3 votes

Strange inequivalence between superdense coding and teleportation

Imagine we have some two-qubit state $\omega$ which Bob holds after the transmission of a qubit from Alice. For superdense coding, he's going to measure it in the Bell basis. Let's assume the answer ...
  • 49.2k
3 votes
Accepted

What is the minimum number of non-Clifford gates does it take to prepare a superposition over all "two-hot" basis vectors?

This can be done efficiently by using amplitude amplification. We are going to want to rotate each qubit such that it has a $2/n$ chance of being ON. For that it helps to have this class of gates: $\...
  • 26.1k
3 votes

Constructing a single qubit gate from S, H and Pauli gates

I go about this in quite a different way (and get a different result). You're trying to make $$ e^{-i\pi Y/4}=\frac{1}{\sqrt{2}}(I-iY). $$ Start by considering Hadamard: $$ H=\frac{X+Z}{\sqrt{2}}. $$ ...
  • 49.2k
3 votes
Accepted

Constructing a single qubit gate from S, H and Pauli gates

There may be a simpler way of doing this, but this certainly works. First find the matrix representation of $U$ by multiplying out the terms. Remember that $e^{i \theta Y} = \cos(\theta) I + i \sin(\...
3 votes

How to factorize a multi-qubit quantum state?

What you ask is even harder than asking whether a state is separable. The latter is considered a complex problem, sometimes NP-hard. See, e.g., https://en.wikipedia.org/wiki/Separable_state for a ...
3 votes

How to implement the Circuit of Steane's code for Quantum Error Correction?

I will do some of the work using a small python library I am writing to play with quantum stabilizer codes. It's called stac. Let's load up the Steane code. ...
3 votes

Can we determine the inner product using a single pair of states?

I guess what they're trying to say is that there is no circuit that can compute inner products of arbitrary states. Indeed, if it existed, we could use it to calculate the inner product of the states $...
2 votes

Prove that uniformly random states have moments ${\bf E}_\psi|\langle x|\psi\rangle|^{2t}\sim1/\binom d t$

The factor in your claim is wrong. It should be $\binom{d+t-1}{t}^{-1}$. The correct claim follows from the identity $$ \int |\psi\rangle\langle\psi|^{\otimes t} d\psi = \binom{d+t-1}{t}^{-1} P_{\...
2 votes
Accepted

Pennylane: take qml.state of one function and use it as the initialization for another

You can totally do this in PennyLane. Check out qml.QubitStateVector :) ...
  • 131
2 votes

what quantum computing simulator can achieve drag-and-drop programing fuction without internet like IBM web composer?

Actually, Quirk can work without internet connection. Just click on Export button and choose the "offline copy" option. You will get a single file which contains Quirk and can run from your ...
2 votes

What is the reason of $ZZ$- and $XX$- interaction in two-qubit system?

This comes down very much to the physics of the individual devices. I'll describe here one relatively simple model which hopefully gives you a little bit of insight. But, as I say, it's different for ...
  • 49.2k
2 votes

How to implement the Circuit of Steane's code for Quantum Error Correction?

For a CSS code, initializing all physical qubits into $|0\rangle$ and then measuring the stabilizers of the code is an encoding circuit for logical $|0\rangle$, and also for logical $|1\rangle$, up to ...
  • 26.1k
1 vote

What is the iToffoli gate?

According to "High-fidelity iToffoli gate for fixed-frequency superconducting qubits" by Kim et la. Similar to the Toffoli gate, the iToffoli gate inverts a target qubit conditioned upon ...
1 vote

In what state is this 3-qubit state?

Try looking up some of the answers on this site about how to create a W state. This is a state of the form $$ \frac{1}{\sqrt{3}}(|001\rangle+|010\rangle+|100\rangle. $$ Let me call the unitary that ...
  • 49.2k
1 vote

How does Quantum Simulation actually solve the problem it poses?

TL/DR: Hamiltonian simulation (quantum simulation) is interesting in itself, as it is likely classically difficult to do, but it is also very interesting as a subroutine for other algorithms that rely ...
  • 8,251
1 vote

How to create superposition of all bitstrings with exactly two ones on 4 qubits?

The desired state may be rewritten$^1$ as $$ |\psi\rangle=|0\rangle\otimes|\overline{W}\rangle+|1\rangle\otimes|W\rangle $$ where $|W\rangle=|001\rangle+|010\rangle+|100\rangle$ and $|\overline{W}\...
  • 15.4k
1 vote
Accepted

What is the result of applying a CNOT to $|01\rangle$?

This tensor product decomposition is not correct: 0 * |00>, 1 * |10>, 0 * |01> and 0 * |11> If we use the following notation $$c=(c(0), c(1))$$ $$t=(t(0), t(1))$$ The tensor product can ...
  • 26
1 vote

How to initialize a function in Qiskit with 3 qubit?

Presumably $A^2 + B^2 + C^2 = 1$ temp = QuantumCircuit(3) temp.initialize([A, 0, 0, 0, B, 0, 0, C]) where I've put A, B, and C into the spots corresponding to 0, 4,...
1 vote

Can separable, but non-valid "states", be used as a resource to generate entanglement?

Yes: LOCC can be used to make convex combinations of states Alice and Bob have at their disposal. Since $$ \tfrac14\lvert 00\rangle\langle 00\rvert+ \tfrac14\lvert 11\rangle\langle 11\rvert+ \tfrac14\...
1 vote

what quantum computing simulator can achieve drag-and-drop programing fuction without internet like IBM web composer?

You can do this with the Circuit Composer widget ...
1 vote

What is the quantum relative entropy between pure states?

Well, if you go back to the definition of quantum relative entropy you'll notice it is not defined for all states. Or more precisely, it is defined as $$S(\rho\|\sigma) = \operatorname{Tr}(\rho\log\...
  • 20.4k
1 vote

How to implement the Circuit of Steane's code for Quantum Error Correction?

A concrete circuit allowing to encode the logical $|\bar{0}\rangle$ can be as follow (source, page 33 of this paper). Now, in practice, this circuit is not fault-tolerant, which means that a single ...
1 vote
Accepted

When do qubits get entangled?

As mentioned before, qubits are only entangled by means of 2-qubit gates and not by 1-qubit gates, which only cause a rotation of the qubit state in question. Therefore, 2-qubit gates are needed to ...
  • 116
1 vote
Accepted

How to perform a basis change on a 2x2 density operator?

I'm not exactly sure what you mean, but I'll try my best. $\newcommand{\ket}[1]{|#1\rangle}\newcommand{\bra}[1]{\langle#1|}$The way I would do this is by first noting that $$\ket{+} = \frac{1}{\sqrt{2}...
  • 78
1 vote

Symbolic library for qubit states

use Wolfram quantum framework, that is the only framework supporting symbolic quantum computations, as far as I know
1 vote

What is size of the state space?

As you say, state space is the set of all possible results (if we are discussing the output of a function) or just the set of all possible states of a system. Normally, it is just a vector space of a ...
1 vote

What is size of the state space?

Here is a blog post that might be helpful. It's a good explanation of classical vs. quantum state spaces, and why the former is linear and the other exponential in the size of the register (i.e. the ...
1 vote

When can pairs of states be transformed into other pairs of states via unitary mapping?

A small rewarding of the argument in this other answer: Given $\{|\psi_1\rangle,|\psi_2\rangle\}$ and $\{|\phi_1\rangle,|\phi_2\rangle\}$ such that $\langle\psi_1|\psi_2\rangle=\langle\phi_1|\phi_2\...
  • 20.4k

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