mimiqcircuits.operations.gates.generalized.rpauli¶

Pauli rotation gate (RPauli).

Classes

RPauli(pauli, theta)

Apply a Pauli string rotation gate of the form:

class mimiqcircuits.operations.gates.generalized.rpauli.RPauli(pauli, theta)[source]¶

Bases: Gate

Apply a Pauli string rotation gate of the form:

\[e^{-i \frac{\theta}{2} (P_1 \otimes P_2 \otimes \dots)}\]

where each \(P_i\) is a Pauli operator from "I", "X", "Y", or "Z", acting on a separate qubit.

This gate represents the time evolution under a tensor product of Pauli operators, which is useful for simulating Hamiltonian dynamics, variational ansätze, and Trotter steps.

Identity-only strings or zero rotation angles are optimized away as no-ops.

Parameters:

pauli (PauliString) – A tensor product of Pauli operators such as "X", "ZIZ", or "IXY".
theta (float or symengine.Basic) – The rotation angle.

Note

The operator acts on all qubits where the Pauli string is non-identity. It decomposes into native gates including Hadamards, RZs, and CNOTs.

Examples:

>>> from mimiqcircuits import *
>>> from symengine import pi
>>> RPauli(PauliString("X"), pi/2)
R("X", (1/2)*pi)

>>> RPauli(PauliString("ZIZ"), 2.0)
R("ZIZ", 2.0)

>>> c = Circuit()
>>> c.push(RPauli(PauliString("YXI"), 2.0), 1, 2, 3)
4-qubit circuit with 1 instruction:
└── R("YXI", 2.0) @ q[1:3]

>>> c.push(RPauli(PauliString("III"), pi), 1, 2, 3)
4-qubit circuit with 2 instructions:
├── R("YXI", 2.0) @ q[1:3]
└── R("III", pi) @ q[1:3]

>>> c.push(RPauli(PauliString("IXY"), pi), 1, 2, 3)
4-qubit circuit with 3 instructions:
├── R("YXI", 2.0) @ q[1:3]
├── R("III", pi) @ q[1:3]
└── R("IXY", pi) @ q[1:3]