Most Popular
1500 questions
6
votes
1 answer
A basic question on circuits and matrix representation
I have several (rather basic) questions on matrix representation of circuits and I would be very grateful to anyone that could clear up my confusion, thank you in advance.
1) When reading circuit diagrams I know that the input qubit goes in the left…
bhapi
- 919
- 7
- 17
6
votes
1 answer
How do the Knill-Laflamme conditions $E_k^\dagger E_l\in{\cal M}$ and $\{M,E_k^\dagger E_l\}=0$ help us correct errors?
Suppose we have a stabilizer group $\mathcal{M}$, the Knill-Laflamme condition for error correction states
An error with Kraus operators $\{E_k\}$ is correctable if either $$E^\dagger_kE_l\in\mathcal{M}\quad\forall\, k,l $$ or there exists…
user2723984
- 1,156
- 8
- 16
6
votes
1 answer
Chose how to map virtual qubits to physical qubits
I'm currently trying to specify an initial_layout for a circuit on a IBM Q device.
Looking at the device's topology I would like to use the less noisy qubits in order to have the best performance.
Thus, I looked at how the circuit is transformed…
Samuel Beaussant
- 355
- 1
- 6
6
votes
1 answer
Finding a global phase that transform the Hadamard gate to an element of $SU(2)$ and propose an evolution operator which implements the operation
I was looking back over an old assignment and I came across a question I wasn't quite sure how to do the problem statement is as follows:
The Hadamard rotation is an element of the group $U(2)$.
Find the global phase with which one needs to…
bhapi
- 919
- 7
- 17
6
votes
3 answers
Maximum number of "almost orthogonal" vectors one can embed in Hilbert space
In a Hilbert space of dimension $d$, how do I calculate the largest number $N(\epsilon, d)$ of vectors $\{V_i\}$ which satisfies the following properties. Here $\epsilon$ is small but finite compared to 1.
$$\left\langle V_i\middle|V_i\right\rangle…
user2669
6
votes
4 answers
Where I can read about protein folding on quantum computers with simple examples?
Where I can read about protein folding on quantum computer (Qiskit will be ideal variant) with simple examples? Thanks
mitrik_bnr
- 143
- 5
6
votes
1 answer
Second reflection in the Grover's algorithm
When interpreted geometrically, the second phase of the Grover's algorithm which corresponds to inversion about the mean is interpreted as reflection over the original state.
Can you explain intuitively the relationship between those two?
usercs
- 481
- 2
- 9
6
votes
1 answer
Can we amplify BPP algorithms with a random quantum circuit?
Suppose we are given a (univariate) polynomial $P$ of degree $d$, and we wish to determine if $P$ is identically $0$. A standard way to do this is to use a classical PRG to randomly sample $n$ bits, drawing a number $r$ uniformly from $[0,S]$; we…
Mark Spinelli
- 15,378
- 3
- 26
- 83
6
votes
1 answer
Motivation for the definition of k-distillability
Definition of k-distillability
For a bipartite state $\rho$, $H=H_A\otimes H_B$ and for an integer $k\geq 1$, $\rho$ is $k$-distillable if there exists a (non-normalized) state $|\psi\rangle\in H^{\otimes k}$ of Schimdt-rank at most $2$ such…
Sanchayan Dutta
- 17,945
- 8
- 50
- 112
6
votes
0 answers
Bell State 11 not working for parity curve
I am currently writing a script to automate the creation of parity curves for a 2 qubit bell state and then calculate fidelity and proving entanglement from that (inspired by this paper). It was going really well. I am able to run simulations…
thewolfaxe
- 101
- 2
6
votes
1 answer
Is the quantum Fourier transform efficient if only one control-phase is allowed in the gate set
I have seen Why can the Discrete Fourier Transform be implemented efficiently as a quantum circuit?. This is not a duplicate.
I am familiar with the decomposition of the QFT from Nielsen&Chuang and Preskill's notes, and it requires to be able to…
dragomang87
- 83
- 5
6
votes
1 answer
Why should we use inverse QFT instead of QFT in Shor's algorithm?
Why should we use inverse QFT instead of QFT in Shor's algorithm? When I tried to simulate Shor's algorithm for small numbers, I got an answer even when I used just QFT instead of inverse QFT.
Tech Solver
- 613
- 4
- 10
6
votes
1 answer
Question on state distinguishability
Consider the following protocol.
We are given either
$|\psi\rangle = \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ or $|\phi\rangle = \alpha_{0} |0\rangle + \alpha_{1}|1\rangle$ where $\alpha_{0}^{2}$ is chosen uniformly at random from $[0, 1]$ and…
NewUser2020
- 63
- 4
6
votes
1 answer
Error syndromes and recovery procedure in bit flip code
This question relates to exercise 10.4 in Nielsen and Chuang.
For syndrome diagnosis, the textbook provides an example where one has four projectors, by which, you can identify where a one qubit error has occurred. In this scheme, the syndrome…
Blackwidow
- 629
- 3
- 9
6
votes
2 answers
What would be the meaning of an $i$ in a qubit state $i\alpha|0\rangle+\beta|1\rangle$?
I do not know if the question is not too easy, but I'll put it here, because I'm interested in it.
So the state of a qubit is often stated in this form:
$$|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$$
An example would…
P_Gate
- 678
- 3
- 17