Most Popular
1500 questions
7
votes
3 answers
How many N-qubit stabilizer states are there?
An N-qubit stabilizer state is a state that can be produced by starting from the $|0\rangle^{\otimes N}$ state and applying only H, CNOT, and S gates. How many N-qubit stabilizer states are there?
Because every stabilizer state can be represented as…
Craig Gidney
- 44,299
- 1
- 41
- 116
7
votes
0 answers
Schumacher compression - comparing with Shannon compression
Background
Shannon's source coding theorem tells us the following. We shall consider a binary alphabet for simplicity. Suppose Alice has $n$ independent and identically distributed instances of a random variable $X\in \{0, 1\}$. Let us call this…
user1936752
- 3,311
- 1
- 9
- 24
7
votes
1 answer
What did exactly Google do in simulating a random quantum circuit on a classical computer in supremacy experiment?
I've been working on Google quantum supremacy paper for quite some time now and I have a problem in understanding how exactly they simulate their actual random quantum circuit on a classical computer.
To be specific, in their quantum random circuit…
Ali s.k
- 313
- 1
- 5
7
votes
3 answers
Does Planck's constant have any role in quantum computing?
I am new to the area of quantum computing, but as I study it I can't help wonder about the role of the Planck's constant. When one studies quantum mechanics one often finds statements that quantum mechanics reduces to classical physics if Planck's…
QC-Novice
- 131
- 2
7
votes
3 answers
What are mailing lists that advertise conferences and academic positions in the area of quantum computing?
I am aware of Oxford's Quantum Foundations mailing list that regularly advertises conferences and openings for academic positions related to quantum theory. What are other mailing lists that advertise stuff like this in the area of quantum…
John
- 546
- 2
- 7
7
votes
3 answers
Quantum circuit to implement matrix exponential
I want to build a circuit which will implement $e^{iAt}$, where $ A=
\begin{pmatrix}
1.5 & 0.5\\
0.5 & 1.5\\
\end{pmatrix}
$ and $t= \pi/2 $.
We see that $A$ can be written as, $A=1.5I+0.5X$. Since $I$ and $X$ commute,…
Omkar
- 341
- 1
- 9
7
votes
2 answers
What are some good resources for learning about photonic qubits?
I am interested in resources that would allow me to learn about the physics behind optical quantum computation, and specifically, the physical properties of photonic qubits. I have some good resources on quantum optics, but is there anything more…
Jack Ceroni
- 1,000
- 7
- 17
7
votes
2 answers
How to represent an $n$-qubit circuit in matrix form?
If a given quantum circuit has $n$ qubit inputs and a certain number of gates, how can we represent the whole circuit in matrix form? Here's an example:
I am sorry, I am confused on how to express the circuit above in matrix form. Especially on…
J.Koko
- 71
- 1
7
votes
1 answer
What limits speed of quantum gates?
I would like to check something.
Consider I am working on cQED (superconducting qubits), or ion trapped, or silicon qubits (I would like to exclude "exotic for me" quantum computing like photon based, or topological Q.C).
The fastest you perform a…
Marco Fellous-Asiani
- 2,220
- 2
- 15
- 42
6
votes
1 answer
Changing qubits coefficients to trigonometric functions in Grover Algorithm
In this paper, in Appendix B.1 (Grover's Search Algorithm and Grover Operator G), it does a change of coefficients, such as what is done for the Bloch Sphere, but for a many qubits system using only two vectors.
First, it separates the uniform…
Bertolino
- 61
- 4
6
votes
1 answer
Understanding Steps in Deutsch's Algorithm
I am currently working my way through the book Quantum Computation and Quantum Information by Chuang and Nielsen. So far it has been a joy to read, however I am hung up on a couple aspects of quantum parallelism and Deutsch's algorithm that I…
user918212
- 227
- 1
- 4
6
votes
2 answers
If an auxiliary qubit is allowed, how to construct toffoli gate in easier way?
We know if we don't use auxiliary, the construction of Toffoli gate will be:
However, if now you are allowed to use one auxiliary qubit, how to realize a CCNOT in a simplier way? (Can we only use X,Y,Z,H and CNOT?)
Dingshan Liu
- 91
- 1
6
votes
1 answer
In Dirac notation, why do we have $\langle cf|g\rangle = c^*\langle f\vert g\rangle$?
A Hilbert space's inner product has the property
$$\langle cf,g\rangle=c\langle f,g\rangle$$
where $f$ and $g$ are the vectors in the Hilbert Space and $c$ is a complex number.
In Dirac Notation:
$$\langle cf|g\rangle = c^*\langle f\vert…
Dragon123
- 207
- 1
- 6
6
votes
1 answer
Is Connes' Embedding Problem akin to the word problem for finitely presented groups?
The complexity class $\mathrm{MIP^*}$ includes the set of languages that can be efficiently verified by a classical, polynomially-bounded verifier, engaging with two quantum provers that can share (potentially infinite) entanglement, but are…
Mark Spinelli
- 15,378
- 3
- 26
- 83
6
votes
1 answer
How to prepare mixed states using IBM quantum experience?
I want to prepare some mixed states regarding a project that I am doing, however, I am not sure how to do that using IBM Q. Experience circuit composer. Basically, I am looking to prepare maximally mixed and non-maximally mixed quantum states.
I…
Hridey Narula
- 61
- 2