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qml.ftqc.ppr_to_mbqc

ppr_to_mbqc()

Specify that the MLIR compiler pass for lowering Pauli Product Rotations (PPR) and Pauli Product Measurements (PPM) to a measurement-based quantum computing (MBQC) style circuit will be applied.

This pass replaces PBC operations (pbc.ppr and pbc.ppm) with a gate-based sequence in the Quantum dialect using universal gates and measurements that are supported as MBQC gate set. For details, see the Figure 2 of Measurement-based Quantum Computation on cluster states.

Conceptually, each Pauli product is handled by:

  • Mapping its Pauli string to the Z basis via per-qubit conjugations (e.g., H for X; specialized RotXZX sequences for Y).

  • Accumulating parity onto the first qubit with a right-to-left CNOT ladder.

  • Emitting the kernel operation: - PPR: apply an RZ with an angle derived from the rotation kind. - PPM: perform a measurement and return an i1 result.

  • Uncomputing by reversing the CNOT ladder and the conjugations.

  • Conjugating the qubits back to the original basis.

Note

This pass expects PPR/PPM operations to be present. In practice, use it after to_ppr.

Parameters:

fn (QNode) – QNode to apply the pass to.

Returns:

QNode

Example

Convert a simple Clifford+T circuit to PPRs, then lower them to an MBQC-style circuit. Note that this pass should be applied before ppr_to_ppm since it requires the actual PPR/PPM operations.

import pennylane as qml
from pennylane.ftqc.decomposition import ppr_to_mbqc
from pennylane.transforms.decompositions import to_ppr

p = [("my_pipe", ["quantum-compilation-stage"])]

@qml.qjit(pipelines=p, target="mlir", keep_intermediate=True)
@ppr_to_mbqc
@to_ppr
@qml.qnode(qml.device("null.qubit", wires=2))
def circuit():
    qml.H(0)
    qml.CNOT([0, 1])
    return

print(circuit.mlir_opt)

Example MLIR excerpt (structure only):

...
%cst = arith.constant -1.5707963267948966 : f64
%cst_0 = arith.constant 1.5707963267948966 : f64
%0 = quantum.alloc( 2) : !quantum.reg
%1 = quantum.extract %0[ 0] : !quantum.reg -> !quantum.bit
%2 = quantum.extract %0[ 1] : !quantum.reg -> !quantum.bit
%out_qubits = quantum.custom "RZ"(%cst_0) %1 : !quantum.bit
%out_qubits_1 = quantum.custom "H"() %out_qubits : !quantum.bit
%out_qubits_2 = quantum.custom "RZ"(%cst_0) %out_qubits_1 : !quantum.bit
%out_qubits_3 = quantum.custom "H"() %out_qubits_2 : !quantum.bit
%out_qubits_4 = quantum.custom "RZ"(%cst_0) %out_qubits_3 : !quantum.bit
%out_qubits_5 = quantum.custom "H"() %2 : !quantum.bit
%out_qubits_6:2 = quantum.custom "CNOT"() %out_qubits_5, %out_qubits_4 : !quantum.bit, !quantum.bit
%out_qubits_7 = quantum.custom "RZ"(%cst_0) %out_qubits_6#1 : !quantum.bit
%out_qubits_8:2 = quantum.custom "CNOT"() %out_qubits_6#0, %out_qubits_7 : !quantum.bit, !quantum.bit
%out_qubits_9 = quantum.custom "H"() %out_qubits_8#0 : !quantum.bit
%out_qubits_10 = quantum.custom "RZ"(%cst) %out_qubits_8#1 : !quantum.bit
%out_qubits_11 = quantum.custom "H"() %out_qubits_9 : !quantum.bit
%out_qubits_12 = quantum.custom "RZ"(%cst) %out_qubits_11 : !quantum.bit
%out_qubits_13 = quantum.custom "H"() %out_qubits_12 : !quantum.bit
%mres, %out_qubit = quantum.measure %out_qubits_13 : i1, !quantum.bit
...
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