6 votes
Accepted

Is 216 qumodes photonic quantum processor equivalent to 216 qubits superconducting quantum processor, in terms of computational power?

My name is Isaac and I work at Xanadu. That’s a really good question! Generally speaking, you can argue that 216 qumodes are more powerful than 216 superconducting (SC) qubits since qumodes encode ...
user avatar
  • 76
5 votes

Is there a quantum gate that can turn any superposition $|\varphi \rangle $ into a unit column vector $|00\cdots 1\cdots 0\rangle $

It depends on what you mean. For a given state $|\varphi\rangle$, it is always possible to find a gate $U_\varphi$ such that $U_\varphi|\varphi\rangle=|i\rangle_{10}$ for some given $i$. However, it ...
user avatar
4 votes
Accepted

Visualize representation of a qubit

One certainly can give examples of the form you're asking for. Here's one: $$ \frac{1}{\sqrt{2}}(e^{i\pi/3}|0\rangle+e^{-i\pi/3}|1\rangle). $$ However, note that you will essentially never see an ...
user avatar
  • 47.1k
3 votes

How to find initial quantum states from the density matrix?

In general, for a given $\rho$ there are many ensembles, i.e. sets of pure states $|\psi_i\rangle$ and probabilities $p_i$ such that $\rho=\sum_i p_i|\psi_i\rangle\langle\psi_i|$. For example, if $\...
user avatar
  • 13.5k
3 votes
Accepted

In what contexts are different notations used for indicating measurement outcomes?

It's an interesting question as to how to the bijection between the measurement eigenvalues $\{+1,-1\}$ and the bits $\{0,1\}$ or the qubits $\{|0\rangle,|1\rangle\}$ are reflected or intuited in the ...
user avatar
  • 7,017
3 votes
Accepted

Difficulty of creating arbitrary amplitude-encoded quantum states

Here's a crude argument (which one can undoubtedly pick holes in, but I think helps with intuition)... Let's say you want to create an arbitrary state of $n$ qubits, so $N=2^n$. This means that you ...
user avatar
  • 47.1k
3 votes

What are the best-known lower bounds on the number of measurements required for quantum state tomography?

This preprint is just submitted a few days ago: An Improved Sample Complexity Lower Bound for Quantum State Tomography by Henry Yuen. It shows that $\Omega(rd/\epsilon)$ copies of an unknown rank-$r$, ...
user avatar
3 votes

What is the actual Hilbert space of a $N$-qubit system?

First off, the Bloch sphere is the complex projective line $\mathbb{C}P^1$, which is homeomorphic to $S^2$, while $SU(2)$ is homeomorphic to $S^3$. $SU(2^N)$ is the group of operators on pure states, ...
user avatar
  • 393
3 votes
Accepted

What is the actual Hilbert space of a $N$-qubit system?

Just a small remark for part of the question: Letting two Hilbert spaces $\mathcal{H}_1$ and $\mathcal{H}_2$ (this can be generalized to any linear space) the tensor product $\mathcal{H}_1 \otimes \...
user avatar
  • 1,456
2 votes

How does a Hadamard gate impact the initial/previous values of a Qubit?

I think you might just be misunderstanding the Hadamard gate slightly. In the computational basis, $H= \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1\end{pmatrix}$ maps $|0\rangle \...
user avatar
  • 226
2 votes

When starting from Qubit State |0>, which operations when applied (from right to left) will result in the qubit state |->

You can start by writing everything down in matrix-vector form. The $|0\rangle$ state is represented in the $Z$-basis by the vector $\begin{bmatrix} 1\\ 0 \end{bmatrix}$. Applying the Hadamard-gate to ...
user avatar
2 votes

Can the phase in a qubit be expressed as a phase on another qubit in a larger system?

We can write the total state as a tensor product of two qubits, but there is only one wavefunction of the total system. In fact $\vert1\rangle \otimes (e^{i\theta}\vert\psi\rangle)$ is exactly the ...
user avatar
2 votes
Accepted

Can someone explain to me what is T gate and tdg like im five?

tdg is the method used to apply $T^\dagger$ (read T dagger). Thus, there are no differences between these two. For a quantum gate $U$, $U^\dagger$ is the inverse of ...
user avatar
2 votes
Accepted

what does it mean to "measure a qubit" if measurement is defined on operators

Measurement is defined with respect to a measurement basis. Given a state $\rho$, and a measurement basis $\{|u_k\rangle\}_k$, the measurement results in the outcome probabilities $p_k = \langle u_k|\...
user avatar
  • 18.7k
2 votes

what does it mean to "measure a qubit" if measurement is defined on operators

I'm not sure if your question is about "what is a measurement", or what does "measuring a qubit" mean if we don't specify the operator or basis. For the first answer, a generic ...
user avatar
2 votes
Accepted

What is the difference between "maximally entangled" and "entangled" states?

A maximally entangled state is a state that maximises some entanglement measure. In the case of bipartite states, this generally means a state that maximises the entanglement entropy, that is, the von ...
user avatar
  • 18.7k
1 vote

How to tell if a state is entangled?

$\alpha\gamma|00\rangle + \alpha\lambda|01\rangle +\beta\gamma|10\rangle+\beta\lambda|11\rangle = (\alpha|0\rangle+\beta|1\rangle)\otimes(\gamma|0\rangle+\lambda|1\rangle)$ is a separable state, so it'...
user avatar
  • 226
1 vote

How to write a code to separate two qubits?

Maybe it should be useful tu use qutip to better understand what you desire (if you are familiar with python) by visualizing exactly the 2 qubits and its state vectors (which I believe is what you ...
user avatar
1 vote

Is there a gate sending $|0\rangle^{\otimes n}$ to a state where some amplitudes are zero?

you can check out qiskit textbook, https://qiskit.org/textbook/ch-gates/phase-kickback.html https://qiskit.org/textbook/ch-quantum-hardware/density-matrix.html#5.-Mixed-States-in-the-Bloch-Sphere-- ...
user avatar
  • 423
1 vote

When starting from Qubit State |0>, which operations when applied (from right to left) will result in the qubit state |->

To answer your question, the correct answer is option $(i)ZH$. This is because mathematically, the gates are applied in the right-to-left order and hence you apply the $H$ gate first taking us from ...
user avatar
1 vote
Accepted

What is the difference between $|+\rangle$ and $|-\rangle$?

States with different complex amplitudes are simply different states with different observable consequences. They are not the same. We need them because they describe the outcomes of measurements. To ...
user avatar
  • 47.1k

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