Quantum Speedup: The Four Kinds Worth Knowing
The main kinds of quantum speedup: exponential, polynomial, provable and heuristic, with Shor’s and Grover’s algorithms as examples.
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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 Resource Estimation: Counting Real Qubits
Resource estimation counts the physical qubits, gates and time an algorithm needs on real hardware. Methods, tools and typical results.
Quantum Optimization Complexity: What Is Provable
What can be proved about quantum optimization: complexity theory, QAOA, annealing and hybrid methods, and where advantage is expected.
Quantum Constraint Satisfaction Problems
Quantum constraint satisfaction problems: how constraints are encoded in qubits, algorithms such as QAOA and Grover, and complexity results.
Quantum Multi-Linear Systems and Tensor Equations
Multilinear systems and tensor equations in quantum computing: the algebra involved, tensor networks, circuits and uses in machine learning.
Quantum Linear Systems Solving: HHL and After
Quantum algorithms for linear systems, from HHL to later improvements: how they work, their caveats and applications in science and finance.
Quantum Semidefinite Programming and Its Speedup
Quantum algorithms for semidefinite programming: how they work, which speedups are claimed and uses in machine learning and quantum information.
Quantum Oracle Query Complexity and Its Bounds
Oracle query complexity counts the queries a quantum algorithm needs. Bounds, amplitude amplification, speedups and practical limitations.
Quantum Computational Geometry and Its Algorithms
Quantum algorithms for computational geometry problems such as convex hulls and point location, and where speedups are possible.
The Hidden Subgroup Problem: Groups That Yield
For which groups the hidden subgroup problem can be solved efficiently on a quantum computer, and why the non-abelian cases remain hard.
Quantum Algorithms: How They Get Their Speedup
Where quantum speedups come from: superposition, interference and entanglement, illustrated with Shor’s and Grover’s algorithms.
Quantum Reduction Techniques Between Problems
Reductions show that solving one problem would solve another. How reductions are used in quantum complexity theory and algorithm design.
