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observables

eigenkit.core.observables

Functions and classes that make observables easy to write.

There are three ways to choose what a circuit measures:

# Pauli algebra
observable = Z(0) * X(1) + 0.5 * Y(2)

# class methods, or a string
observable = Observable.from_string("Z0 X1 + 0.5 Y2")
observable = Observable.z(0)

# no observable at all: by default, Circuit measures Z on every qubit

PauliExpr is a simple builder. It collects terms, each made of a coefficient and a tensor product of Pauli operators, and it converts them to an Observable when needed. A product of two operators on the same qubit is simplified when the two operators are equal (P * P = I). A product of different Pauli operators on the same qubit (X * Y = iZ and so on) needs complex arithmetic and is not supported.

PauliExpr

A sum of terms, each a coefficient times a product of Pauli operators.

In each term, the Pauli operators act on distinct qubits, so the product is a tensor product.

constant property

The coefficient of the identity term, or 0.0 when there is none.

__init__(terms)

Build an expression from raw terms.

Parameters:

Name Type Description Default
terms Iterable[_Term]

Internal records of the terms. Prefer the X, Y and Z functions and ordinary arithmetic, such as 0.5 * Z(0) + X(1). They build the same expression without creating these records directly.

 required

single(operator, qubit, coeff=1.0) classmethod

Return coeff times a single Pauli operator on qubit.

Parameters:

Name Type Description Default
operator str

The Pauli operator: "X", "Y" or "Z".

 required
qubit int

The index of the qubit.

 required
coeff float

The coefficient. Default: 1.0.

 1.0

Returns:

Type Description
'PauliExpr'

The expression, which has a single term.

to_observable()

Convert the expression to an Observable.

The terms with the same Pauli string are combined, and the terms whose coefficient is 0 (at most 1e-15 in magnitude) are dropped.

An Observable holds only Pauli terms, so a non-zero identity term raises an error. Such a term comes from a scalar offset, or from P * P = I. Dropping it without an error would shift every expectation value. To measure such an expression, measure expr - expr.constant and add expr.constant to the result. The chemistry entry points take this constant as offset.

Returns:

Type Description
Observable

The observable.

Raises:

Type Description
ValueError

If the expression has a constant term that is not 0, or if no term that can be measured is left.

X(qubit)

Return Pauli X on qubit, as an expression that can be added and scaled.

Parameters:

Name Type Description Default
qubit int

The index of the qubit.

 required

Returns:

Type Description
PauliExpr

The expression.

Y(qubit)

Return Pauli Y on qubit, as an expression that can be added and scaled.

Parameters:

Name Type Description Default
qubit int

The index of the qubit.

 required

Returns:

Type Description
PauliExpr

The expression.

Z(qubit)

Return Pauli Z on qubit, as an expression that can be added and scaled.

Parameters:

Name Type Description Default
qubit int

The index of the qubit.

 required

Returns:

Type Description
PauliExpr

The expression.

all_z(n_qubits)

Return one Z observable for each qubit.

This is useful as a default measurement.

Parameters:

Name Type Description Default
n_qubits int

The number of qubits of the circuit.

 required

Returns:

Type Description
list[Observable]

One Observable for each qubit.

from_string(text)

Parse an observable from a string.

This function is a shortcut for Observable.from_string.

Parameters:

Name Type Description Default
text str

The string to parse.

 required

Returns:

Type Description
Observable

The parsed observable.