The global transverse-field Ising model with non-monotonic time-dependent transverse field is polynomially equivalent to the gate model of quantum computation.
Quantum approximate optimization is computationally universal
12 Pith papers cite this work. Polarity classification is still indexing.
12
Pith papers citing it
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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Analytical expression for dynamical Lie algebra of QAOA-MaxCut on complete graphs with proof that loss variance scales linearly in qubit number.
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.
Develops an invariant-based framework connecting Pauli Lie algebras to transvection-generated Clifford subgroups for quantum reachability and dynamics analysis.
The Projector Variational Ansatz (PVA) is a new VQE ansatz that can match ISQ-QSP or ADAPT-VQE structures and converges with shallower circuits than standard ADAPT-VQE in experiments.
A Pauli-constraint-based programming model for quantum computers is proved equivalent to the standard circuit model, universal for BQP, with O(D^2 N log N) emulation 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.
Numerical study of five symmetry-preserving HVAs for Z2 gauge theory finds overparametrization eliminates local minima and loss decay rate scales linearly with number of parameters.
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.
HUBO formulations for logistics problems offer qubit savings over QUBO at the expense of higher circuit depth, validated classically and simulated quantumly for small cases.
citing papers explorer
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Polynomial equivalence of the global transverse-field Ising model and the gate model of quantum computation
The global transverse-field Ising model with non-monotonic time-dependent transverse field is polynomially equivalent to the gate model of quantum computation.
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The Dynamical Lie Algebra of QAOA-MaxCut on the Complete Graph
Analytical expression for dynamical Lie algebra of QAOA-MaxCut on complete graphs with proof that loss variance scales linearly in qubit number.
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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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From Pauli Strings to Quantum Dynamics: A Unified Characterization
Develops an invariant-based framework connecting Pauli Lie algebras to transvection-generated Clifford subgroups for quantum reachability and dynamics analysis.
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Projector Quantum Variational Ansatz
The Projector Variational Ansatz (PVA) is a new VQE ansatz that can match ISQ-QSP or ADAPT-VQE structures and converges with shallower circuits than standard ADAPT-VQE in experiments.
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Quantum circuit design via dynamic Pauli constraints
A Pauli-constraint-based programming model for quantum computers is proved equivalent to the standard circuit model, universal for BQP, with O(D^2 N log N) emulation 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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Symmetries and overparametrization properties of Hamiltonian variational ansatzes for the $(1+1)$d $\mathbb{Z}_2$ lattice gauge theory
Numerical study of five symmetry-preserving HVAs for Z2 gauge theory finds overparametrization eliminates local minima and loss decay rate scales linearly with number of parameters.
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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.
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Quantum optimization beyond QUBO for industrial logistics and scheduling
HUBO formulations for logistics problems offer qubit savings over QUBO at the expense of higher circuit depth, validated classically and simulated quantumly for small cases.