Quantum Homomorphisms and Graph Structure
Quantum graph homomorphisms extend graph homomorphisms using entangled strategies in non-local games. What they reveal about graph structure.
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739 articles
Quantum Algorithmic Probability and Universal Priors
Quantum algorithmic probability extends Solomonoff’s universal prior and Kolmogorov complexity to quantum information. Ideas and uses.
Quantum Sampling Problems and Quantum Advantage
Sampling problems such as boson sampling and random circuit sampling were used to demonstrate quantum advantage. Why they are hard classically.
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.
Quantum Circuit Lower Bounds: Proving Hardness
Lower bounds for quantum circuits prove how many gates or how much depth a task needs. Methods, known results and why they matter.
Matrix Product States for Quantum Simulation
Matrix product states represent weakly entangled quantum states efficiently. How they work and why they are central to quantum simulation.
Quantum Embedding Problems: Fitting Systems Together
Quantum embedding methods treat a small, important part of a system on a quantum computer and the rest classically. How they work and scale.
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.