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Separating Hype from Actual Threat
Quantum computers are not faster classical computers. They are a different computational model that exploits quantum mechanical interference to solve specific problems faster than any known classical algorithm. They break some cryptographic schemes completely while barely affecting others. The distinction matters for deciding what to migrate now.


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What a Qubit Actually Is
A qubit is not "0 and 1 at the same time." It is a probability amplitude: a unit vector (alpha, beta) in a 2-dimensional complex Hilbert space where |alpha|^2 + |beta|^2 = 1. Measuring the qubit collapses it to the classical state 0 with probability |alph

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Quantum Gates and Interference
Quantum gates are unitary matrices acting on qubit state vectors. The Hadamard gate H maps |0> to (|0> + |1>)/sqrt(2) — equal superposition of both outcomes. A register of n qubits can be put in superposition of all 2^n computational basis states simultan

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Grover's Algorithm: Symmetric Key Impact
Grover's algorithm searches an unsorted database of N items in O(sqrt(N)) quantum queries versus O(N) classical queries. Applied to brute-forcing a symmetric key or hash preimage, it squares the search space that must be covered — equivalent to halving th

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Shor's Algorithm: Asymmetric Key Catastrophe
Shor's algorithm factors integers and computes discrete logarithms in polynomial time by using the quantum Fourier transform to find the period of the function f(x) = a^x mod N. Period-finding on a quantum computer is efficient; extracting factors from th

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The Harvest-Now-Decrypt-Later Threat
An adversary can record encrypted traffic today and decrypt it once a cryptographically relevant quantum computer (CRQC) exists. Secrets with long confidentiality requirements — government, medical, financial — are at risk now even though no CRQC exists. 

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Go Deeper: Post-Quantum Algorithms Have Been Standardized
Shor's algorithm breaks discrete log and factoring-based cryptography — but NIST finalized post-quantum standards in 2024 that rely on problems quantum computers cannot solve efficiently. Understanding those algorithms requires a different branch of mathematics: lattice theory.


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https://slatesource.com/s/1024
The algorithms being standardized right now to survive the quantum era — and the new mathematics they rely on.

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https://quantum.country/qcvc
Quantum Computing for the Very Curious