Crate tileuniverse_quantum 

tileuniverse-quantum

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

This crate does not simulate arbitrary quantum circuits. It stores compact representations for state families whose nonzero amplitudes are already known.

The 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);
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");

// Symbolic W-states check the stored formula algebraically.
let w = create_graham_w();
let wv = w.verify();
assert!(wv.is_valid);
assert!(wv.total_probability.is_one());

Structs

Complex64

Complex number with f64 precision

MinimalGhzState

Ultra-minimal GHZ state representation.

MinimalGhzVerification

Verification results for MinimalGhzState

SparseQuantumGridVec

Fast Vec-based sparse quantum grid.

SymbolicBinomial

Symbolic binomial coefficient C(n,k) = n!/(k!(n-k)!)

SymbolicDickeState

Symbolic Dicke state |D_n^k> for labels such as Graham’s number, TREE(3), or a formal infinity label.

SymbolicDickeVerification

Verification result for SymbolicDickeState

SymbolicFraction

Symbolic fraction for probability calculations.

SymbolicGhzState

GHZ endpoint representation with a symbolic qubit-count label.

SymbolicGhzVerification

Verification results for SymbolicGhzState

SymbolicWState

Symbolic W-state formula object for labels such as Graham’s number, TREE(3), or a formal infinity label.

SymbolicWVerification

Verification result for SymbolicWState.

UnlimitedGhzState

GHZ endpoint representation using a BigUint qubit-count label.

UnlimitedGhzVerification

Verification results for UnlimitedGhzState

VecBlock

A single block of 128 complex amplitudes

WStateVerificationVec

Verification result for W state

Enums

SimplifiedBinomial

Result of simplifying a binomial coefficient

SymbolicAmplitude

Symbolic representation of quantum amplitudes.

SymbolicEntropy

Symbolic representation of entropy.

SymbolicNumber

Symbolic representation of incomprehensibly large numbers.

Constants

BLOCK_SHIFT

BLOCK_SIZE

Block size: 128 amplitudes (2^7) per block

Functions

create_ghz_power_of_10

Create a GHZ state with a 10^exponent BigUint qubit count.

create_graham_dicke

Create a Dicke state with Graham’s number of qubits and k excitations

create_graham_ghz

Create a GHZ state with Graham’s number of qubits

create_graham_w

Create a W-state with Graham’s number of qubits

create_infinite_dicke

Create a Dicke state with a formal infinity label and k excitations

create_infinite_ghz

Create a GHZ state with a formal infinity label

create_infinite_w

Create a W-state with a formal infinity label (aleph_0)

create_minimal_ghz

Create a minimal GHZ state for a positive usize qubit count.

create_symbolic_dicke

Create a Dicke state with symbolic qubit and excitation counts

create_symbolic_ghz

Create a GHZ state with symbolic qubit count

create_symbolic_w

Create a W-state with symbolic qubit count

create_tree_dicke

Create a Dicke state with TREE(t) qubits and k excitations

create_tree_ghz

Create a GHZ state with TREE(n) qubits

create_tree_w

Create a W-state with TREE(n) qubits

create_unlimited_ghz

Create a GHZ state from a BigUint qubit count.