A compression protocol for controlled time evolution of local translationally invariant Hamiltonians achieves O(t polylog(t N/ε)) circuit depth with additive control overhead, demonstrated via 414 CNOT gates for iterative phase estimation on a 6×6 triangular lattice and sub-1% energy errors on a 4×4
Lloyd, Universal quantum simulators, Science 273, 1073 (1996)
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HQRN creates an exact functional match to classical residual networks on basis inputs while using quantum correlations for better performance on mixed states in digit recognition and entanglement classification.
Quantum geometry in lattice compact scalar fields induces pair-dependent Chern couplings that produce non-identical anyons.
Rigorous worst- and average-case error bounds show comparable worst-case scaling for digital and analog quantum simulators under perturbative noise, with distinct average-case error cancellation and concentration bounds for Gaussian and Brownian noise.
Shallow Trotter circuits qualitatively simulate resonant tunneling (up to 4 steps) and localization (dozens of steps) in continuous-time spin evolution.
citing papers explorer
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Phase Estimation with Compressed Controlled Time Evolution
A compression protocol for controlled time evolution of local translationally invariant Hamiltonians achieves O(t polylog(t N/ε)) circuit depth with additive control overhead, demonstrated via 414 CNOT gates for iterative phase estimation on a 6×6 triangular lattice and sub-1% energy errors on a 4×4
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Bridge the Gap between Classical and Quantum Neural Networks with Residual Connections
HQRN creates an exact functional match to classical residual networks on basis inputs while using quantum correlations for better performance on mixed states in digit recognition and entanglement classification.
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Non-identical anyon algebras from compact-field quantum geometry
Quantum geometry in lattice compact scalar fields induces pair-dependent Chern couplings that produce non-identical anyons.
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Stability of digital and analog quantum simulations under noise
Rigorous worst- and average-case error bounds show comparable worst-case scaling for digital and analog quantum simulators under perturbative noise, with distinct average-case error cancellation and concentration bounds for Gaussian and Brownian noise.
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Qualitative quantum simulation of resonant tunneling and localization with the shallow quantum circuits
Shallow Trotter circuits qualitatively simulate resonant tunneling (up to 4 steps) and localization (dozens of steps) in continuous-time spin evolution.