PauliRegister (Encodings)

PauliRegister Type

Namespace: Encodings
Assembly: Encodings.dll
Parent Module: PauliRegister
Base Type: obj

Represents a tensor product of single-qubit Pauli operators with a complex coefficient.

A PauliRegister of size n represents an operator on n qubits:

   coefficient

where each Pᵢ ∈ {I, X, Y, Z} is a single-qubit Pauli operator.

Examples:

"XII" with coefficient 1.0 = X₀ ⊗ I₁ ⊗ I₂
"ZZ" with coefficient -0.5 = -0.5 · (Z₀ ⊗ Z₁)

Constructors

Constructor	Description
`PauliRegister(ops, coefficient)` Full Usage: `PauliRegister(ops, coefficient)` Parameters: ops : `Pauli seq` - Sequence of Pauli operators. coefficient : `Complex` - The complex coefficient for this term. Returns: `PauliRegister`	Creates a PauliRegister from a sequence of Pauli operators. ops : `Pauli seq` Sequence of Pauli operators. coefficient : `Complex` The complex coefficient for this term. Returns: `PauliRegister`
`PauliRegister(ops, coefficient)` Full Usage: `PauliRegister(ops, coefficient)` Parameters: ops : `Pauli list` - List of Pauli operators [P₀; P₁; ...; Pₙ₋₁]. coefficient : `Complex` - The complex coefficient for this term. Returns: `PauliRegister`	Creates a PauliRegister from a list of Pauli operators. ops : `Pauli list` List of Pauli operators [P₀; P₁; ...; Pₙ₋₁]. coefficient : `Complex` The complex coefficient for this term. Returns: `PauliRegister`
`PauliRegister(ops, coefficient)` Full Usage: `PauliRegister(ops, coefficient)` Parameters: ops : `string` - A string like "XYZII" where each character is I, X, Y, or Z. coefficient : `Complex` - The complex coefficient for this term. Returns: `PauliRegister`	Creates a PauliRegister from a string of Pauli characters. ops : `string` A string like "XYZII" where each character is I, X, Y, or Z. coefficient : `Complex` The complex coefficient for this term. Returns: `PauliRegister` Example `let reg = PauliRegister("XZI", Complex.One) // X₀ ⊗ Z₁ ⊗ I₂` val reg: obj
`PauliRegister(n, ?coefficient)` Full Usage: `PauliRegister(n, ?coefficient)` Parameters: n : `uint32` - The number of qubits (register size). ?coefficient : `Complex` - Optional complex coefficient (default: 1.0). Returns: `PauliRegister`	Creates a new PauliRegister with all identity operators. n : `uint32` The number of qubits (register size). ?coefficient : `Complex` Optional complex coefficient (default: 1.0). Returns: `PauliRegister`

Instance members

Instance member	Description
`this.Coefficient` Full Usage: `this.Coefficient` Returns: `Complex`	Gets the complex coefficient of this Pauli term. Returns: `Complex`
`this[i]` Full Usage: `this[i]` Parameters: i : `int` - The zero-based qubit index. Returns: `Pauli option` Some Pauli if index is valid; None otherwise.	Gets the Pauli operator at the given qubit index. i : `int` The zero-based qubit index. Returns: `Pauli option` Some Pauli if index is valid; None otherwise.
`this.PhaseConjunction` Full Usage: `this.PhaseConjunction` Returns: `string`	Gets a formatted conjunction string for combining terms in a sum. Used when building sum expressions like "X + iY - Z". Returns: `string`
`this.PhasePrefix` Full Usage: `this.PhasePrefix` Returns: `string`	Gets a formatted string prefix representing the coefficient phase. Used for display purposes, e.g., "+", "-", "+i", "-i". Returns: `string`
`this.ResetPhase` Full Usage: `this.ResetPhase` Parameters: p : `Complex` - The new complex coefficient. Returns: `PauliRegister` A new PauliRegister with the same operators but different coefficient.	Creates a copy of this register with a new coefficient. p : `Complex` The new complex coefficient. Returns: `PauliRegister` A new PauliRegister with the same operators but different coefficient.
`this.Signature` Full Usage: `this.Signature` Returns: `string` A string like "XYZII" representing the tensor product structure.	Gets the signature string of this register (operators without coefficient). The signature uniquely identifies the Pauli structure and is used as a dictionary key when combining like terms in a PauliRegisterSequence. Returns: `string` A string like "XYZII" representing the tensor product structure.
`this.WithOperatorAt` Full Usage: `this.WithOperatorAt` Parameters: i : `int` - The zero-based qubit index to modify. op : `Pauli` - The new Pauli operator to place at index i. Returns: `PauliRegister` A new PauliRegister with the updated operator.	Returns a new PauliRegister with the operator at index i replaced. This operation is immutable - it returns a new register without modifying the original. i : `int` The zero-based qubit index to modify. op : `Pauli` The new Pauli operator to place at index i. Returns: `PauliRegister` A new PauliRegister with the updated operator.

Static members

Static member Description

Static member	Description
`l * r` Full Usage: `l * r` Parameters: l : `PauliRegister` - The left PauliRegister. r : `PauliRegister` - The right PauliRegister. Returns: `PauliRegister` A new PauliRegister representing the product, with coefficients and phases properly combined.	Multiplies two PauliRegisters component-wise. Multiplication is performed qubit-by-qubit in O(n) time: `(c = (c` where φ is the accumulated phase from all the individual Pauli multiplications. If registers have different sizes, missing qubits are treated as identity. l : `PauliRegister` The left PauliRegister. r : `PauliRegister` The right PauliRegister. Returns: `PauliRegister` A new PauliRegister representing the product, with coefficients and phases properly combined.

Full Usage: l * r

Parameters:

l : PauliRegister - The left PauliRegister.

r : PauliRegister - The right PauliRegister.

Returns: PauliRegister A new PauliRegister representing the product, with coefficients and phases properly combined.

Multiplies two PauliRegisters component-wise.

Multiplication is performed qubit-by-qubit in O(n) time:

   (c
   = (c

where φ is the accumulated phase from all the individual Pauli multiplications. If registers have different sizes, missing qubits are treated as identity.

l : PauliRegister: The left PauliRegister.
r : PauliRegister: The right PauliRegister.

Returns: PauliRegister: A new PauliRegister representing the product, with coefficients and phases properly combined.