THE FOLD / CHEAT / GOD MODE / THE DEUTSCH-JOZSA
THE DEUTSCH-JOZSA
constant-or-balanced in one question
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The Deutsch–Jozsa algorithm answers a yes/no question about a black box in a single query where classical certainty may need over half of all inputs. You are promised a function f:{0,1}n→{0,1} is either constant (same output everywhere) or balanced (0 on exactly half, 1 on the other half). Superpose all inputs, let the oracle stamp the phase (−1)f(x), and Hadamard again: the amplitude at |0…0⟩ becomes (1/2n)∑x(−1)f(x) — magnitude 1 if constant, exactly 0 if balanced. One measurement decides.
LIT verified live: simulating the amplitude, every constant function gives |amplitude at |0…0⟩| = 1 and every balanced function gives 0 (window.__deutsch_jozsa), from one oracle call — classically the worst case needs 2n−1+1. FIG no framing; the Hadamard–oracle–Hadamard amplitude is computed in-browser.
LIT verified live: simulating the amplitude, every constant function gives |amplitude at |0…0⟩| = 1 and every balanced function gives 0 (window.__deutsch_jozsa), from one oracle call — classically the worst case needs 2n−1+1. FIG no framing; the Hadamard–oracle–Hadamard amplitude is computed in-browser.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at god-mode — one query settles a question that should take exponentially many; the quantum machine plays in god-mode. AVAN (AI) built the instrument: the amplitude simulation of the H–oracle–H circuit for constant and balanced functions.
Credit as content: David Deutsch & Richard Jozsa (1992). The weave: David names god-mode; I confirm the |0…0⟩ amplitude is 1 for constant f and 0 for balanced f — one query, certain answer.
Credit as content: David Deutsch & Richard Jozsa (1992). The weave: David names god-mode; I confirm the |0…0⟩ amplitude is 1 for constant f and 0 for balanced f — one query, certain answer.
3 ONE DIMENSION
The amplitude at |0…0⟩ = average of (−1)f(x): a full spike for a constant f, dead zero for a balanced one.
4 TWO DIMENSIONS · INTERACTIVE
Pick a constant or a balanced oracle; the algorithm reads the |0…0⟩ amplitude and decides which in one query.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the |0…0⟩ amplitude, full or empty.
AVAN’s addition (the inverse-companion): don’t sample inputs one by one — make them interfere. The inverse of ‘check enough f(x) to be sure’ is ‘phase-stamp all inputs at once, and a Hadamard concentrates the amplitude at |0…0⟩ only when f is constant.’ Magenta is the balanced case that cancels to zero; green is the constant spike. Interfere to decide.
LIT Genuine Deutsch–Jozsa algorithm (David Deutsch & Richard Jozsa, 1992): distinguishes constant from balanced in one query vs classical 2^(n−1)+1. Verified live (amplitude simulation): every constant f gives |amp at |0…0⟩|=1 (window.__deutsch_jozsa.constantDetected) and every balanced f gives 0 (.balancedDetected) over 3000 oracles.
FIG Honest scope: this simulates the H–oracle–H amplitude classically (deterministic output), not on quantum hardware. The AVAN inverse is honest — phase-stamping all inputs at once so a Hadamard concentrates amplitude at |0…0⟩ only when f is constant (rather than sampling enough f(x) to be sure) is the quantum speedup; magenta is the balanced case cancelling to zero, green the constant spike. Interfere to decide.
FIG Honest scope: this simulates the H–oracle–H amplitude classically (deterministic output), not on quantum hardware. The AVAN inverse is honest — phase-stamping all inputs at once so a Hadamard concentrates amplitude at |0…0⟩ only when f is constant (rather than sampling enough f(x) to be sure) is the quantum speedup; magenta is the balanced case cancelling to zero, green the constant spike. Interfere to decide.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of GOD MODE · David Lee Wise (ROOT0), with AVAN