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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An adiabatic protocol for quantum phase estimation that reaches optimal scaling T = O(1/ε log(1/δ)) by encoding eigenvalues in computational basis populations rather than phases.
A hybrid method uses fixed quantum annealing states as boundary resources for classical MERA tensor networks to improve ground-state approximations without deeper quantum circuits.
Deep Boltzmann Quantum States with natural-gradient optimization and annealing-like training match exact or best-known solutions for large infinite-range Ising spin glasses and solve job shop scheduling instances.
Simulations find that the inverse energy gap in 2D Edwards-Anderson spin glasses develops a fat-tailed distribution with infinite variance for large N, while the Sherrington-Kirkpatrick model shows a finite-variance gap scaling roughly as N to the power -1/3.
HAVQDS achieves higher approximation ratios on 6-14 qubit SK instances than adiabatic or CD methods while cutting CNOT counts by 1-2 orders of magnitude.
Kibble-Zurek defect scaling does not generally correspond to quantum criticality in representative quasi-1D Fermi models.
Conjectures that for quenches within the same phase the initial ground state has largest overlap with post-quench ground state; confirmed analytically and numerically for TFIM and special case of ANNNI.
AL-QHD benchmarks on nonconvex test functions and ACOPF power problems show useful accuracy at fixed qubit cost but require roughly 10^8 T gates for realistic instances.
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Separation of the Kibble-Zurek Mechanism from Quantum Criticality
Kibble-Zurek defect scaling does not generally correspond to quantum criticality in representative quasi-1D Fermi models.
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Extension of the Adiabatic Theorem
Conjectures that for quenches within the same phase the initial ground state has largest overlap with post-quench ground state; confirmed analytically and numerically for TFIM and special case of ANNNI.