# Tag Info

1 vote

### How can I produce the state $\frac{1}{\sqrt{2}^N} (|1,0^{N-1}\rangle + |01,0^{N-2}\rangle + ...+|0^{N-1},1\rangle)$

It is not possible to construct the above state using the specified gates. States that can be prepared using these gates are called stabilizer states. To quote this stack exchange post, "for a ...
• 111

### How to shift the eigenvalues of a quantum Hermitian operator G to ±r?

Consider a gate $\mathcal{G}(\mu)=e^{-i \mu G}$ generated by a Hermitian operator G. If G has just two distinct eigenvalues(which can be repeated) we can, without loss of generality, shift the ...
• 606
1 vote

### How to shift the eigenvalues of a quantum Hermitian operator G to ±r?

Say the eigenvalues of $G$ are $\lambda_1, \lambda_2$ with $\lambda_1 \neq \lambda_2$. Writing the $2\times 2$ Hermitian matrix $G$ in its eigenbasis (we can pick any basis, since unitary ...
• 5,610
1 vote

### How can I implement an n-bit Toffoli gate?

EDIT: You can simply use mct gate: https://qiskit.org/documentation/stubs/qiskit.circuit.QuantumCircuit.mct.html As of Qiskit 'qiskit': '0.19.6', this process is ...
1 vote

• 51.1k
1 vote

### Minimum number of 2-qubit gates required to implement a Toffoli gate

There are some techniques to decompose Toffoli gate. Here I mention two useful techniques. Toffoli gate can be decomposed into six CNOTs (two qubit gate) gates with transpile technique of Qiskit and ...
• 11