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.
Gottesman, The Heisenberg Representation of Quantum Computers, arXiv:quant- ph/9807006
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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.
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.
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Measuring the largest coefficients of a quantum state
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.
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Qutrit Clifford+T gates by two-body angular momentum couplings, rotations and one-axis-twistings
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.
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Computing quantum magic of state vectors
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.
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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.
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Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics
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.