VariationalCircuits (Encodings)

VariationalCircuits Module

Namespace: Encodings
Assembly: Encodings.dll

Symbolic support for VQE measurement programs and QPE resource estimation.

Provides tools for grouping Hamiltonian terms into qubit-wise commuting measurement bases (reducing the number of measurement circuits needed in VQE), shot-budget estimation, and QPE circuit resource estimation using first-order Trotterization.

Types

Type	Description
MeasurementBasis	A measurement basis for simultaneous measurement of commuting Pauli terms.
MeasurementProgram	Complete measurement program for estimating ⟨H⟩.
QPEResourceEstimate	QPE resource estimate for a Hamiltonian simulation circuit.

Functions and values

Function or value	Description
`estimateShots epsilon hamiltonian` Full Usage: `estimateShots epsilon hamiltonian` Parameters: epsilon : `float` - Target precision for the energy estimate. hamiltonian : `PauliRegisterSequence` - The Hamiltonian as a sum of Pauli strings. Returns: `int` Estimated number of measurement shots (rounded up).	Estimate total measurement shots needed for precision ε on ⟨H⟩. Uses the formula: shots ≈ (Σ\|cₖ\|)² / ε², derived from the variance of the estimator for the expectation value of a sum of Pauli terms. epsilon : `float` Target precision for the energy estimate. hamiltonian : `PauliRegisterSequence` The Hamiltonian as a sum of Pauli strings. Returns: `int` Estimated number of measurement shots (rounded up).
`groupCommutingTerms hamiltonian` Full Usage: `groupCommutingTerms hamiltonian` Parameters: hamiltonian : `PauliRegisterSequence` - The Hamiltonian as a sum of Pauli strings. Returns: `MeasurementProgram` A MeasurementProgram describing the grouped bases.	Group Hamiltonian terms into qubit-wise commuting measurement bases. Uses a greedy algorithm: sort terms by \|coefficient\| descending, then assign each term to the first compatible group. This is a heuristic — optimal grouping is NP-hard in general. hamiltonian : `PauliRegisterSequence` The Hamiltonian as a sum of Pauli strings. Returns: `MeasurementProgram` A MeasurementProgram describing the grouped bases.
`qpeResources precisionBits hamiltonian dt` Full Usage: `qpeResources precisionBits hamiltonian dt` Parameters: precisionBits : `int` - Number of ancilla bits for phase readout. hamiltonian : `PauliRegisterSequence` - The Hamiltonian as a sum of Pauli strings. dt : `float` - Trotter time step size. Returns: `QPEResourceEstimate` A QPEResourceEstimate with circuit resource counts.	QPE resource estimation for a given precision and Hamiltonian. Estimates the resources for quantum phase estimation using first-order Trotterization for the controlled-U circuit. The number of controlled-U applications scales as 2^(precisionBits) - 1. precisionBits : `int` Number of ancilla bits for phase readout. hamiltonian : `PauliRegisterSequence` The Hamiltonian as a sum of Pauli strings. dt : `float` Trotter time step size. Returns: `QPEResourceEstimate` A QPEResourceEstimate with circuit resource counts.
`qubitWiseCommutes a b` Full Usage: `qubitWiseCommutes a b` Parameters: a : `PauliRegister` - First Pauli register. b : `PauliRegister` - Second Pauli register. Returns: `bool` true if the two registers qubit-wise commute.	Two Pauli operators qubit-wise commute if at each position either both are the same or at least one is I. a : `PauliRegister` First Pauli register. b : `PauliRegister` Second Pauli register. Returns: `bool` true if the two registers qubit-wise commute.