A hierarchical prefix-tree algorithm identifies the dominant Pauli coefficients of sparse quantum states using Bell sampling on two copies, with sample-complexity bounds tied to the number of coefficients and state purity.
The Heisenberg representation of quantum computers
8 Pith papers cite this work. Polarity classification is still indexing.
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Qutrit Clifford+T gates are realized using two-body angular momentum couplings, rotations, and one-axis-twisting operations, with extensions to bosonic modes via Jordan-Schwinger and cross-Kerr.
Efficient algorithms compute stabilizer Rényi entropy and mana for quantum states from vectors at O(N d^{2N}) cost using fast Hadamard transform, with open-source implementation.
Quantum algorithms achieve exponential fast-forwarding for structured Lindbladian dynamics and coherence-dependent exponential speedup in Gibbs state property estimation.
Reformulates Pauli and Clifford groups in geometric algebra with a greedy rotor decomposition algorithm for Clifford operators and geometric view of Clifford+T universality.
Absence of simple slow operators implies that typical low-complexity states thermalize in quantum systems.
A measurement-only model with fermionic and ancilla chains generates volume-law entanglement and mutual information via local non-random non-commuting measurements, including using only one-body operators.
Magic distributions are computed for EW processes (reproducing QED at low energy, new at high energy/Z resonance) and dark-sector scatterings, reaching maximal magic at mass ratios m_f/m_χ → 0 and → 1.83929.
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Simple slow operators and quantum thermalization
Absence of simple slow operators implies that typical low-complexity states thermalize in quantum systems.