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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Sample complexity for fidelity estimation to a rank-r reference state is O(r²/ε²) with lower bound Ω(r/ε²); O(r²/ε⁴) when unknown state also has rank ≤r.
Quantum algorithm prepares exact Hadamard product state of two function states with N-independent query complexity when either function has finitely many non-zero Fourier coefficients.
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.
AtomTreeSearch embeds a neutral-atom quantum MWIS subroutine inside Monte Carlo Tree Search and matches or exceeds OR-Tools and simulated annealing on TSP instances up to 100 cities.
Coupling-Grouped XY-QAOA enables joint anomaly-feature selection via a constraint-preserving grouped-angle QAOA variant, achieving 45.9-61.3% circuit depth reduction and larger feasible executions (64 qubits at p=2) on IBM Heron hardware compared to standard approaches.
Quantum rejection sampling applied to truncated Klein proposals yields quadratic speedup in dual-attack lattice Gaussian sampling, cutting Kyber attack costs by 9, 4, and 13 bits.
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.
Quantum algorithm for 1D NLSE via Lax-pair scattering performs time evolution analytically in the scattering domain and reconstructs solutions with QSVT.
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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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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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.
- Learning PDEs for Portfolio Optimization with Quantum Physics-Informed Neural Networks