Optimal algorithms achieve query complexities Θ(d/ε²) for incoherent access, Θ(d/ε) for coherent access, and Θ(√d/ε) for source-code access in quantum channel certification to unitary, exactly matching prior lower bounds.
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Quantum amplitude amplification and estimation
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2026 10representative citing papers
A one-ancilla framework for QSAMPLE preparation via GQSP-based selective phase compilation embedded in fixed-point amplitude amplification, improving overlap dependence to inverse square-root minimum overlap.
A quantum multi-level framework achieves near-optimal query complexity for q-Tsallis entropy estimation for q>1 and a speedup for q<1 over classical methods.
A new method for unitary synthesis on quantum hardware cuts CNOT gates by up to 36% and compiles up to 553 times faster than standard tools on square and heavy-hex lattices.
A recursive construction preserves O(sqrt(N)) quantum search complexity with local operations on tensor-decomposable partitions, eliminating the need for global diffusion via degeneracy in reflection angles.
Quantum PINNs using tensor-rank polynomials solve the Merton portfolio optimization PDE more accurately and with far fewer parameters than classical neural networks.
Quantum rejection sampling yields a quadratically faster discrete Gaussian sampler on lattices, enabling two improved versions of quantum dual attacks with trade-offs in speed and memory.
Data-driven approximation methods are derived for the unitary Koopman-von Neumann operator, its eigenvalues and eigenfunctions, with explicit quantum-circuit representations for finite-dimensional projections.
QFlow-SD matches canonical UCCSD energies for tested molecules while using substantially fewer qubits via reduced active spaces and constant-depth circuits, with a composite classical-quantum downfolding strategy demonstrated for water.
Hybrid quantum interior point methods for linear programming have no practical runtime advantage over classical solvers like HiGHS on realistic instances because their quantum lower bounds already exceed classical performance under optimistic assumptions.
citing papers explorer
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Strict Hierarchy for Quantum Channel Certification to Unitary
Optimal algorithms achieve query complexities Θ(d/ε²) for incoherent access, Θ(d/ε) for coherent access, and Θ(√d/ε) for source-code access in quantum channel certification to unitary, exactly matching prior lower bounds.
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Ancilla-Efficient QSAMPLE Preparation for Reversible Markov Chains
A one-ancilla framework for QSAMPLE preparation via GQSP-based selective phase compilation embedded in fixed-point amplitude amplification, improving overlap dependence to inverse square-root minimum overlap.
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Quantum Multi-Level Estimation of Functionals of Discrete Distributions
A quantum multi-level framework achieves near-optimal query complexity for q-Tsallis entropy estimation for q>1 and a speedup for q<1 over classical methods.
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Architecture-aware Unitary Synthesis
A new method for unitary synthesis on quantum hardware cuts CNOT gates by up to 36% and compiles up to 553 times faster than standard tools on square and heavy-hex lattices.
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Quantum Search without Global Diffusion
A recursive construction preserves O(sqrt(N)) quantum search complexity with local operations on tensor-decomposable partitions, eliminating the need for global diffusion via degeneracy in reflection angles.
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Learning PDEs for Portfolio Optimization with Quantum Physics-Informed Neural Networks
Quantum PINNs using tensor-rank polynomials solve the Merton portfolio optimization PDE more accurately and with far fewer parameters than classical neural networks.
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Quantum algorithm for Discrete Gaussian Sampling
Quantum rejection sampling yields a quadratically faster discrete Gaussian sampler on lattices, enabling two improved versions of quantum dual attacks with trade-offs in speed and memory.
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Numerical approximation of the Koopman-von Neumann equation: Operator learning and quantum computing
Data-driven approximation methods are derived for the unitary Koopman-von Neumann operator, its eigenvalues and eigenfunctions, with explicit quantum-circuit representations for finite-dimensional projections.
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Quantum Flow algorithm: quantum simulations of chemical systems using reduced quantum resources and constant depth quantum circuits
QFlow-SD matches canonical UCCSD energies for tested molecules while using substantially fewer qubits via reduced active spaces and constant-depth circuits, with a composite classical-quantum downfolding strategy demonstrated for water.
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Practical lower bounds for hybrid quantum interior point methods in linear programming
Hybrid quantum interior point methods for linear programming have no practical runtime advantage over classical solvers like HiGHS on realistic instances because their quantum lower bounds already exceed classical performance under optimistic assumptions.