Skip to main content
OverflowAI is here! AI power for your Stack Overflow for Teams knowledge community. Learn more
5 votes

Is there a strategy for a single-shot identification of a Pauli gate?

Prepare a Bell pair $|00\rangle + |11\rangle$. Apply the gate to one of its qubits (either one; doesn't matter). Do a Bell basis measurement. The four possible measurement results are the four ...
Craig Gidney's user avatar
  • 37.5k
4 votes

Expressing a quantum state as a polynomial

I assume $f$ is real because, in your example, the polynomial you gave appears to be real. The dependence on the number of qubits $n$ is pretty straightforward to see. Once you see that, you realize ...
MonteNero's user avatar
  • 2,646
4 votes

What are classical analogies for the notions of superposition, entanglement, and interference?

Unfortunately, classical analogies generally can't capture the interesting properties of quantum systems and these analogies are no exception. One challenge is that quantum states can look like they ...
forky40's user avatar
  • 7,073
4 votes

How to mathematically describe the action of CNOT on the control qubit alone?

The action $\mathcal{E}$ of CNOT on just the control qubit is the composition of two functions: the action \begin{align} \mathcal{C}(\rho)=\text{CNOT}\,\rho\,\text{CNOT}\tag1 \end{align} of CNOT on ...
Adam Zalcman's user avatar
  • 22.9k
3 votes
Accepted

Relation between Rz gate and Phase gate

The $RZ(\theta)$ gate is defined by: $$RZ(\theta)=\begin{pmatrix}\mathrm{e}^{-\mathrm{i}\frac\theta2}&0\\0&\mathrm{e}^{\mathrm{i}\frac\theta2}\end{pmatrix}=\mathrm{e}^{-\mathrm{i}\frac\theta2}\...
Tristan Nemoz's user avatar
  • 6,432
2 votes

How to calculate eigenvalues by phase estimation?

Quantum Principal Component Analysis uses what the authors call a quantum phase algorithm. This refers to the HHL algorithm, not quantum phase estimation which requires a copy of an eigenvector to ...
Benjamin Rodrigues de Miranda's user avatar
2 votes
Accepted

How is the controlled-n NOT gate represented in Qiskit?

For multi-controlled X gate, use Qiskit's class MCXGate which can be added to your circuit as follows: circ.mcx(range(7), 7)
Egretta.Thula's user avatar
2 votes
Accepted

IBM quantum computer backend cycle time and real gate duration

The integers in the InstructionDurations() are the multipliers of the real-system timestep dt. So for example, consider the ...
Shravan Patel's user avatar
2 votes

Is there a strategy for a single-shot identification of a Pauli gate?

Deterministically, no you cannot. Specifically, not with a strategy that looks like: prepare some single-qubit input $\rho$, apply the gate $U$ to it, and then measure with some POVM. Given any input $...
glS's user avatar
  • 25.2k
2 votes

Finding the effect of conjugate transpose on a state $|b\rangle$

For a unitary $U$, the conjugate transpose $U^\dagger$ is the inverse of $U$, i.e. the linear operator such that$^1$ $U^\dagger U=UU^\dagger=I$. Guess and check The inverse is unique$^2$, so a general ...
Adam Zalcman's user avatar
  • 22.9k
2 votes

Alternative gate sets for universal Clifford computation?

You can choose $CZ$ and/or $CNOT$ gate. You can choose $\sqrt{X}$ and/or $S$. Any extension of a generator set is also a generator. You may find useful to introduce the Pauli operators $X, Y, Z$.
Daniele Cuomo's user avatar
1 vote

How to mathematically describe the action of CNOT on the control qubit alone?

In the ZX calculus, the CNOT gate factors into a Z type node for the control linked to an X type node for the target. The Z type node (the "control part of the operation") has three ports: $...
Craig Gidney's user avatar
  • 37.5k
1 vote

Universality of adding gate to Cliffords without inverses

Note that there are non-Clifford gates with no inverse. For example: measurement in a non-Pauli basis. Consider $M_{X+Y}$, which measures if a single qubit state is in the positive or negative ...
Craig Gidney's user avatar
  • 37.5k
1 vote
Accepted

Universality of adding gate to Cliffords without inverses

TL;DR: Yes, in a finite dimensional Hilbert space, $G^{-1}$ can be approximated to arbitrary accuracy as a finite power of $G$. If $G$ has finite order $r$, this follows from $G^{-1}=G^{r-1}$. The ...
Adam Zalcman's user avatar
  • 22.9k
1 vote

What's the result of applying a CNOT gate followed by a Hadamard?

Your calculations are correct. Make the following three observations: $|\psi\rangle=|{++}\rangle$, $X|+\rangle=|+\rangle$, so $\text{CNOT}|{++}\rangle=|{++}\rangle$, $H|{+}\rangle=|0\rangle$. ...
Adam Zalcman's user avatar
  • 22.9k
1 vote

What's the result of applying a CNOT gate followed by a Hadamard?

Your formuals are correct 💯 It is also makes sense as if you would apply the reverse order on the output, you will get the input mentioned
Ron Cohen's user avatar
  • 1,304
1 vote

How to analyse a quantum circuit with an uncertain gate F?

Disclaimer: analysis below works only for gates $F$ changing phase only. Once absolute values of amplitudes are changed, other results than predicted below are returned. Lets analyze your circuit step ...
Martin Vesely's user avatar
1 vote

Construct operator for controlled gate with qubits in-between

The controlled-unitary of your case is $$|0\rangle\langle 0|\otimes \mathbb{1}\otimes \mathbb{1} + |1\rangle\langle 1| \otimes \mathbb{1}\otimes U.$$ In this example you can find the matrix (to the ...
Daniele Cuomo's user avatar
1 vote
Accepted

Construct operator for controlled gate with qubits in-between

To construct a controlled gate with qubits in-between, you can use the following general form for a controlled gate: $$U = |0\rangle\langle0| \otimes I + |1\rangle\langle1| \otimes G$$ Here, $|0\...
Jonathan Reese's user avatar
1 vote

Easiest hash function to implement on Qiskit

I wrote an example hash function in the documentation of the qlasskit library; the result is directly exportable to qiskit, so it may be the answer for your question: https://dakk.github.io/qlasskit/...
Davide Gessa's user avatar
1 vote

How can I implement an n-bit Toffoli gate?

You can use MCXGate: def toffoli_general(qr, control, target): qr.append(MCXGate(num_ctrl_qubits=len(control)), control + [target]) With for example ...
antomax33's user avatar
1 vote

What is the input when simulating a quantum state?

A general single-qubit quantum state is described, as you mentioned, as $|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$. Numbers $\alpha$ and $\beta$ are called probability amplitudes and they are ...
Martin Vesely's user avatar
1 vote

Can we somehow relate quantum volume with the total number of gates present in a circuit which the machine can succesfully run without large errors

Quantum volume is a metric designed to quantify the performance and capabilities of a quantum computer. It encompasses various factors like gate fidelity, connectivity, coherence time, and others to ...
Shravan Patel's user avatar
1 vote

Fault Tolerance of 2-transversal gates

I think you are right that such a 2-local gate would be fault tolerant with "fault-tolerant distance 3" as you say. I think the reason that you don't see this idea around is that it is more ...
Ian Gershon Teixeira's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible