PauliBasisChange
class qiskit.opflow.converters.PauliBasisChange(destination_basis=None, traverse=True, replacement_fn=None)
Bases: ConverterBase
Deprecated: 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 changeofbasis CircuitOps
and destination PauliOps
. Several convenient outofthebox replacement functions have been added as static methods, such as measurement_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: 9781107002173), which involves diagonalizing the singlequbit Paulis with H and S† gates, mapping the eigenvectors of the diagonalized origin Pauli to the diagonalized destination Pauli using CNOTS, and then dediagonalizing any single qubit Paulis to their nondiagonal destination values. Many other methods are possible, as well as variations on this method, such as the placement of the CNOT chains.
The class qiskit.opflow.converters.pauli_basis_change.PauliBasisChange
is deprecated as of qiskitterra 0.24.0. It will be removed no earlier than 3 months after the release date. For code migration guidelines, visit https://qisk.it/opflow_migration.
Parameters

destination_basis (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 subOperators, such as ListOp, traverse the Operator and apply the conversion to every applicable suboperator within it.

replacement_fn (Callable  None) –
A function specifying what to do with the basischange
CircuitOp
and destinationPauliOp
when converting an Operator and replacing converted values. By default, this will be For 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 nonStateFn 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.
Attributes
destination
The destination PauliOp
, or None
if using the default destination, the diagonal basis.
Methods
construct_cnot_chain
construct_cnot_chain(diag_pauli_op1, diag_pauli_op2)
Construct a CircuitOp
(or PauliOp
if equal to the identity) which takes the eigenvectors of diag_pauli_op1
to the eigenvectors of diag_pauli_op2
, assuming both are diagonal (or performing this operation on their diagonalized Paulis implicitly if not). This works by the insight that the eigenvalue of a diagonal Pauli’s eigenvector is equal to or 1 if the parity is 1 and 1 if the parity is 0, or 1  (2 * parity). Therefore, using CNOTs, we can write the parity of diag_pauli_op1’s significant bits onto some qubit, and then write out that parity onto diag_pauli_op2’s significant bits.
Parameters
Returns
The PrimitiveOp
performs the mapping.
Return type
convert
convert(operator)
Given a PauliOp
, or an Operator containing PauliOps
if _traverse
is True, converts each Pauli into the basis specified by self._destination and a basischangecircuit, calls replacement_fn
with these two Operators, and replaces the PauliOps
with the output of replacement_fn
. For example, for the builtin operator_replacement_fn
below, each PauliOp p will be replaced by the composition of the basischange Clifford CircuitOp
c with the destination PauliOp d and c†, such that p = c·d·c†, up to global phase.
Parameters
operator (OperatorBase) – The Operator to convert.
Returns
The converted Operator.
Return type
get_cob_circuit
get_cob_circuit(origin)
Construct an Operator which maps the +1 and 1 eigenvectors of the origin Pauli to the +1 and 1 eigenvectors of the destination Pauli. It does so by
 converting any i+⟩ or i+⟩ eigenvector bits in the origin to +⟩ and ⟩ with S†s, then
 converting any +⟩ or +⟩ eigenvector bits in the converted origin to 0⟩ and 1⟩ with Hs, then
 writing the parity of the significant (Zmeasured, rather than I) bits in the origin to a single “origin anchor bit,” using cnots, which will hold the parity of these bits,
 swapping the parity of the pauli anchor bit into a destination anchor bit using a swap gate (only if they are different, if there are any bits which are significant in both origin and dest, we set both anchors to one of these bits to avoid a swap).
 writing the parity of the destination anchor bit into the other significant bits of the destination,
 converting the 0⟩ and 1⟩ significant eigenvector bits to +⟩ and ⟩ eigenvector bits in the destination where the destination demands it (e.g. pauli.x == true for a bit), using Hs 8) converting the +⟩ and ⟩ significant eigenvector bits to i+⟩ and i⟩ eigenvector bits in the destination where the destination demands it (e.g. pauli.x == true and pauli.z == true for a bit), using Ss
Parameters
origin (Pauli PauliOp) – The Pauli
or PauliOp
to map.
Returns
A tuple of a PrimitiveOp
which equals the basis change mapping and a PauliOp
which equals the destination basis.
Raises
 TypeError – Attempting to convert from nonPauli origin.
 ValueError – Attempting to change a nonidentity Pauli to an identity Pauli, or vice versa.
Return type
get_diagonal_pauli_op
get_diagonal_pauli_op(pauli_op)
Get the diagonal PualiOp
to which pauli_op
could be rotated with only singlequbit operations.
Parameters
pauli_op (PauliOp) – The PauliOp
whose diagonal to compute.
Returns
The diagonal PauliOp
.
Return type
get_diagonalizing_clifford
get_diagonalizing_clifford(pauli)
Construct a CircuitOp
with only singlequbit gates which takes the eigenvectors of pauli
to eigenvectors composed only of 0⟩ and 1⟩ tensor products. Equivalently, finds the basischange circuit to take pauli
to a diagonal PauliOp
composed only of Z and I tensor products.
Note, underlying Pauli bits are in Qiskit endianness, so we need to reverse before we begin composing with Operator flow.
Parameters
pauli (Pauli PauliOp) – the Pauli
or PauliOp
to whose diagonalizing circuit to compute.
Returns
The diagonalizing CircuitOp
.
Return type
get_tpb_pauli
get_tpb_pauli(list_op)
Gets the Pauli (not PauliOp
!) whose diagonalizing singlequbit rotations is a superset of the diagonalizing singlequbit rotations for each of the Paulis in list_op
. TPB stands for Tensor Product Basis.
Parameters
list_op (ListOp) – the ListOp
whose TPB Pauli to return.
Returns
The TBP Pauli.
Return type
measurement_replacement_fn
static measurement_replacement_fn(cob_instr_op, dest_pauli_op)
A builtin convenience replacement function which produces measurements isomorphic to an OperatorStateFn
measurement holding the origin PauliOp
.
Parameters
 cob_instr_op (PrimitiveOp) – The basischange
CircuitOp
.  dest_pauli_op (PauliOp PauliSumOp ListOp) – The destination Pauli type operator.
Returns
The ~StateFn @ CircuitOp
composition equivalent to a measurement by the original PauliOp
.
Return type
operator_replacement_fn
static operator_replacement_fn(cob_instr_op, dest_pauli_op)
A builtin convenience replacement function which produces Operators isomorphic to the origin PauliOp
.
Parameters
 cob_instr_op (PrimitiveOp) – The basischange
CircuitOp
.  dest_pauli_op (PauliOp PauliSumOp ListOp) – The destination
PauliOp
.
Returns
The ~CircuitOp @ PauliOp @ CircuitOp
composition isomorphic to the original PauliOp
.
Return type
pad_paulis_to_equal_length
pad_paulis_to_equal_length(pauli_op1, pauli_op2)
If pauli_op1
and pauli_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. Padding is applied to the end of the Paulis. Note that the Terra represents Paulis in bigendian order, so this will appear as padding to the beginning of the Pauli x and z bit arrays.
Parameters
Returns
A tuple containing the padded PauliOps.
Return type
statefn_replacement_fn
static statefn_replacement_fn(cob_instr_op, dest_pauli_op)
A builtin convenience replacement function which produces state functions isomorphic to an OperatorStateFn
state function holding the origin PauliOp
.
Parameters
 cob_instr_op (PrimitiveOp) – The basischange
CircuitOp
.  dest_pauli_op (PauliOp PauliSumOp ListOp) – The destination Pauli type operator.
Returns
The ~CircuitOp @ StateFn
composition equivalent to a state function defined by the original PauliOp
.
Return type