Quantum Algorithms for Graph Problems
Quantum algorithms for graph problems: quantum walks, search speedups and subgraph questions, with an honest view of where advantages hold.
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Quantum Algorithms
Shor, Grover, QAOA, VQE and the rest — what each quantum algorithm does, the problem it targets and where the promised speedup really comes from.
85 articles
Quantum Circuit Design: Algorithms and Compilers
How quantum circuits are designed and compiled: gate decomposition, qubit mapping, depth reduction, parallelization, synthesis and benchmarking.
Quantum Oracles: The Black Box in Quantum Algorithms
What a quantum oracle is, how algorithms query it as a black box, how oracles are built as circuits, and why they matter for speedup claims.
Quantum Chemistry Algorithms: What Runs Today
Which quantum chemistry algorithms run on today’s hardware, what they compute, and how they may help drug discovery and materials science.
Quantum Eigenvalue Estimation: Methods Compared
How quantum computers estimate eigenvalues: phase estimation, variational methods and their uses in chemistry, physics and data analysis.
Quantum Amplitude Estimation and Its Speedup
Quantum amplitude estimation measures a probability with quadratically fewer samples than classical Monte Carlo. The circuit, precision and applications.
Quantum Gibbs Sampling: Thermal States on a Computer
Quantum Gibbs sampling prepares thermal states of quantum systems. How it differs from classical sampling and its uses in simulation and machine learning.
Boson Sampling: The Photonic Route to Quantum Advantage
Boson sampling sends photons through a network of beam splitters. Why its output is hard to simulate classically and what the experiments have shown.
The Quantum Adiabatic Algorithm, Explained
The quantum adiabatic algorithm slowly evolves a simple Hamiltonian into one encoding a problem. The adiabatic theorem, annealing and hardware limits.
Quantum Algorithms for Diophantine Equations
What quantum algorithms can and cannot do for Diophantine equations, with the roles of Shor’s, Grover’s and HHL algorithms and variational methods.
Quantum Order-Finding: The Core of Shor’s Algorithm
Order finding is the quantum core of Shor’s algorithm. How phase estimation and the quantum Fourier transform find the period of modular exponentiation.
Quantum Algorithms for Solving Pell’s Equation
How quantum algorithms solve Pell’s equation, a number theory problem linked to cryptography, using period finding and the quantum Fourier transform.
