Quantum Parallelism: What It Does and Does Not Give
Quantum parallelism evaluates a function on many inputs at once, but measurement returns only one result. What it gives and what it does not.
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Quantum Dephasing: How Phase Information Is Lost
Dephasing destroys the phase relation between parts of a superposition without changing populations. Causes, T2 times, measurement and mitigation.
The Quantum Threshold Theorem, Explained
The threshold theorem says arbitrarily long quantum computations are possible if physical error rates stay below a threshold. What that requires.
Quantum Property Testing: Deciding With Few Queries
Quantum property testing decides whether a state or operation has a property using few measurements. Methods such as entanglement witnesses.
The Quantum PCP Conjecture and Why It Is Open
The quantum PCP conjecture asks whether local Hamiltonian problems stay hard to approximate. Why it matters, partial results and why it is still open.
Quantum Circuit Complexity: Depth, Width and Cost
How the complexity of a quantum circuit is measured by gate count, depth and width, and the techniques used to optimize circuits.
Quantum Information Complexity, Explained
Quantum information complexity studies how much information protocols must reveal or exchange. Its links to communication, cryptography and storage.
Quantum Query Complexity: Counting Oracle Calls
Query complexity counts how often an algorithm must query an oracle. How quantum queries give speedups such as Grover’s and where limits lie.
Quantum Lower Bounds: Proving What Cannot Be Faster
Quantum lower bounds prove that a problem needs a minimum number of steps. The polynomial and adversary methods and their effect on algorithm design.
QMA-Complete Problems: The Local Hamiltonian Family
QMA-complete problems such as the local Hamiltonian problem are the hardest problems in QMA. Their origin, proofs and applications.
Quantum Computational Efficiency: How It Is Measured
How quantum computational efficiency is measured: gate counts, circuit depth and speedup, and where parallelism and interference help.
QPCP: The Quantum PCP Conjecture, Explained
The quantum PCP conjecture asks whether quantum proofs can be checked by reading only a few qubits. Its forms, known results and open questions.