Shadow Quantum Singular Value Transformation with Shallow Quantum Circuits

arXiv:2609.40167 · quant-ph, cs.DS · Submitted 2026-09-30 · Read on arXiv

quant-ph, cs.DS

Submitted: 2026-09-30

Updated: 2026-10-06

Terminology

• Sample Complexity — 23× in this paper · explained in 15 episodes
• Block Encoding — 21× in this paper · explained in 4 episodes
• Quantum Singular Value Transformation — 8× in this paper
• Accuracy — 7× in this paper · explained in 1 episode
• Quantum Circuits — 5× in this paper · explained in 2 episodes
• Query Complexity — 5× in this paper · explained in 2 episodes
• Post-Selection — 2× in this paper · explained in 2 episodes
• Resource Constraints — 2× in this paper · explained in 3 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Adaptive Selection — 1× in this paper · explained in 1 episode
• Ancilla Qubits — 1× in this paper · explained in 1 episode
• Quantum Singular Value Transformation (QSVT) — 1× in this paper · explained in 4 episodes

Sources

• Krylov Polynomials and Quantum Query Complexity
• An efficient algorithm for approximate shadow Hamiltonian simulation
• A shortcut to an optimal quantum linear system solver
• Faster quantum linear system solver beyond the condition number
• A New Quantum Linear System Algorithm Beyond the Condition Number and Its Application to Solving Multivariate Polynomial Systems
• Quantum linear system algorithm with optimal queries to initial state preparation
• Quantum Linear System Solvers: A Survey of Algorithms and Applications

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