Necessary and sufficient conditions for Pauli strings to generate su(2^n) with applications to limited-control Heisenberg Hamiltonians.
Full classification of pauli lie algebras
11 Pith papers cite this work, alongside 1 external citations. Polarity classification is still indexing.
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A randomized algorithm recovers the exact Pauli decomposition of k-sparse n-qubit matrices in poly(n, k, log(1/δ)) time with high probability under sparse query access.
A first-moment operator diagnostic reveals exponentially many inequivalent initialization distributions avoid barren plateaus in variational quantum algorithms, with numerics indicating distinct attained minima.
Symmetry-adapted Pauli-orbit and modified Gell-Mann bases make polynomial-dimensional dynamical Lie algebras practically simulable beyond free fermions.
Introduces Closest Accessible Symmetry reduction to analyze spectra of Hamiltonian interpolations by projecting onto closest accessible symmetries, yielding weakly coupled sectors that capture quantum phase transition signatures.
Develops an invariant-based framework connecting Pauli Lie algebras to transvection-generated Clifford subgroups for quantum reachability and dynamics analysis.
Stabilizer redundancy from error-correcting codes reduces the choice of physical operators for a logical target to a least-squares problem with closed-form solution, allowing native hardware Hamiltonians to replace costly swaps.
Random states from symplectic and orthogonal unitaries show exponentially large strong state complexity and near-orthogonality, with average-case hardness for learning circuits from these groups.
A frustration graph formalism for prime-d qudit observables yields a unitary map to generalized Pauli form plus bounds on observable sums used for qudit entanglement quantification.
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.
Quantum simulation methods for Thirring and Gross-Neveu fermionic models with arbitrary flavors, including gate complexity bounds and ground-state preparation up to 20 qubits.
citing papers explorer
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Necessary and Sufficient Conditions for Universal Gates with Pauli Strings and Beyond
Necessary and sufficient conditions for Pauli strings to generate su(2^n) with applications to limited-control Heisenberg Hamiltonians.
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An efficient Pauli decomposition algorithm for structured matrices
A randomized algorithm recovers the exact Pauli decomposition of k-sparse n-qubit matrices in poly(n, k, log(1/δ)) time with high probability under sparse query access.
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Exponentially many initializations to avoid barren plateaus
A first-moment operator diagnostic reveals exponentially many inequivalent initialization distributions avoid barren plateaus in variational quantum algorithms, with numerics indicating distinct attained minima.
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Enabling Lie-Algebraic Classical Simulation beyond Free Fermions
Symmetry-adapted Pauli-orbit and modified Gell-Mann bases make polynomial-dimensional dynamical Lie algebras practically simulable beyond free fermions.
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Closest Accessible Symmetry reduction: a tool for Hamiltonian interpolation analysis
Introduces Closest Accessible Symmetry reduction to analyze spectra of Hamiltonian interpolations by projecting onto closest accessible symmetries, yielding weakly coupled sectors that capture quantum phase transition signatures.
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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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Stabilizers for Compiling Logical Circuits under Hardware Constraints
Stabilizer redundancy from error-correcting codes reduces the choice of physical operators for a logical target to a least-squares problem with closed-form solution, allowing native hardware Hamiltonians to replace costly swaps.
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On the Complexity of Quantum States and Circuits from the Orthogonal and Symplectic Groups
Random states from symplectic and orthogonal unitaries show exponentially large strong state complexity and near-orthogonality, with average-case hardness for learning circuits from these groups.
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Frustration graph formalism for qudit observables
A frustration graph formalism for prime-d qudit observables yields a unitary map to generalized Pauli form plus bounds on observable sums used for qudit entanglement quantification.
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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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Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors
Quantum simulation methods for Thirring and Gross-Neveu fermionic models with arbitrary flavors, including gate complexity bounds and ground-state preparation up to 20 qubits.