Struct QuantumTunnelingSimulator 

pub struct QuantumTunnelingSimulator { /* private fields */ }

Quantum Tunneling Simulator

Models quantum tunneling through energy barriers in optimization landscapes. The tunneling rate is estimated via the semiclassical WKB approximation:

T ≈ exp(-2 ∫_x1^x2 √(2m(V(x) - E)) dx)

For discrete problems, the tunneling Hamiltonian is H_T = -Γ Σ_i σ_i^x, where Γ is the transverse field strength. The tunnelling rate between two local minima separated by a barrier is approximated via the imaginary-time instanton action.

Implementations

impl QuantumTunnelingSimulator

pub fn new(transverse_field: f64, trotter_steps: usize, beta: f64) -> Self

Create a new tunnelling simulator.

• transverse_field — Γ in the TFIM; large Γ ↔ strong tunnelling.
• trotter_steps — discretisation of the imaginary-time path integral.
• beta — inverse temperature (1 / T); higher ↔ lower temperature.

pub fn tunneling_rate(&self, barrier_height: f64) -> f64

Estimate the instantaneous tunnelling rate between two energy minima.

Uses a one-dimensional WKB approximation along the linear path connecting the two spin configurations (treated as a real-valued coordinate). The barrier height barrier_height is the maximum energy along this path relative to the lower minimum.

Returns the dimensionless tunnelling amplitude T ∈ (0, 1].

pub fn instanton_action(&self, barrier_profile: &[f64]) -> f64

Instanton action for a path through the energy barrier.

The instanton connects two degenerate minima in imaginary time. The action S_inst = ∫_0^β V(τ) dτ is approximated by summing the potential over trotter_steps evenly spaced imaginary-time slices using the trapezoidal rule.

barrier_profile gives the potential energy at each imaginary-time slice along the tunnelling path. Returns the total instanton action.

pub fn simulate_annealing(&self, n_steps: usize, problem_gap: f64) -> f64

Simulate quantum annealing from initial_state and return the probability of ending in the ground state.

The annealing schedule linearly ramps Γ from transverse_field to 0 over n_steps. At each step the instantaneous gap Δ(s) = 2Γ(s) is used to estimate the non-adiabatic transition probability via the Landau-Zener formula:

P_LZ = 1 - exp(-π Δ² / (2 |dΔ/dt|))

Returns an estimated success probability in [0, 1].