Multivariate Quantum Signal Processing

arXiv:2610.01125 · quant-ph · Submitted 2026-10-01 · Read on arXiv

quant-ph

Submitted: 2026-10-01

Updated: 2026-10-01

Comments: 305 pages, 34 figues, 14 tables

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

Terminology

• Quantum Signal Processing — 325× in this paper
• Multivariate Quantum Signal Processing — 315× in this paper
• Block Encoding — 45× in this paper · explained in 4 episodes
• Trace — 40× in this paper · explained in 2 episodes
• Accuracy — 34× in this paper · explained in 1 episode
• Hilbert Space — 34× in this paper · explained in 2 episodes
• Query Complexity — 16× in this paper · explained in 2 episodes
• Alignment — 15× in this paper · explained in 1 episode
• Effective Hamiltonian — 10× in this paper · explained in 2 episodes
• Trace Distance — 9× in this paper · explained in 3 episodes
• Core — 8× in this paper · explained in 2 episodes
• Calibration — 4× in this paper · explained in 7 episodes
• Consistency — 4× in this paper · explained in 3 episodes
• Embeddings — 4× in this paper · explained in 2 episodes
• Approximation Bound — 3× in this paper · explained in 1 episode
• Benchmark — 3× in this paper · explained in 2 episodes
• Spectral Gap — 3× in this paper · explained in 5 episodes
• Adiabatic Evolution — 2× in this paper · explained in 2 episodes
• Anisotropy — 2× in this paper · explained in 3 episodes
• Quantization — 2× in this paper · explained in 12 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Unitary Dynamics — 2× in this paper · explained in 2 episodes
• Admissibility — 1× in this paper · explained in 2 episodes
• Admissibility Conditions — 1× in this paper · explained in 1 episode
• Algorithmic Primitives — 1× in this paper · explained in 1 episode
• Alternation — 1× in this paper · explained in 1 episode
• Ancillary Qubits — 1× in this paper · explained in 1 episode
• Angular Error — 1× in this paper · explained in 1 episode
• Anisotropic Filtering — 1× in this paper · explained in 1 episode
• Frustration — 1× in this paper · explained in 2 episodes
• Hamiltonian Learning — 1× in this paper · explained in 2 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Kernel decomposition — 1× in this paper · explained in 2 episodes
• Matrix Completion — 1× in this paper · explained in 3 episodes
• Memory Decay — 1× in this paper · explained in 3 episodes
• Modularity — 1× in this paper · explained in 9 episodes
• Self-consistency — 1× in this paper · explained in 2 episodes
• Semi-supervised Learning — 1× in this paper · explained in 4 episodes
• Sum-of-Squares-Spectral Amplification — 1× in this paper
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters
• Quantum simulation of non-Markovian dynamical systems
• Unbounded loops in quantum programs: categories and weak while loops
• Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization
• Improved Techniques for Preparing Eigenstates of Fermionic Hamiltonians
• Quantum simulations of excited states with active-space downfolded Hamiltonians
• A new quantum ripple-carry addition circuit
• Quantum-Assisted Barrier Sequential Quadratic Programming for Nonlinear Optimal Control
• Spectral amplification for ground-state energy estimation of electronic structure in first quantization
• Uniform approximation of sgn(x) by polynomials and entire functions
• Quantum Subroutine Composition
• The cost of solving linear differential equations on a quantum computer: fast-forwarding to explicit resource counts
• On the Schr\"odingerization method for linear non-unitary dynamics with optimal dependence on matrix queries
• Quantum simulation with sum-of-squares spectral amplification
• An adversary bound for quantum signal processing
• Hamiltonian Simulation by Uniform Spectral Amplification
• A Denser Planar Surface Code
• Trading T gates for dirty qubits in state preparation and unitary synthesis
• Well-conditioned multiproduct Hamiltonian simulation
• Quantum linear system algorithm with optimal queries to initial state preparation

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• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians