Quantum Computing Lab by ScienceVR (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 / Paper	Year	Problem Solved	Key Innovation	Math/Group Structure
Deutsch (6 lectures)	1985	Is f(0) = f(1)?	First quantum parallelism	Z₂
Deutsch-Jozsa	1992	Constant vs. balanced	Exponential speedup	Z₂ⁿ
Bernstein-Vazirani	1993	Find bitstring s	Single-shot string extraction	Z₂ⁿ (linear)
Simon's	1994	Find XOR period s	Hidden subgroup approach	Z₂ⁿ (group)
Shor's (Discrete Log)	1994	g^x ≡ a (mod p)	QFT for 2D periods	Z_p-1 × Z_p-1
Shor's (Factoring)	1994	Factors of N	Order-finding to factoring	Z_r ⊂ Z_N
Grover's	1996	Unstructured search	Amplitude amplification	Quadratic (sqrt(N))
Cleve et al. (Revisited)	1998	Unified framework	Deterministic phase kickback	The circuit model
Shor's (ECDLP)	Later	Find k in P = kQ	2D QFT over elliptic curves	Elliptic curve group

Check out CPHASE gate circuit simulator (designed based on Artur Ekert's talks and Craig Gidney's Quirk).

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.

Select subgroup order n (predefined)

Selected curve is ready (p is a prime).

Specify a public point (public key)

Generate public point (Q = kG) or use manual Q (x,y)

Choose secret k (1 < k < n)

Shor's Algorithm Phase Registers (a/b qubits)

Control qubits (A=B)

Measurements/Shots

Number of shots

Drop circuit measurement JSON(or click to browse)

Elliptic Curvey² = x³ + 7 mod 31

Selected G: (1, 16) · n=21

Generator (G)

Public Point (Q=kG)

Curve Point (nG)

Classical computing

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