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Is there a practical architecture-independent benchmark suitable for adversarial proof of quantum supremacy?
Recent quantum supremacy claims rely, among other things, on extrapolation, which motivates the question in the title, where the word "adversarial" is added to exclude such extrapolation-based quantum supremacy claims.
To clarify the exact meaning…
fiktor
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Can one quantify entanglement between different parts of a system?
Consider some state $|\psi\rangle$ of $n$ qubits. One can take any subsystem $A$ and compute its density matrix $\rho_A =Tr_{B} |\psi\rangle \langle\psi|$. The entanglement between subsystem $A$ and the rest of the system $B$ is quantified for…
Nikita Nemkov
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Complexity of $n$-Toffoli with phase difference
I'm interested in the $n$-Toffoli gates with phase differences. I found a quadratic technique in section 7.2 of this paper.
Here's the front page of the paper.
Here's an image of the section that I'm referring to.
Does anyone know if there has…
Minh Pham
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Cascade/Feedforward quantum circuits
I would like to know if it is possible implement the following situation in Qiskit (either using the simulators or real quantum computers).
Consider this illustrative toy example:
The arrows illustrate that the outcomes $\{\sigma_1,...,\sigma_i\}$…
fcrp
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Solving linear system $Ax=b$ with exponential speed-up via binary optimization?
The main disadvantage of HHL algorithm for solving $A|x\rangle = |b\rangle$ is that exponential speed-up is reached only in case we are interested in value $\langle x|M|x\rangle$, where $M$ is a matrix. In case we want to know solution $|x\rangle$…
Martin Vesely
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7
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Bernstein–Vazirani problem in book as exercise
I´ve solved the Exercise 7.1.1 (Bernstein–Vazirani problem) of the book "An introduction to quantum computing" (Mosca et altri). The problem is the following:
Show how to find $a \in Z_2^n$ given one application of a black box that maps…
asdf
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How do we understand Jordan's Lemma?
In quantum computing protocols, jordan's lemma keeps cropping up. See, for example, here: https://cims.nyu.edu/~regev/teaching/quantum_fall_2005/ln/qma.pdf
For any two projectors $\phi_1$, $\phi_2$, there exists an orthogonal decomposition of the…
snickers_stickers
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Quantum annealing - studies showing empirical evidence for better performance in comparison with classical computers
Currently, it is not known wheter quantum anneling or algorithms like VQE and QAOA for general purpose quantum computers bring about any increase in computational power. However, there are some studies indicating that in some cases quantum annealing…
Martin Vesely
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3 answers
Is it possible to make a Toffoli gate using only CNOTS and ancillas?
I have tried to make a Toffoli gate using only CNOTs and some ancilla qubits but I do not get the unitary. It seems it is not possible without additional gates? What could I do to prove it?
I have tried something like…
Mauricio
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Biggest variance of $h=\sum_i H_i$?
What's the biggest variance of $h=\sum_i H_i$ where $H_i$ is the hamiltonian act on the ith qubit?
If the n qubits state is separable, i.e., the state is $\mid\psi_1\rangle\otimes\mid\psi_2\rangle\otimes\cdots\mid\psi_n\rangle$. Obviously, the…
narip
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Quantum teleportation of a mixed state through a pure state?
Let's assume we have a register of qubits present in a mixed state
$$\rho = \sum_i^n p_i|\psi_i\rangle \langle \psi_i|$$
and we want to teleport $\rho$ through a random pure state $|\phi\rangle$. What would be the result of this…
Thomas
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What is meant by "perfect state transfer"?
In discussions on many quantum algorithms especially related to quantum walks, I have seen the term "perfect state transfer" used to describe some property apparently related to the periodicities of the walk/algorithm, but I cannot quite grasp the…
Mark Spinelli
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3 answers
Can the theory of quantum computation assist in the miniaturization of transistors?
In his inaugural lecture, Ronald de Wolf states
People are working with quantum objects, but trying to make them behave as classical as possible. (...) Instead of suppressing them to make systems behave as classically as possible, why not try to
…
Discrete lizard
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Why do I get this extra factor when working out the dynamics of an adiabatic quantum computation?
I was trying to revise my understanding of adiabatic quantum computation via a simple example. I'm familiar with the overall concept -- that you have an overall Hamiltonian
$$
H(s)=(1-s)H_0+s H_f
$$
where $s$ is a function of time, starting from…
DaftWullie
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'Best practices' for making Stim run as fast as possible?
I'm currently testing out an error-correction surface code circuit in Stim.
I've tried a 19x19 surface code over 10k rounds of syndrome extraction sampled 256 times, and this takes about 165 seconds. This comes out to roughly ~100s of nanoseconds…
squiggles
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