Quantum Error Detection: Knowing Without Fixing
Quantum error detection flags errors without correcting them. Syndrome measurement, detection codes and their role in fault-tolerant systems.
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Quantum Random Walks: Discrete and Continuous
Discrete and continuous quantum random walks compared with classical walks, and their uses in algorithms, cryptography and models of biology.
The Quantum Discrete Logarithm Algorithm
How Shor’s algorithm also solves the discrete logarithm problem, which threatens Diffie-Hellman and elliptic curve cryptography.
Quantum Factoring: Breaking RSA, In Theory
How Shor’s algorithm would factor RSA moduli, how many qubits that needs, the records achieved so far and why migration to new schemes has begun.
Quantum Symmetric-Key Cryptography and Grover
Why Grover’s algorithm halves the effective security of symmetric keys, why AES-256 remains safe, and how quantum approaches to symmetric keys work.
Quantum Public-Key Cryptography: State of the Art
What quantum public-key cryptography means, how it differs from QKD and post-quantum schemes, and where research on it stands.
Quantum One-Way Functions and Their Assumptions
Quantum one-way functions are easy to compute and hard to invert, even for quantum computers. Their definitions and role in quantum cryptography.
Quantum Oracle Separations: Proof by Black Box
Oracle separations show that quantum and classical computers differ relative to a black box. Key results, from Simon’s problem to BQP versus PH.
Quantum NP: What Non-Determinism Means for Qubits
What non-determinism means for quantum computers, how QMA and NQP are defined, and why quantum computers are not expected to solve NP-complete problems.
Quantum Probabilistic Polynomial Time, Explained
Probabilistic polynomial time in the quantum setting: how BQP and PP are defined, how error probability is bounded, and how they relate to P and NP.
Quantum Counting Complexity: Classes and Results
Quantum counting complexity covers classes such as #P and their quantum analogues. Algorithms, speedups, oracle results and known bounds.
The Quantum Polynomial Hierarchy and Its Levels
The quantum polynomial hierarchy extends the classical hierarchy to quantum verifiers. Its levels, relation to classical classes and open questions.