Tapering (Encodings)

Tapering Module

Namespace: Encodings
Assembly: Encodings.dll

Symbolic qubit tapering utilities for Pauli Hamiltonians.

v1: diagonal Z2 tapering (single-qubit Z generators).

v2: general Z₂ symmetry detection via symplectic representation, independent generator selection over GF(2), Clifford rotation synthesis, and a unified tapering pipeline.

Types

Type	Description
CliffordGate	Elementary Clifford gate for tapering rotation.
SymplecticVector	Binary (GF(2)) symplectic vector representing an n-qubit Pauli string. Layout: [x₀ x₁ … xₙ₋₁ \| z₀ z₁ … zₙ₋₁] where I=(0,0), X=(1,0), Y=(1,1), Z=(0,1).
TaperingMethod	Tapering method selection.
TaperingOptions	Options for the unified tapering pipeline.
TaperingResult	Result of the unified tapering pipeline (extends v1 result).
Z2TaperingResult	Result of a Z2 tapering operation.

Functions and values

Function or value	Description
`applyClifford gates hamiltonian` Full Usage: `applyClifford gates hamiltonian` Parameters: gates : `CliffordGate list` hamiltonian : `PauliRegisterSequence` Returns: `PauliRegisterSequence`	Apply a sequence of Clifford gates to a PauliRegisterSequence. Uses the symplectic representation for exact conjugation. gates : `CliffordGate list` hamiltonian : `PauliRegisterSequence` Returns: `PauliRegisterSequence`
`applyGatesToSymplectic gates sv` Full Usage: `applyGatesToSymplectic gates sv` Parameters: gates : `CliffordGate list` sv : `SymplecticVector` Returns: `SymplecticVector`	Apply a sequence of Clifford gates to a symplectic vector. gates : `CliffordGate list` sv : `SymplecticVector` Returns: `SymplecticVector`
`commutes a b` Full Usage: `commutes a b` Parameters: a : `SymplecticVector` b : `SymplecticVector` Returns: `bool`	Returns true if two Pauli strings commute (symplectic inner product = 0 mod 2). a : `SymplecticVector` b : `SymplecticVector` Returns: `bool`
`defaultTaperingOptions` Full Usage: `defaultTaperingOptions` Returns: `TaperingOptions`	Defaults: +1 sector, no cap, full Clifford. Returns: `TaperingOptions`
`diagonalZ2Generators hamiltonian` Full Usage: `diagonalZ2Generators hamiltonian` Parameters: hamiltonian : `PauliRegisterSequence` Returns: `PauliRegister[]`	Returns single-qubit Z generators for all detected diagonal Z2 symmetries. hamiltonian : `PauliRegisterSequence` Returns: `PauliRegister[]`
`diagonalZ2SymmetryQubits hamiltonian` Full Usage: `diagonalZ2SymmetryQubits hamiltonian` Parameters: hamiltonian : `PauliRegisterSequence` Returns: `int[]`	Detects qubit indices i such that all terms are diagonal (I or Z) on qubit i. hamiltonian : `PauliRegisterSequence` Returns: `int[]`
`findCommutingGenerators hamiltonian` Full Usage: `findCommutingGenerators hamiltonian` Parameters: hamiltonian : `PauliRegisterSequence` Returns: `SymplecticVector[]`	Find all Pauli strings (as symplectic vectors) that commute with every term in the Hamiltonian. This is the commutant / symmetry group. hamiltonian : `PauliRegisterSequence` Returns: `SymplecticVector[]`
`fromSymplectic sv` Full Usage: `fromSymplectic sv` Parameters: sv : `SymplecticVector` Returns: `PauliRegister`	Convert a symplectic vector back to a PauliRegister with coefficient +1. sv : `SymplecticVector` Returns: `PauliRegister`
`independentGenerators generators` Full Usage: `independentGenerators generators` Parameters: generators : `SymplecticVector[]` Returns: `SymplecticVector[]`	Select a maximal linearly independent subset of symplectic vectors over GF(2). generators : `SymplecticVector[]` Returns: `SymplecticVector[]`
`symplecticInnerProduct a b` Full Usage: `symplecticInnerProduct a b` Parameters: a : `SymplecticVector` b : `SymplecticVector` Returns: `bool`	Symplectic inner product mod 2: returns true if the two Pauli strings anti-commute. Two n-qubit Paulis commute iff ⟨a, b⟩_s = Σᵢ (aₓᵢ bᵤᵢ ⊕ aᵤᵢ bₓᵢ) = 0 (mod 2). a : `SymplecticVector` b : `SymplecticVector` Returns: `bool`
`synthesizeTaperingClifford generators` Full Usage: `synthesizeTaperingClifford generators` Parameters: generators : `SymplecticVector[]` Returns: `CliffordGate list * int[]`	Synthesize a Clifford circuit that rotates a set of independent generators each onto a single-qubit Z operator. Returns the gate list and target qubit indices (one per generator). generators : `SymplecticVector[]` Returns: `CliffordGate list * int[]`
`taper options hamiltonian` Full Usage: `taper options hamiltonian` Parameters: options : `TaperingOptions` hamiltonian : `PauliRegisterSequence` Returns: `TaperingResult`	Unified tapering pipeline: detect Z₂ symmetries, synthesize Clifford rotation, apply it, then taper the rotated Hamiltonian diagonally. options : `TaperingOptions` hamiltonian : `PauliRegisterSequence` Returns: `TaperingResult`
`taperAllDiagonalZ2WithPositiveSector hamiltonian` Full Usage: `taperAllDiagonalZ2WithPositiveSector hamiltonian` Parameters: hamiltonian : `PauliRegisterSequence` Returns: `Z2TaperingResult`	Convenience helper: taper all detected diagonal Z2 symmetries in the +1 sector. hamiltonian : `PauliRegisterSequence` Returns: `Z2TaperingResult`
`taperDiagonalZ2 sector hamiltonian` Full Usage: `taperDiagonalZ2 sector hamiltonian` Parameters: sector : `(int * int) list` - List of (qubitIndex, eigenvalue) pairs with eigenvalue in {+1,-1}. hamiltonian : `PauliRegisterSequence` - Input Hamiltonian as a Pauli sum. Returns: `Z2TaperingResult`	Tapers a Hamiltonian by fixing diagonal Z2 symmetry sectors and removing those qubits. sector : `(int * int) list` List of (qubitIndex, eigenvalue) pairs with eigenvalue in {+1,-1}. hamiltonian : `PauliRegisterSequence` Input Hamiltonian as a Pauli sum. Returns: `Z2TaperingResult`
`toSymplectic r` Full Usage: `toSymplectic r` Parameters: r : `PauliRegister` Returns: `SymplecticVector`	Convert a PauliRegister to its symplectic binary representation. Coefficient/phase is discarded — only the Pauli structure matters. r : `PauliRegister` Returns: `SymplecticVector`
`z2SymmetryCount hamiltonian` Full Usage: `z2SymmetryCount hamiltonian` Parameters: hamiltonian : `PauliRegisterSequence` Returns: `int`	Count the number of independent Z₂ symmetries of the Hamiltonian. This equals the maximum number of qubits that can be tapered. hamiltonian : `PauliRegisterSequence` Returns: `int`