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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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What are examples of extremal non-projective POVMs?
Fix some finite-dimensional space $\mathcal X$. Define a POVM as a collection of positive operators summing to the identity: $\mu\equiv \{\mu(a):a\in\Sigma\}\subset{\rm Pos}(\mathcal X)$ such that $\sum_{a\in\Sigma}\mu(a)=I_{\mathcal X}$, where…
glS
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List of problems that can be reduced to finding the ground state of a Hamiltonian
I'm doing some reading into Variational Quantum Eigensolvers (VQEs), Quantum Approximate Optimization Algorithms (QAOAs), and other similar algorithms.
I know that the point is to find the ground state of a Hamiltonian. I'm interested in…
johndont
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Why is the time ordering omitted in the trotterised version of the time-dependent evolution operator?
The unitary evolution of a time-dependent hamiltonian is given by the time-ordered matrix exponential
$$\begin{aligned}
U(t)&=\mathcal T\exp\left[-i\int_0^tH(\tau)d\tau\right]\\
&=I-i\int_0^td\tau\,H(\tau)-\frac12\int_0^td\tau\int_0^t…
Dyon J Don Kiwi van Vreumingen
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Decoherence of spin-entangled triplet-pair states in the solid state: local vs delocalized vibrations
The context: We are in the solid state. After a photon absortion by a system with a singlet ground state, the system undergoes the spin-conserving fission of one spin singlet exciton into two spin triplet excitons (for context, see The entangled…
agaitaarino
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3 answers
A sample quantum algorithm, useful for demonstrating languages
I'm looking for a quantum algorithm which I can use to demonstrate the syntax of different quantum-languages. My question is similar to this, however, for me, "good" means:
What it does could be described in 1-2 paragraphs, and should be easy to…
klenium
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How to know if your gate set is "complete"
In Daniel Greenbaum's paper, "Introduction to Gate Set Tomography", in page 20, he claims the gate sets $G = \{\{\}, X_{\pi/2}, Y_{\pi/2}\}$ and $G' = \{ \{\}, X_{\pi/2}, Y_{\pi/2}, X_{\pi}\}$ with $F_k \in G$, $F_k |\rho\rangle\rangle$ are able to…
Cuhrazatee
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Continued fractions with Shor's algorithm: which convergent?
Suppose I am using Shor's order finding algorithm to calculate the order $r$ of $x\leq N$ with respect to $N$. After some run of the QPE subroutine, I obtain a good, $L$-bit approximation to $s/r$ for some $s\leq r$. According to, say, Nielsen and…
Jacob
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In Cirq, how do you display circuit diagrams that are "prettier" than the ones displayed by default?
This is a duplicate of a question that was asked on the Cirq issues page. I'm duplicating this question to increase it's visibility.
Victory Omole
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Classical algorithm with complexity similar to Shor's discovered: Are there more efficient quantum algorithms than Shor's?
In the article Fast Factoring Integers by SVP Algorithms the author claims that he discovered classical algorithm for factoring integers in polynomial time. The Quantum Report mentioned here that it has similar performance to Shor algorithm which is…
Martin Vesely
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4 answers
How does the NOT gate generalize beyond binary?
If we are working with qudits instead of qubits, how do the NOT and CNOT gates work? If the control state for a qubit system is $|1\rangle$, what is it for a $d$-ary qudit system, and why?
For instance, in a qutrit system with three basis states…
worthlesspear
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Can the analysis or design of quantum algorithms benefit from parameterised algorithmics?
In the last decades, the field of parameterised algorithms, with fixed parameter tractibility (FPT) as its main tool has been provided new methods to analyse old algorithms and design techniques for new algorithms.
The basic idea of parameterised…
Discrete lizard
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2 answers
Why does QAOA achieve quantum supremacy in an algorithmic sense?
In the paper Quantum Supremacy through the Quantum Approximate Optimization Algorithm the authors claim (last sentence of page 15):
"If [...] the QAOA outperforms all known classical algorithms then it will achieve Quantum Supremacy in an…
Nepomuk Hirsch
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What are tentpole topics in quantum computing?
Lots of beginners are starting to learn quantum computing. But there are also experienced people that have been working in this field for many years.
What are some topics that might be considered important for a beginner to learn thoroughly?
By…
user27286
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If quantum computing always return random measurement (or uncertain measurement), why do we still need it?
I am very new to quantum computing and currently studying quantum computing on my own through various resources (Youtube Qiskit, Qiskit website, book).
As my mindset is still "locked" with classical computation, where input and output are very…
KamWoh Ng
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