How to implement the -I matrix using Pauli gates

Question

I'm trying to build a quantum walk circuit. I have the C0 matrix as follows

import numpy as np

C0 = np.array([[-1, 0], [0, -1]])

As we can see, it's the (-)Identity matrix. How to build the -I matrix using quantum gates?

OPENQASM 2.0;
include "qelib1.inc";
gate unitary139793144506800 p0 {
    u3(0,pi,pi) p0;
}
qreg q[2];
unitary139793144506800 q[0];
unitary139793144506800 q[1];

I obtained the above using qiskit unitary. Is there a way to decompose this into Pauli gates?

Answer 1

If you add $-I$ gate, a $I$ gate or nothing, it is not going to make any difference because it is just a global phase. However if you still insist to get one, here it's the decomposition of $-I$ using Pauli's anticommutativity ($XY-YX=iZ$): $$(XY)^2=XYXY=-I$$