tileuniverse-quantum

Structured sparse quantum-state representations with GHZ and W-state helpers.

This crate is not a general-purpose quantum circuit simulator. It stores compact representations for state families whose nonzero amplitudes are already known.

Key Insight

GHZ state |GHZ_n> = (|00...0> + |11...1>)/sqrt(2) has exactly 2 non-zero amplitudes regardless of n. Store only those two amplitudes; the qubit count is metadata.

use tileuniverse_quantum::*;

// Fixed endpoint-block memory for this concrete usize qubit count.
let ghz = MinimalGhzState::new(1_000_000_000);
let v = ghz.verify();
assert!((v.fidelity - 1.0).abs() < 1e-10);

State Types

Struct	Count Representation	Use Case
`MinimalGhzState`	`usize`	Fixed-size endpoint GHZ representation
`UnlimitedGhzState`	Materialized `BigUint`	Endpoint GHZ representation with large integer labels
`SymbolicGhzState`	Symbolic labels	Graham's number, TREE(3), and formal infinity labels
`SparseQuantumGridVec`	`usize`	Materialized W-state excitation amplitudes with O(n) memory

W-State Example

use tileuniverse_quantum::SparseQuantumGridVec;

// W-states materialize one amplitude per excitation position: O(n), not O(2^n).
let grid = SparseQuantumGridVec::new(1_000);
assert_eq!(grid.n_qubits(), 1_000);

Symbolic Example

use tileuniverse_quantum::*;

// Graham's number as a symbolic qubit-count label.
let ghz = SymbolicGhzState::graham();
let v = ghz.verify();
assert!((v.fidelity - 1.0).abs() < 1e-10);
assert_eq!(v.size_class, "Graham-class");

Installation

Add to your Cargo.toml:

[dependencies]
tileuniverse-quantum = "0.1"

Features

GHZ endpoint states: fixed endpoint-block storage for usize, BigUint, and symbolic labels
W-states: O(n) memory for materialized n-qubit W-states via sparse block grid (BLOCK_SIZE=128)
Symbolic labels: qubit counts as symbolic expressions (Graham's number, TREE(3), Knuth up-arrow, tetration, BigUint, and formal infinity labels)
Dicke states: Generalized states with k excitations among n qubits
Symbolic amplitudes/fractions: Algebraic verification of probabilities, entropy, binomial coefficients
Parallel verification: Rayon-accelerated doctest examples

Doctests

All public API includes runnable doctests:

cargo test --doc -p tileuniverse-quantum

License

MIT

tileuniverse-quantum 0.1.1