The conjecture that breaking all non-trivial graph automorphisms suffices for universality in globally controlled qubit systems is disproved by connected graphs with trivial automorphism groups whose generated Lie algebras are nonetheless non-universal.
Lloyd, Quantum approximate optimization is compu- tationally universal, (2018), arXiv:1812.11075 [quant- ph]
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The quantum approximate optimization algorithm (QAOA) applies two Hamiltonians to a quantum system in alternation. The original goal of the algorithm was to drive the system close to the ground state of one of the Hamiltonians. This paper shows that the same alternating procedure can be used to perform universal quantum computation: the times for which the Hamiltonians are applied can be programmed to give a computationally universal dynamics. The Hamiltonians required can be as simple as homogeneous sums of single-qubit Pauli X's and two-local ZZ Hamiltonians on a one-dimensional line of qubits.
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Defines a Pauli-constraint model of quantum circuits proven equivalent to coupling-graph-restricted circuits, universal for BQP with O(D² N log N) overhead.
QAOA for random k-SAT derives efficacy from an adiabatic manifold that supports rigorous performance guarantees at depth Θ(n²) and sublinear parameter optimization via SAMP at depth O(n).
QEL is the first quantum end-to-end learning framework for contextual combinatorial optimization using QAOA with a context re-uploading phase-separator, achieving competitive performance with fewer parameters.
Generalized Krylov complexity predicts the minimum time to realize target operations in analog quantum simulators such as Rydberg atom arrays.
Presents a universal parametrized quantum circuit ansatz based on Euler-Cartan decompositions, benchmarked on energy spectra of lattice QFT models with short- and long-range interactions.
citing papers explorer
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Obstructions to universality in globally controlled qubit graphs
The conjecture that breaking all non-trivial graph automorphisms suffices for universality in globally controlled qubit systems is disproved by connected graphs with trivial automorphism groups whose generated Lie algebras are nonetheless non-universal.
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Quantum circuit design via dynamic Pauli constraints
Defines a Pauli-constraint model of quantum circuits proven equivalent to coupling-graph-restricted circuits, universal for BQP with O(D² N log N) overhead.
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Mechanism of Efficacy in QAOA for Random k-SAT: From Adiabatic Manifold to Sublinear Parameter Optimization
QAOA for random k-SAT derives efficacy from an adiabatic manifold that supports rigorous performance guarantees at depth Θ(n²) and sublinear parameter optimization via SAMP at depth O(n).
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Quantum End-to-End Learning for Contextual Combinatorial Optimization
QEL is the first quantum end-to-end learning framework for contextual combinatorial optimization using QAOA with a context re-uploading phase-separator, achieving competitive performance with fewer parameters.
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Bridging Krylov Complexity and Universal Analog Quantum Simulator
Generalized Krylov complexity predicts the minimum time to realize target operations in analog quantum simulators such as Rydberg atom arrays.
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Universal Euler-Cartan Circuits for Quantum Field Theories
Presents a universal parametrized quantum circuit ansatz based on Euler-Cartan decompositions, benchmarked on energy spectra of lattice QFT models with short- and long-range interactions.