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What is the difference between $\vert 0 \rangle + \vert 1 \rangle$ and $\vert 0 \rangle \langle 0 \vert + \vert 1 \rangle \langle 1 \vert$?

In a discussion with Jay Gambetta on the QISKit Slack channel, Jay told me that "T2 is the time that $\vert 0 \rangle + \vert 1 \rangle$ goes to $\vert 0 \rangle \langle 0 \vert + \vert 1 \rangle \langle 1 \vert$". My question is: what is the…
Adrien Suau
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How do you represent the output of a quantum gate in terms of its basis vectors?

I'm stuck while trying to understand the Hadamard Gate in a more linear algebra understanding. (I understand the algebraic way). This is because I want to program a simulation of a quantum computer. To apply a gate you multiply each ket by the…
Vitulus
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Is entanglement an operation or a stored state for qubits?

I am going through this video of Quantum Computing for Computer Scientists. I am not able to understand the entanglement state of qubits. Is entanglement just an operation, or is it a state which can be stored. If it's a state which is stored then…
rusty
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Solving linear systems represented by NxN matrices with N not power of 2

As far as I have seen, when it comes to solving linear systems of equations it is assumed to have a matrix with a number of rows and columns equal to a power of two, but what if it is not the case? If for instance I have the equation $Ax=b$ where A…
FSic
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What are the pros/cons of Trapped Ion Qubits, Superconducting Qubits and Si Spin Qubits?

Among available qubit technologies for universal quantum computing these 3 come up as promising. NV centers and Majorana qubits also underway but relatively new. I find superconducting qubits and Trapped Ion qubits very hard to scale. Also…
mando
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How to verify whether a state is a stabilizer state?

Given an arbitrary $n$-qudit state vector $|\psi\rangle =\sum_i c_i| i \rangle \in \mathbb{C}_d^n$ for some orthonormal basis $\{|i\rangle\}$, what is the most efficient way one can: Verify whether the state is a stabilizer state (i.e. can be…
SLesslyTall
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Is there something like GitHub for quantum programming?

I'm just learning about quantum computer but some of it has been available for people to research & practice so I'd like to study it myself. The only kind of quantum computing I found so far is IBM cloud service and Q# quantum simulator but the…
7
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Does "quantum registers with $n$ qubits are able to hold $2^n$ values and therefore scale exponentially" actually hold that straightforwardly?

A lot of people claim that quantum provides exponential speedup whereas classical computers scale linearly. I have seen examples (such as Shor's algorithm and Simon's) that I believe, but the layman's explanation appears to boil down to "quantum…
Thomas Hubregtsen
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Are qubits preferred over qumode, and if so, why?

Qubit and qumode are different forms of quantum computation. But most existing quantum computers/chips seems to be of discrete variables. I heard that a group chose qubit for a quantum optical frequency comb experiment relating to quantum computing…
raycosine
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Query regarding BQP belonging to PP

I found the following proof of BQP belonging to PP (the original document is here). There is a part of the proof that I have trouble understanding. First, the structure is given below. We try to simulate a polynomial-time generated quantum circuit …
BlackHat18
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What are reliable references on analytical and/or numerical studies of threshold theorems under faulty quantum error correction?

By "faulty", I mean that you can have errors on the ancilla qubits, you can have faulty syndrome extraction, etc.
Sherif F.
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What is the purpose of the TDG gate in QISKit?

The QISKIT documentation doesn't explain what a TDG gate does and I can't find it anywhere else online.
7
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Arbitrary powers of NOT and SWAP

The square-root of not and square-root of swap gates are often singled out for discussion of gates displaying important properties relating to quantum computers. How do I define arbitrary (non-integer) powers of the square-root of NOT or…
DaftWullie
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Are classical shadows useful?

according to the paper https://doi.org/10.1038/s42254-022-00535-2 , the advantage of classical shadows is doing measurements first and asking questions later. But in real experiments, who would do measurement first and ask questions later, being…
yuanyi_thu
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Which Clifford groups are 2-designs?

Let $ X $ be the $ q \times q $ shift matrix sending $ |y \rangle \mapsto |y+1 \rangle $ where the ket index $ y=0,\dots, q-1 $ is taken mod $ q $. Let $ Z $ be the diagonal $ q \times q $ clock matrix sending $ |y \rangle \mapsto (e^{2 \pi i…