Questions tagged [quantum-gate]

For questions regarding usage, performance, implementation, application or theory related to quantum gates.

1,078 questions
Filter by
Sorted by
Tagged with
43 views

Find a circuit implementing a 3-qubit unitary matrix preparing $|b\rangle\simeq(0,c,c,c,c,c,c,0)$ with $c=1/\sqrt6$

I am trying to find a circuit to represent a 3 Qubit unitary matrix such that $U|0\rangle = |b\rangle$ for $b = \left[0~c~c~c~c~c~c~0\right]$, where $c = 1/\sqrt{6}$. Although I am working in Qiskit, ...
23 views

Parameterized swap test and perfect swap test

Suppose one has parameterized a swap test by using an ansatz $U(\theta) = \exp(-i\theta \text{ CSWAP})$, and one tries to find an angle $\theta$ such that one can distinguish given two quantum states ...
29 views

541 views

Quantum Fourier Transform without SWAPs

The Quantum Fourier Transform from Nielsen and Chuang chapter 5 is pictured here: In the textbook the author refers to "swap gates at the end of the circuit which reverse the order of the qubits". ...
855 views

What is the mathematical justification for the "universality" of the universal set of quantum gates (CNOT, H, Z, X and π/8)?

In this answer I mentioned that the CNOT, H, X, Z and $\pi/8$ gates form a universal set of gates, which given in sufficient number of gates can get arbitrarily close to replicating any unitary ...
110 views

Do quantum gates rotate a qubit around the Bloch sphere, or do quantum gates rotate the Bloch sphere around a qubit?

Do quantum gates rotate a qubit around the Bloch sphere? Or do quantum gates rotate the Bloch sphere around a qubit? "The simplest quantum gates are the Paulis: X, Y, and Z. Their action is to ...
390 views

Is a quantum circuit with a controlled-T gate possible?

This diagram comes from the textbook, Quantum information (Author: Stephen Barnett), fig. 6.13. The problem is what I know that T gate isn't a multi-qubit gate, so is it possible that T gate becomes ...
68 views

Show that the effect of a Controlled Unitary on qubits followed by a measurement is unchanged depending on when measurement is taken

I understand that a Controlled Unitary is just a generalization of a control gate, such as CNOT etc, and that it is given in state representation as \hat C_U = |0\rangle\langle0|\otimes\mathbb{I} + |...
49 views

555 views

Understanding quantum circuit diagrams: a circuit that compares two states $|YX\rangle$ and $|AB\rangle$

I have a quantum circuit which I would like to understand, which compares two standard basis states $|YX\rangle$ and $|AB\rangle$. It operates on the corresponding bits in each of the two states: i.e.,...
62 views

Implication of SWAP being not positive in terms of quantum channel

I am going over chapter 3 of Preskill's lecture notes regarding complete positivity. Specifically, on page 19, it is mentioned that since SWAP has eigenstates with eigenvalue -1, it is not positive, ...
566 views