The stabilizer group generated by a set of generators is the set of all elements that can be obtained by multiplying the generators together in any order and any number of times.

The generators given are {XZZXI, IXZZX, XIXZZ, ZXIXZ}.

Each of these generators is a 5-qubit Pauli operator. The Pauli group on n qubits is a group of size 4^n, and the stabilizer group of a state is a subgroup of the Pauli group.

In this case, n=5, so the Pauli group has size 4^5 = 1024.

The size of the stabilizer group is 2^n = 2^5 = 32.

This is because each generator can be either included or not included in the multiplication, giving 2 choices for each of 5 generators.

So, the stabilizer group generated by the set of generators {XZZXI, IXZZX, XIXZZ, ZXIXZ} has 32 elements.

Question

The stabilizer group generated by a set of generators is the set of all elements that can be obtained by multiplying the generators together in any order and any number of times.

The generators given are {XZZXI, IXZZX, XIXZZ, ZXIXZ}.

Each of these generators is a 5-qubit Pauli operator. The Pauli group on n qubits is a group of size 4^n, and the stabilizer group of a state is a subgroup of the Pauli group.

In this case, n=5, so the Pauli group has size 4^5 = 1024.

The size of the stabilizer group is 2^n = 2^5 = 32.

This is because each generator can be either included or not included in the multiplication, giving 2 choices for each of 5 generators.

So, the stabilizer group generated by the set of generators {XZZXI, IXZZX, XIXZZ, ZXIXZ} has 32 elements.

Knowee AI · Accepted Answer

The stabilizer group generated by a set of generators is the set of all elements that can be obtained by multiplying the generators together in any order and any number of times.

The generators given are {XZZXI, IXZZX, XIXZZ, ZXIXZ}.

Each of these generators is a 5-qubit Pauli operator. The Pauli group on n qubits is a group of size 4^n, and the stabilizer group of a state is a subgroup of the Pauli group.

In this case, n=5, so the Pauli group has size 4^5 = 1024.

The size of the stabilizer group is 2^n = 2^5 = 32.

This is because each generator can be either included or not included in the multiplication, giving 2 choices for each of 5 generators.

So, the stabilizer group generated by the set of generators {XZZXI, IXZZX, XIXZZ, ZXIXZ} has 32 elements.

How many elements are in the stabilizer group generated by the following set of generators?{XZZXI,IXZZX,XIXZZ,ZXIXZ}{𝑋𝑍𝑍𝑋𝐼,𝐼𝑋𝑍𝑍𝑋,𝑋𝐼𝑋𝑍𝑍,𝑍𝑋𝐼𝑋𝑍}

Question

Solution

Similar Questions

Upgrade your grade with Knowee