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1500 questions
16
votes
1 answer
How does the vectorization map relate to the Choi and Kraus representations of a channel?
I know that the Choi operator is a useful tool to construct the Kraus representation of a given map, and that the vectorization map plays an important role in such construction.
How exactly does the vectorization map work in this context, and how…
Tobias Fritzn
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16
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2 answers
State of the art gate speeds and decoherence times
I am interested in the state of the art gate speeds and decoherence times for the qubit types I know are being pursued by companies presently:
superconducting qubits,
ion trap qubits,
photonic qubits.
Where can I find these, and is there a place…
user1271772 No more free time
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16
votes
2 answers
Graphical Calculus for Quantum Circuits
So far I have read a little bit about zx-calculus & y-calculus.
From the first chapter of Reversible Computation:
The zx-calculus is a graphical language for describing quantum systems.
The zx-calculus is an equational theory, based on rewriting…
user820789
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16
votes
1 answer
Status of Google's quantum supremacy claim 2022
More than a year ago a couple of scientists made a splash by presenting a classical algorithm that took less than a week to simulate Sycamore's circuits on a small GPU cluster. Also, their simulations produced exact results and not estimates.
This…
MonteNero
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16
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1 answer
Violation of the Quantum Hamming bound
The quantum Hamming bound for a non-degenerate $[[N,k,d]]$ quantum error correction code is defined as:
\begin{equation}
2^{N-k}\geq\sum_{n=0}^{\lfloor d/2\rfloor}3^n\begin{pmatrix}N \\ n\end{pmatrix}.
\end{equation}
However, there is no proof…
Josu Etxezarreta Martinez
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16
votes
1 answer
What is the difference between QAOA and Quantum Annealing?
Edward Farhi's paper on the Quantum Approximate Optimization Algorithm
introduces a way for gate model quantum computers to solve combinatorial optimization algorithms. However, D-Wave style quantum annealers have focused on combinatorial…
hopefully coherent
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16
votes
2 answers
Representation of real numbers in quantum computers
In classical binary computers, real numbers are often represented using the IEEE 754 standard. With quantum computers you can of course do this as well - and for measurements this (or a similar standard) will probably be necessary since the result…
blalasaadri
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15
votes
2 answers
Does higher channel fidelity imply higher entanglement fidelity?
Consider two noisy quantum channels (CPTP maps), $\Phi_1^A$ and $\Phi_2^A$, acting on a system $A$. Suppose that for any pure state $\left|\psi\right>\in \mathcal H_A$,
$$
F\big(\psi, \Phi_1^A(\psi)\big) \geq F\big(\psi,…
UncertainTea
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15
votes
2 answers
How and why does swap test works?
I am having some trouble understanding why a SWAP test would work. I meant I read that and understood the concepts as follows:
If the two input states are equal, the output register always results
in a state of $|1\rangle$, so a $1$ outcome will be…
Hamza
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15
votes
3 answers
How to calculate an Expected Value of some operator acting on qubits?
I'm trying to implement the Variational Quantum Eigensolver in Qiskit.
Suppose, I have an operator $A = \sigma_1^z\sigma_2^z$ acting on some two-qubit state $|\psi\rangle$. After a measurement I get a set of probabilities corresponding to states…
C-Roux
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15
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1 answer
Why isn't there a contradiction between the existence of CNOT gate/entanglement and the no-cloning theorem?
Of course I am not implying that I am right and the no cloning theorem is wrong, but I am trying to figure out what is wrong with my reasoning and yet I couldn't find the mistake. Based on Wikipedia:
In physics, the no-cloning theorem states that…
u185619
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15
votes
2 answers
How many two-qubit gates are required to implement a general N-qubit unitary?
Is there a known formula or a scaling behaviour for how many two-qubit gates are required to construct a general N-qubit unitary?
I suppose there are several cases to consider:
Exact representation of the gates
Approximate decompositions to a given…
as2457
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15
votes
6 answers
Is there any online Bloch sphere simulator?
While writing this answer I realized it would be really helpful if I could show the OP a video or .gif of how qubit states in Bloch spheres transform under certain unitary operations. I googled up a bit and could find only these two…
Sanchayan Dutta
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15
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4 answers
How is the Grover-Algorithm applied to a database?
Question
I want to use the Grover-Algorithm to search an unsorted database for an element $x$. Now the question arises, how do I initialize index and value of the database with the qubits?
Example
Let's say I have $4$ qubits. Thus, $2 ^ 4 = 16$…
alex
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15
votes
3 answers
Simulate hamiltonian evolution
I'm trying to figure out how to simulate the evolution of qubits under the interaction of Hamiltonians with terms written as a tensor product of Pauli matrices in a quantum computer. I have found the following trick in Nielsen and Chuang's book…
Apo
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