4. Quantum Operators¶

4.1. `cudaq::spin_op`¶

[1] CUDA-Q provides a native spin_op data type in the cudaq namespace for the expression of quantum mechanical spin operators.

[2] The spin_op provides an abstraction for a general tensor product of Pauli spin operators, and sums thereof:

\[H = \sum_{i=0}^M P_i, P_i = \prod_{j=0}^N \sigma_j^a\]

for \(a = {x,y,z}\), \(j\) the qubit index, and \(N\) the number of qubits.

[3] The spin_op exposes common C++ operator overloads for algebraic expressions.

[4] CUDA-Q defines static functions to create the primitive X, Y, and Z Pauli operators on specified qubit indices which can subsequently be used in algebraic expressions to build up more complicated Pauli tensor products and their sums.

C++

auto h = 5.907 - 2.1433 * cudaq::spin_op::x(0) * cudaq::spin_op::x(1) - \
         2.1433 * cudaq::spin_op::y(0) * cudaq::spin_op::y(1) + \
         .21829 * cudaq::spin_op::z(0) - 6.125 * cudaq::spin_op::z(1);

Python

from cudaq import spin
h = 5.907 - 2.1433 * spin.x(0) * spin.x(1) - 2.1433 * spin.y(0) * spin.y(1) + \
         .21829 * spin.z(0) - 6.125 * spin.z(1)

[5] The spin_op also provides a mechanism for the expression of circuit synthesis tasks within quantum kernel code. Specifically, operations that encode \(N\)^thorder trotterization of exponentiated spin_op rotations, e.g. \(U = \exp(-i H t)\), where \(H\) is the provided spin_op. Currently, H is limited to a single product term.

[6] The spin_op can be created within classical host code and quantum kernel code, and can also be passed by value to quantum kernel code from host code.

4. Quantum Operators¶

4.1. cudaq::spin_op¶

4.1. `cudaq::spin_op`¶