Quantum Estimation of Non-Hermitian Pseudospectra

arXiv:2603.16214 · quant-ph, cs.NA, math.NA · Submitted 2026-03-17 · Read on arXiv

quant-ph, cs.NA, math.NA

Submitted: 2026-03-17

Updated: 2026-09-27

Comments: Accepted by Physical Review A. Retitled with no substantive changes

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Ancilla Qubits — 5× in this paper · explained in 1 episode
• Spectral Gap — 5× in this paper · explained in 5 episodes
• Quantum Singular Value Transformation (QSVT) — 4× in this paper · explained in 4 episodes
• Trace — 4× in this paper · explained in 2 episodes
• Accuracy — 3× in this paper · explained in 1 episode
• Benchmark — 2× in this paper · explained in 2 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Exceptional Point (EP) — 1× in this paper · explained in 5 episodes
• Heisenberg Scaling — 1× in this paper · explained in 4 episodes
• Lindblad master equation — 1× in this paper · explained in 2 episodes
• Non-Hermitian Skin Effect — 1× in this paper · explained in 2 episodes
• Query Complexity — 1× in this paper · explained in 2 episodes
• Symmetry Breaking — 1× in this paper · explained in 3 episodes

Sources

• Resolvent-based quantum phase estimation: Towards estimation of parametrized eigenvalues
• Heisenberg limited multiple eigenvalue estimation via off-the-grid compressed sensing
• Exponential quantum advantages for practical non-Hermitian eigenproblems
• Quantum Eigensolver for Non-Normal Matrices via Ground State Energy Estimation
• Heisenberg-Limited Quantum Eigenvalue Estimation for Non-normal Matrices
• Quantum computing with Qiskit
• 3-Local Hamiltonian is QMA-complete
• Lecture Notes on Quantum Algorithms for Scientific Computation

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