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1 vote

What is the maximally entangled state in Choi matrix?

For the Choi-Jamiołkowski isomorphism you need the bipartite maximally entangled state of dimension $d$, while the GHZ state is a multipartite entangled state of dimension 2. The normalization is also ...
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-1 votes

What is a Haar random quantum state?

Please read my paper. We have discussed Haar uniformity. It will help. https://iopscience.iop.org/article/10.1088/1367-2630/ac37c8/meta Section 2.1 "Haar uniform random states and probability ...
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2 votes

Cirq: Getting The Instances (samples) of a Quantum Circuit with Probabilistic Unitaries or Mixtures

There's no such function built in, but you can use map_operations to iterate through the circuit and replace mixture ops with a selected unitary gate as follows. <...
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1 vote
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Basis for permutation invariant states

No. Take the case $n=k=1$. Then your basis contains a single element, $\Phi$, whereas the permutation-invariant subspace of two qubits has dimension 10. More generally, there's no need to reinvent the ...
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2 votes

When we say that 4 qubits can represent $2^4$ binary bit sequences, how do we iterate to the desired bit sequence?

Quantum computing can solve certain problems exponentially faster, but not all. A classical computer with $n$ bits can store a single number with value up to $2^n$, while a quantum computer with $n$ ...
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1 vote

Basis for permutation invariant states

Your dimensions don't appear to work out. You're considering states of dimension $2^n$, but when $n=1$ you've written down a state for a Hilbert space of dimension $4$. Anyway, I don't think $\Phi$ ...
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1 vote

When we say that 4 qubits can represent $2^4$ binary bit sequences, how do we iterate to the desired bit sequence?

Even if qubits can represent those combinations at the same time, when I need a definite answer, how does the path to that answer differs from the path followed in binary bit computer? That's not how ...
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1 vote

How to get statevector of qubits after running quantum circuits on IBMQ real hardware to calculate the fidelity of all qubits individually?

I’m almost sure that results from real devices will be in the form of counts so you can’t turn that into a statevector. Each shot of the experiment will end up in a different statevector after all. ...
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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-$r$, ...
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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, ...
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3 votes
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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 \...
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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 \...
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  • 246
0 votes

Can a polynomial-sized superposition of computational basis states be prepared with a polynomial-sized quantum circuit?

I think so. Let me rephrase what you're asking and hopefully it captures what you want: Suppose you have $N$ distinct circuits $U_i$ such that $U_i|0\rangle = |\psi_i\rangle$, each with complexity $O(...
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  • 1,661
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 $\...
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3 votes
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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 ...
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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 ...
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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 ...
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4 votes
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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 ...
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