Contour-integral based quantum eigenvalue transformation: analysis and applications

arXiv:2601.11959 · quant-ph, cs.NA, math.NA · Submitted 2026-01-17 · Read on arXiv

quant-ph, cs.NA, math.NA

Submitted: 2026-01-17

Updated: 2026-09-20

Comments: 39 pages including appendix

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

Terminology

• Ancilla Qubits — 28× in this paper · explained in 1 episode
• Query Complexity — 5× in this paper · explained in 2 episodes
• Unitary Dynamics — 4× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Chebyshev Polynomials — 2× in this paper · explained in 2 episodes
• Gibbs State — 2× in this paper · explained in 2 episodes
• Computational overhead — 1× in this paper · explained in 2 episodes
• Entanglement — 1× in this paper · explained in 3 episodes
• Generalization — 1× in this paper · explained in 13 episodes

Sources

• A shortcut to an optimal quantum linear system solver
• A New Quantum Linear System Algorithm Beyond the Condition Number and Its Application to Solving Multivariate Polynomial Systems
• Optimal quantum simulation of linear non-unitary dynamics
• Exponentially Reduced Circuit Depths Using Trotter Error Mitigation
• Quantum linear system algorithm with optimal queries to initial state preparation
• Quantum Simulation of Non-Hermitian Special Functions and Dynamics via Contour-based Matrix Decomposition
• Quantum eigenvalue processing
• Laplace transform based quantum eigenvalue transformation via linear combination of Hamiltonian simulation
• Lecture Notes on Quantum Algorithms for Scientific Computation
• Creating superpositions that correspond to efficiently integrable probability distributions
• Quantum state preparation without coherent arithmetic
• Fast-forwarding quantum algorithms for linear dissipative differential equations
• Quantum Differential Equation Solvers with Low State Preparation Cost: Eliminating the Time Dependence in Dissipative Equations

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity