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A geometric approach to quantum circuit lower bounds
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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A Mathematical Theory of Communication
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Quantum Lower Bounds by Quantum Arguments
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Introduction to Smooth Manifolds
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Spin Dynamics: A Paradigm for Time Optimal Control on Compact Lie Groups
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Cartan decomposition of SU(2n) and control of spin systems
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Quantum computations: algorithms and error correction
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Time optimal control in spin systems
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Optimally shaped terahertz pulses for phase retrieval in a Rydberg-atom data register
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Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries
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Characterization of nonlocal gates
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Optimal control theory for unitary transformations
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Optimal control of quantum dissipative dynamics: Analytic solution for cooling the three-level Λ system
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Erratum: Sub-Riemannian geometry and time optimal control of three spin systems: Quantum gates and coherence transfer [Phys. Rev. A65, 032301 (2002)]
inferredcites →https://doi.org/10.1103/physreva.71.052330openalex-snapshot
Quantum circuits with uniformly controlled one-qubit gates
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Interaction Cost of Nonlocal Gates
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Quantum Computation with Vibrationally Excited Molecules
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Quantum Computing by an Optimal Control Algorithm for Unitary Transformations
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Practical Scheme for Quantum Computation with Any Two-Qubit Entangling Gate
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Exact Two-Qubit Universal Quantum Circuit
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Reducing quantum computations to elementary unitary operations
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Optimal control of two-level quantum systems
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Fast parallel circuits for the quantum Fourier transform
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OPTIMAL SMOOTHING FOR CONVEX POLYTOPES
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Quantum Computation and Quantum Information
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Geometric Complexity Theory I: An Approach to the P vs. NP and Related Problems
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Strengths and Weaknesses of Quantum Computing
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Sub-Finslerian Metric Associated to an Optimal Control System
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Modern Differential Geometry for Physicists
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Some complexity questions related to distributive computing(Preliminary Report)
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ACTIVE CONTROL OF THE DYNAMICS OF ATOMS AND MOLECULES
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Mathematics of Quantum Computation
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Geometric Complexity III: on deciding positivity of Littlewood-Richardson coefficients
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Lower Bounds on Quantum Query Complexity
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Quantum Lower Bounds by Polynomials
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Stabilizer Codes and Quantum Error Correction
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Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Volume complexity for Janus AdS3 geometries
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Subsystem complexity after a local quantum quench
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Krylov complexity of deformed conformal field theories
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Late-time saturation of black hole complexity
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Cosmological complexity of the modified dispersion relation
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Wasserstein complexity of quantum circuits
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Berry phases in the bosonization of nonlinear edge modes
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Spread complexity rate as proper momentum
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Time-optimal unitary operations
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Complexity and Floquet dynamics: Nonequilibrium Ising phase transitions
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Complexity geometry of a single qubit
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First law of holographic complexity
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Volume complexity of dS bubbles
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Complexity geometry in Hermitian and non-Hermitian quantum dynamics
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Geometric measure of quantum complexity in cosmological systems
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Properties of Krylov state complexity in qubit dynamics
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Finite complexity of the de Sitter vacuum
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Quantum complexity and negative curvature
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Complexity growth in massive gravity theories, the effects of chirality, and more
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Time evolution of complexity in Abelian gauge theories
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Complexity for quantum field theory states and applications to thermofield double states
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Topological and time dependence of the action-complexity relation
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Thoughts on holographic complexity and its basis dependence
inferred← citeshttps://doi.org/10.1103/physrevd.98.106011openalex-snapshot
Complexity growth rate during phase transitions
inferred← citeshttps://doi.org/10.1103/physrevd.98.126001openalex-snapshot
Circuit complexity in fermionic field theory
inferred← citeshttps://doi.org/10.1103/physrevd.98.126012openalex-snapshot
Properties of the (un)complexity of subsystems
inferred← citeshttps://doi.org/10.1103/physrevd.98.126014openalex-snapshot
Complexity growth of rotating black holes with a probe string
inferred← citeshttps://doi.org/10.1103/physrevd.99.026011openalex-snapshot
Circuit complexity for fermionic thermofield double states
inferred← citeshttps://doi.org/10.1103/physrevd.99.106013openalex-snapshot
Holographic complexity and charged scalar fields
inferred← citeshttps://doi.org/10.1103/physreve.110.034201openalex-snapshot
Spread complexity and quantum chaos for periodically driven spin chains
inferred← citeshttps://doi.org/10.1103/physrevlett.103.080502openalex-snapshot
Quantum Adiabatic Brachistochrone
inferred← citeshttps://doi.org/10.1103/physrevlett.114.100502openalex-snapshot
Solution to the Quantum Zermelo Navigation Problem
inferred← citeshttps://doi.org/10.1103/physrevlett.124.101602openalex-snapshot
Renormalized Circuit Complexity
inferred← citeshttps://doi.org/10.1103/physrevlett.128.051601openalex-snapshot
Complexity for Conformal Field Theories in General Dimensions
inferred← citeshttps://doi.org/10.1103/physrevlett.132.160402openalex-snapshot
A Relation between Krylov and Nielsen Complexity
inferred← citeshttps://doi.org/10.1103/physrevresearch.2.013323openalex-snapshot
Circuit complexity across a topological phase transition
inferred← citeshttps://doi.org/10.1103/physrevresearch.2.043438openalex-snapshot
Geometry of complexity in conformal field theory
inferred← citeshttps://doi.org/10.1103/spd2-l836openalex-snapshot
Explicit connections between Krylov and Nielsen complexity
inferred← citeshttps://doi.org/10.1103/vpyr-b3fbopenalex-snapshot
Spread complexity and the saturation of wormhole size
inferred← citeshttps://doi.org/10.1103/y8nw-n1wbopenalex-snapshot
Geometric quantum control and the random Schrödinger equation
inferred← citeshttps://doi.org/10.1117/12.2256267openalex-snapshot
Time-optimal quantum control via differential geometry
inferred← citeshttps://doi.org/10.1117/12.918323openalex-snapshot
Finsler metrics in quantum circuit optimization
inferred← citeshttps://doi.org/10.1126/science.1121541openalex-snapshot
Quantum Computation as Geometry
inferred← citeshttps://doi.org/10.1134/s1547477125701742openalex-snapshot
On Complexity and Supersymmetry
inferred← citeshttps://doi.org/10.1140/epjc/s10052-019-6600-3openalex-snapshot
Principles and symmetries of complexity in quantum field theory
inferred← citeshttps://doi.org/10.1140/epjc/s10052-021-09563-1openalex-snapshot
Complexity growth of massive black hole with a probe string
inferred← citeshttps://doi.org/10.1140/epjc/s10052-022-10037-1openalex-snapshot
Quantum computational complexity from quantum information to black holes and back
inferred← citeshttps://doi.org/10.1140/epjc/s10052-026-15490-wopenalex-snapshot
Krylov complexity of thermal state in early universe
inferred← citeshttps://doi.org/10.1142/s0217732321502400openalex-snapshot
Circuit complexity in U(1) gauge theory
inferred← citeshttps://doi.org/10.1142/s0217979212430047openalex-snapshot
ASPECTS OF THE RIEMANNIAN GEOMETRY OF QUANTUM COMPUTATION
inferred← citeshttps://doi.org/10.1142/s0219887820500309openalex-snapshot
Quantum state manifold and geometric, dynamic and topological phases for an interacting two-spin system
inferred← citeshttps://doi.org/10.1143/ptp.127.997openalex-snapshot
Quantum Computational Riemannian and Sub-Riemannian Geodesics
inferred← citeshttps://doi.org/10.11606/d.76.2023.tde-27092023-092932openalex-snapshot
Purificação quântica para incluir ruído ambiental na investigação do conceito de complexidade quântica
inferred← citeshttps://doi.org/10.11606/t.3.2017.tde-21032017-103535openalex-snapshot
Controlabilidade de sistemas de hardware para computação quântica: definição do problema e discussão de aspectos analíticos e numéricos.
inferred← citeshttps://doi.org/10.11606/t.43.2021.tde-08042021-094350openalex-snapshot
Aspects of entanglement, chaos and complexity: from many-body to high energy systems
inferred← citeshttps://doi.org/10.11606/t.43.2023.tde-25042023-095647openalex-snapshot
Aspectos de complexidade em teoria quântica de campos e holografia
inferred← citeshttps://doi.org/10.11606/t.76.2023.tde-16012024-093809openalex-snapshot
Redes neurais no uso de Teoria de Controle para a síntese de transformações unitárias em processamento quântico em contexto ruidoso
inferred← citeshttps://doi.org/10.17169/refubium-25515openalex-snapshot
Complexity and entanglement for thermofield double states
inferred← citeshttps://doi.org/10.17771/pucrio.acad.59800openalex-snapshot
EVOLVING QUANTUM ERROR CORRECTION CODES
inferred← citeshttps://doi.org/10.21468/scipost.report.5098openalex-snapshot
Report on scipost_202203_00020v1
inferred← citeshttps://doi.org/10.21468/scipost.report.5106openalex-snapshot
Report on scipost_202203_00020v1
inferred← citeshttps://doi.org/10.21468/scipost.report.5159openalex-snapshot
Report on scipost_202204_00030v1
inferred← citeshttps://doi.org/10.21468/scipost.report.5479openalex-snapshot
Report on scipost_202204_00030v1
inferred← citeshttps://doi.org/10.21468/scipost.report.7876openalex-snapshot
Report on scipost_202307_00036v1
inferred← citeshttps://doi.org/10.21468/scipost.report.8099openalex-snapshot
Report on scipost_202307_00036v1
inferred← citeshttps://doi.org/10.21468/scipostphys.13.4.090openalex-snapshot
Bounds on quantum evolution complexity via lattice cryptography
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