Quantum Computing Lab Alpha Preview


The goal of this project is to provide an interactive, educational sandbox for learning about quantum algorithms and their classical counterparts, with a focus on Shor's algorithm for the Elliptic Curve Discrete Logarithm Problem (ECDLP). This simulator allows you to explore the problem space, run classical k-recovery algorithms, and see resource estimates for quantum approaches. For a deeper dive into the history and math behind these algorithms, check out the timeline below.
Algorithm / PaperYearProblem SolvedKey InnovationMath/Group Structure
Deutsch1985Is f(0) = f(1)?First quantum parallelismZ2
Deutsch-Jozsa1992Constant vs. balancedExponential speedupZ2n
Bernstein-Vazirani1993Find bitstring sSingle-shot string extractionZ2n (linear)
Simon's1994Find XOR period sHidden subgroup approachZ2n (group)
Shor's (Discrete Log)1994gx ≡ a (mod p)QFT for 2D periodsZp-1 × Zp-1
Shor's (Factoring)1994Factors of NOrder-finding to factoringZr ⊂ ZN
Grover's1996Unstructured searchAmplitude amplificationQuadratic (sqrt(N))
Cleve et al. (Revisited)1998Unified frameworkDeterministic phase kickbackThe circuit model
Shor's (ECDLP)LaterFind k in P = kQ2D QFT over elliptic curvesElliptic curve group

Learn more about Shor's Algorithm on Knowledge Layer. Or check out CPHASE gate circuit simulator.

Elliptic Curve Discrete Logarithm Problem (ECDLP) Simulator

This is an Elliptic Curve Cryptography (ECC) simulator focusing on SECP256k1-like curves: y² = x³ + 7 mod p (with much smaller p and order N in this simulator). The 256-bit prime field P and 256-bit order N that are impossible to solve in both classic and quantum settings. Pick a curve based on the subgroup of order n = 2^s - 1, then generate a public point (public key) Q = kG and run k-recovery routines.

Classical computing

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