Most Popular
1500 questions
13
votes
1 answer
What is the leading edge technology for creating a quantum computer with the fewest errors?
Which technological path seems most promising to produce a quantum processor with a greater quantum volume (preferring fewer errors per qubit over more qubits), than Majorana fermions?
The preferred format for the answer would be similar to:
"Group…
Rob
- 2,339
- 1
- 16
- 30
13
votes
3 answers
Why does a Hamiltonian have to be Hermitian?
Starting from:
$$
-i\hbar \frac{d|\psi⟩}{dt} = H|\psi⟩
$$
I was able to do some working to prove that $U$ in the corresponding discrete representation
$$
U(t_1,t_2) = exp\frac{-iH(t_2-t_1)}{\hbar}
$$
is unitary if and only if $H$ is Hermitian. That…
Alexander Soare
- 656
- 4
- 16
13
votes
1 answer
How can I decompose a matrix in terms of Pauli matrices?
I need to see an example of how Hamiltonian, i.e. any Hermitian matrix, can be decomposed into a linear combination of Pauli matrices.
I would prefer an option to do this in larger than 2 dimensions, if that is possible.
yishairasowsky
- 241
- 2
- 4
12
votes
3 answers
Does the quantum Fourier transform have many applications beyond period finding?
(This is a somewhat soft question.)
The quantum Fourier transform is formally quite similar to the fast Fourier transform, but exponentially faster.
The QFT is famously at the core of Shor's algorithm for period finding. It also comes up in a few…
tparker
- 2,939
- 13
- 26
12
votes
1 answer
Quantum algorithms for Prolog or automated theorem proving?
Are there quantum algorithms for Prolog (SLD resolution - unification and depth-first-search) or for automated theorem proving in general (negation, resolution, and SAT)?
Usually automated theorem proving involves SAT problem for the negation of…
TomR
- 423
- 2
- 7
12
votes
2 answers
Understanding Google's “Quantum supremacy using a programmable superconducting processor” (Part 1): choice of gate set
I was recently going through the paper titled "Quantum supremacy using a programmable superconducting processor" by NASA Ames Research Centre and the Google Quantum AI team (note that the paper was originally posted on the NASA NTRS but later…
Sanchayan Dutta
- 17,945
- 8
- 50
- 112
12
votes
3 answers
Big Endian vs. Little Endian in Qiskit
I've noticed that Q# favors Little Endian. Meaning that most operations are designed for this type of encoding.
Is is it the same with Qiskit?
Sorin Bolos
- 621
- 5
- 11
12
votes
2 answers
How to create quantum circuits from scratch
I am doing self-study at the moment using primarily the book: Quantum Computing a Gentle Introduction by Eleanor Rieffel and Wolfgang Polak.
Getting through the earlier chapters and exercises went quite well (fortunately the earlier chapters had…
Joery
- 173
- 1
- 8
12
votes
1 answer
Separating NP from BQP relative to an oracle
I was looking at this lecture note where the author gives an oracle separation between $\mathsf{BQP}$ and $\mathsf{NP}$. He hints at how "standard diagonalisation techniques can be used to make this rigorous".
Can someone detail a diagonalisation…
BlackHat18
- 1,527
- 9
- 22
12
votes
1 answer
Sampling random circuits vs Solovay-Kitaev compiler
Suppose I want to obtain a gate sequence representing a particular 1 qubit unitary matrix.
The gate set is represented by a discrete universal set, e.g. Clifford+T gates or $\{T,H\}$ gates.
A well known approach to solve the problem is to use…
Yaroslav Kharkov
- 141
- 4
12
votes
2 answers
Is there a general method of expressing optimization problem as a Hamiltonian?
Let's say, that we have an optimization problem in the form:
$$ \min_x f(x) \\ g_i(x) \leq 0, i = 1, ..., m \\ h_j(x) = 0, j = 1, ..., p,
$$
where $f(x)$ is an objective function, $g_i(x)$ are inequality constraints and $h_j(x)$ are equality…
brzepkowski
- 1,069
- 7
- 19
12
votes
4 answers
How to quickly calculate the custom U3 gate parameters $\theta, \phi$ and $\lambda$ for any unitary?
In IBM Qiskit and Quantum Experience, the custom U3 gate is defined as
$$
U(\theta, \phi, \lambda) =
\begin{pmatrix}
\cos\left(\frac{\theta}{2}\right) & -e^{i\lambda} \sin\left(\frac{\theta}{2}\right) \\
e^{i\phi}…
Sanchayan Dutta
- 17,945
- 8
- 50
- 112
12
votes
2 answers
State produced by spontaneous parametric down-conversion (SPDC)
I'm researching SPDC's efficacy for use in an optical quantum computing model and I've been trying to figure out exactly what state the photons are in when they come out (as represented by a vector, for example), if I'm using type 1 SPDC and I'm…
auden
- 3,489
- 1
- 21
- 50
12
votes
3 answers
Why do we have to uncompute rather than simply set registers to zero?
In implementing a quantum subroutine it is important to uncompute temporary registers after use, to ensure the output state of the subroutine is not entangled with them (which would affect its behaviour).
Why is it necessary to perform this through…
Sideshow Bob
- 427
- 2
- 10
12
votes
1 answer
Superconducting qubit researchers: Do your TLS's move?
I have a superconducting system with tens of qubits, each of which can be tuned using DC flux.
One of the main tasks for coherent manipulation of the qubits is to find good idling frequencies and operating points for entangling gates. This effort is…
psitae
- 1,390
- 8
- 25