I am trying to implement a density matrix simulator of a quantum computer. The quantum gates that act of the qubit density matrix state do so in an embarrassingly parallel fashion. More precisely:
A single qubit gate operation on the density matrix of size 2^N by 2^N, where N is the number of qubits, can be computed through doing a 2 by 2 matric multiplication on the elements of 2^(2N  2) different slices. The elements of one slice are unique to that slice. There is no sharing between slices.
I wish to use rayons parallel for_each function to iterate over the unique elements in parallel. The density_matrix (an nalgebra matrix) can be Gigabytes in size. Therefore, copying the data is impractical.
The code I have so far is:
fn single_qubit_gate(state: &mut State, qubit: &Qubit, u: Matrix2x2) {
debug!("density matrix before:\n{}", state.density_matrix);
let mut density_matrix = Arc::new( &state.density_matrix);
(0..1 << state.number_of_qubits)
.into_par_iter()
.step_by(2)
.for_each(i_offset:usize {
let swap_qubits: Box<dyn Fn(usize) > Qubit> = match qubit {
0 => Box::new(x: usize x),
_ => Box::new(x: usize swap_two_qubits(x, (&qubit, &0))),
};
let mut rho = Matrix2x2::zeros();
(0..(1 << state.number_of_qubits))
.step_by(2)
.for_each(j_offset {
for (i, j) in iproduct!(0..2, 0..2) {
rho[(i, j)] = density_matrix[(swap_qubits(i_offset + i), swap_qubits(j_offset + j))];
}
rho = u * rho * u.adjoint();
for (i, j) in iproduct!(0..2, 0..2) {
density_matrix[(swap_qubits(i_offset + i), swap_qubits(j_offset + j))] = rho[(i, j)]
}
});
});
However, this errors with the stack trace:
error[E0596]: cannot borrow data in an `Arc` as mutable
> src/gates.rs:85:25

85  density_matrix[(swap_qubits(i_offset + i), swap_qubits(j_offset + j))] = rho[(i, j)]
 ^^^^^^^^^^^^^^ cannot borrow as mutable

= help: trait `DerefMut` is required to modify through a dereference, but it is not implemented for `Arc<&Matrix<Complex<f64>, Dynamic, Dynamic, VecStorage<Complex<f64>, Dynamic, Dynamic>>>`
I would really appreciate a pointer in the right direction, using the Arc was rather my final hope.