Trotterization (Encodings)

Trotterization Module

Namespace: Encodings
Assembly: Encodings.dll

Symbolic Trotter decomposition of Pauli Hamiltonians.

Decomposes the time evolution operator exp(−iHΔt) into a sequence of Pauli rotations exp(−iθₖPₖ), and further into elementary quantum gates using the CNOT staircase construction. All operations are purely symbolic — no matrix exponentiation or state-vector simulation is performed.

Supports first-order and second-order (symmetric) Suzuki–Trotter decompositions, along with circuit resource estimation (CNOT count, Pauli weight statistics).

Types

Type	Description
CircuitStats	Circuit resource statistics for a Trotter step.
Gate	Elementary quantum gate for circuit synthesis.
PauliRotation	A single Pauli rotation exp(−iθP).
TrotterOrder	Trotter decomposition order.
TrotterStep	One complete Trotter step (a product of Pauli rotations).

Functions and values

Function or value	Description
`compareTrotterCosts encodings dt` Full Usage: `compareTrotterCosts encodings dt` Parameters: encodings : `(string * PauliRegisterSequence)[]` - Array of (name, Hamiltonian) pairs. dt : `float` - Time step size for the comparison. Returns: `(string * CircuitStats) array`	Compare CNOT costs across multiple encoded Hamiltonians. encodings : `(string * PauliRegisterSequence)[]` Array of (name, Hamiltonian) pairs. dt : `float` Time step size for the comparison. Returns: `(string * CircuitStats) array`
`decomposeRotation rotation` Full Usage: `decomposeRotation rotation` Parameters: rotation : `PauliRotation` Returns: `Gate[]`	Decompose a single Pauli rotation exp(−iθP) into elementary gates. For weight-w Pauli string P on qubits {q₁,…,qw}: Basis change: H on X positions, S†H on Y positions CNOT staircase: w−1 CNOTs linking non-identity qubits Rz(2θ) on the last qubit Reverse CNOT staircase Reverse basis change Total: 2(w−1) CNOTs + 1 Rz + basis-change single-qubit gates. rotation : `PauliRotation` Returns: `Gate[]`
`decomposeTrotterStep step` Full Usage: `decomposeTrotterStep step` Parameters: step : `TrotterStep` Returns: `Gate[]`	Decompose a full Trotter step into elementary gates. step : `TrotterStep` Returns: `Gate[]`
`firstOrderTrotter dt hamiltonian` Full Usage: `firstOrderTrotter dt hamiltonian` Parameters: dt : `float` hamiltonian : `PauliRegisterSequence` Returns: `TrotterStep`	First-order Trotter decomposition. exp(−iHΔt) ≈ Πₖ exp(−icₖPₖΔt) where H = Σₖ cₖPₖ. dt : `float` hamiltonian : `PauliRegisterSequence` Returns: `TrotterStep`
`pauliWeight register` Full Usage: `pauliWeight register` Parameters: register : `PauliRegister` Returns: `int`	Pauli weight of a register: the number of non-identity positions. register : `PauliRegister` Returns: `int`
`secondOrderTrotter dt hamiltonian` Full Usage: `secondOrderTrotter dt hamiltonian` Parameters: dt : `float` hamiltonian : `PauliRegisterSequence` Returns: `TrotterStep`	Second-order (symmetric) Trotter decomposition. Forward pass at half-angle followed by reverse pass at half-angle. The resulting step is palindromic. dt : `float` hamiltonian : `PauliRegisterSequence` Returns: `TrotterStep`
`trotterCnotCount step` Full Usage: `trotterCnotCount step` Parameters: step : `TrotterStep` Returns: `int`	Quick CNOT count from Pauli weights (no gate decomposition needed). Each weight-w rotation contributes 2(w−1) CNOTs. step : `TrotterStep` Returns: `int`
`trotterStepStats step` Full Usage: `trotterStepStats step` Parameters: step : `TrotterStep` Returns: `CircuitStats`	Compute full circuit resource statistics for a Trotter step. step : `TrotterStep` Returns: `CircuitStats`
`trotterize order` Full Usage: `trotterize order` Parameters: order : `TrotterOrder` Returns: `float -> PauliRegisterSequence -> TrotterStep`	Trotter decomposition dispatching on order. order : `TrotterOrder` Returns: `float -> PauliRegisterSequence -> TrotterStep`