PauliBasisChange¶
- class PauliBasisChange(destination_basis=None, traverse=True, replacement_fn=None)[source]¶
Bases:
qiskit.opflow.converters.converter_base.ConverterBase
Converter for changing Paulis into other bases. By default, the diagonal basis composed only of Pauli {Z, I}^n is used as the destination basis to which to convert. Meaning, if a Pauli containing X or Y terms is passed in, which cannot be sampled or evolved natively on some Quantum hardware, the Pauli can be replaced by a composition of a change of basis circuit and a Pauli composed of only Z and I terms (diagonal), which can be evolved or sampled natively on the Quantum hardware.
The replacement function determines how the
PauliOps
should be replaced by their computed change-of-basisCircuitOps
and destinationPauliOps
. Several convenient out-of-the-box replacement functions have been added as static methods, such asmeasurement_replacement_fn
.This class uses the typical basis change method found in most Quantum Computing textbooks (such as on page 210 of Nielsen and Chuang’s, “Quantum Computation and Quantum Information”, ISBN: 978-1-107-00217-3), which involves diagonalizing the single-qubit Paulis with H and S† gates, mapping the eigenvectors of the diagonalized origin Pauli to the diagonalized destination Pauli using CNOTS, and then de-diagonalizing any single qubit Paulis to their non-diagonal destination values. Many other methods are possible, as well as variations on this method, such as the placement of the CNOT chains.
- Parameters
destination_basis (
Union
[Pauli
,PauliOp
,None
]) – The Pauli into the basis of which the operators will be converted. If None is specified, the destination basis will be the diagonal ({I, Z}^n) basis requiring only single qubit rotations.traverse (
bool
) – If true and the operator passed into convert contains sub-Operators, such as ListOp, traverse the Operator and apply the conversion to every applicable sub-operator within it.replacement_fn (
Optional
[Callable
]) –A function specifying what to do with the basis-change
CircuitOp
and destinationPauliOp
when converting an Operator and replacing converted values. By default, this will beFor StateFns (or Measurements): replacing the StateFn with ComposedOp(StateFn(d), c) where c is the conversion circuit and d is the destination Pauli, so the overall beginning and ending operators are equivalent.
For non-StateFn Operators: replacing the origin p with c·d·c†, where c is the conversion circuit and d is the destination, so the overall beginning and ending operators are equivalent.
Methods Defined Here
Construct a
CircuitOp
(orPauliOp
if equal to the identity) which takes the eigenvectors ofdiag_pauli_op1
to the eigenvectors ofdiag_pauli_op2
, assuming both are diagonal (or performing this operation on their diagonalized Paulis implicitly if not).Given a
PauliOp
, or an Operator containingPauliOps
if_traverse
is True, converts each Pauli into the basis specified by self._destination and a basis-change-circuit, callsreplacement_fn
with these two Operators, and replaces thePauliOps
with the output ofreplacement_fn
.Construct an Operator which maps the +1 and -1 eigenvectors of the origin Pauli to the +1 and -1 eigenvectors of the destination Pauli.
Get the diagonal
PualiOp
to whichpauli_op
could be rotated with only single-qubit operations.Construct a
CircuitOp
with only single-qubit gates which takes the eigenvectors ofpauli
to eigenvectors composed only of |0⟩ and |1⟩ tensor products.Gets the Pauli (not
PauliOp
!) whose diagonalizing single-qubit rotations is a superset of the diagonalizing single-qubit rotations for each of the Paulis inlist_op
.A built-in convenience replacement function which produces measurements isomorphic to an
OperatorStateFn
measurement holding the originPauliOp
.A built-in convenience replacement function which produces Operators isomorphic to the origin
PauliOp
.If
pauli_op1
andpauli_op2
do not act over the same number of qubits, pad identities to the end of the shorter of the two so they are of equal length.A built-in convenience replacement function which produces state functions isomorphic to an
OperatorStateFn
state function holding the originPauliOp
.Attributes