.
citing papers explorer
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Complexity Inequalities for Quantum Subsystems
Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for complexity inequalities.
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Generalized Complexity Distances and Non-Invertible Symmetries
Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
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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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Generalized CV Conjecture and Krylov Complexity in Two-Mode Hermitian Systems via Information Geometry
Krylov complexity equals Fubini-Study volume for closed and open two-mode squeezed states, providing analytic support for the generalized CV conjecture via information geometry.
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Holographic complexity of the Klebanov-Strassler background
Studies holographic complexity in the Klebanov-Strassler background, reporting common scaling with confinement scale across functionals and more complex UV divergences than in AdS.
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Holographic complexity of conformal fields in global de Sitter spacetime
Holographic complexity of CFTs in global dS_d is computed via volume and action prescriptions in AdS foliation and brane setups, then compared to results from static and Poincare patches.
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Post-Selection Probability and Fidelity of Bidirectional Teleportation
Post-selection probability and fidelity of bidirectional teleportation are expressed via the Loschmidt echo, revealing initial-state dependence of fidelity and stability of probability in integrable models.
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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.
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Holographic entanglement entropy and complexity for the cosmological braneworld model
Time-dependent holographic entanglement entropy and complexity are computed perturbatively for braneworld FLRW universes with radiation, matter, and exotic matter by using time-dependent brane positions in black brane bulk geometries.