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A rigorous definition for an exponential quantum advantage
Let's assume that we have an algorithmic problem to solve. This problem takes an integer $n$ as input to describe it and provides as output a bit string providing the answer we are expecting.
For some tasks, such as factoring, quantum computers are…
Marco Fellous-Asiani
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HHL algorithm -- why isn't the required knowledge on eigenspectrum a major drawback?
This question is a continuation of Quantum phase estimation and HHL algorithm - knowledge on eigenvalues required?.
In the question linked above, I asked about the necessity for HHL to have information on the eigenspectrum of the matrix $A$…
Adrien Suau
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Can a quantum computer break quantum cryptography?
I’m not sure if this makes sense, but I know that there is quantum and post-quantum encryption, and I’m curious whether quantum computing can break a quantum encryption.
Gejolop
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What is the relation between these two forms of a single-qubit unitary operation?
I want to understand the relation between the following two ways of deriving a (unitary) matrix that corresponds to the action of a gate on a single qubit:
1) HERE, in IBM's tutorial, they represent the general unitary matrix acting on a qubit…
Mathist
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What components are needed to realize a photonic CNOT gate?
In Realization of a photonic CNOT gate sufficient for quantum computation FIG. 1 there is a "scheme to obtain a photonic realization of a CNOT gate with two independent qubits."
What components are needed to realize a photonic CNOT gate?
user820789
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7 answers
Why do quantum computers have more qubits than classical computers have bits?
Sorry if this is a dumb question.
With conventional processors we increase cores, clock speed and IPC etc. With quantum computers the race seems to be to have the most qubits, seemingly in conflict with how we improve conventional processors. I…
ArduinoBen
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Quantum algorithm for linear systems of equations (HHL09): Step 2 - Preparation of the initial states $|\Psi_0\rangle$ and $|b\rangle$
This is a continuation of Quantum algorithm for linear systems of equations (HHL09): Step 2 - What is $|\Psi_0\rangle$?
In the paper: Quantum algorithm for linear systems of equations (Harrow, Hassidim & Lloyd, 2009), the details of the actual…
Sanchayan Dutta
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If Majorana qubits are analogous to surface codes, why do the diagrams use lines instead of squares?
If you go to some random Majorana paper or talk, you will find a diagram like this one. Note that the diagram is using lines. Making the lines longer should exponentially increase the error suppression:
If you go to some random surface code paper…
Craig Gidney
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How to show whether a bipartite high-dimensional system is entangled?
"How do I show that a two-qubit state is an entangled state?" includes an answer which references the Peres–Horodecki criterion. This works for $2\times 2$ and $2\times3$ dimensional cases; however, in higher dimensions, it is "inconclusive." It is…
user820789
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What does it mean for a density matrix to "act on a Hilbert space $\mathcal{H}"$?
For a Hilbert space $\mathcal{H}_A$, I have seen the phrase
density matrices acting on $\mathcal{H}_A$
multiple times, e.g. here.
It is clear to me that if $\mathcal{H}_A$ has finite Hilbert dimension $n$, then this makes sense mathematically,…
Peter
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Quantum algorithm for linear systems of equations (HHL09): Step 2 - What is $|\Psi_0\rangle$?
This is a sequel to Quantum algorithm for linear systems of equations (HHL09): Step 1 - Confusion regarding the usage of phase estimation algorithm and Quantum algorithm for linear systems of equations (HHL09): Step 1 - Number of qubits needed.
In…
Sanchayan Dutta
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4 answers
Why does the twirl of a quantum channel give a depolarizing channel?
I would like to understand in detail why the twirl of a quantum channel gives depolarizing channel, which is the starting point of randomized benchmarking. To be self-contained, let me set up the notation.
Let $\hat{U}$ denote a superoperator that…
fagd
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Time Entangled Quantum Blockchain
This answer cites a paper[$\dagger$] which purposes a quantum blockchain using entanglement in time.
"The weakness is that the research only presents a conceptual design." - QComp2018
How could a quantum blockchain which leverages time entanglement…
user820789
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How to check if a matrix is a valid density matrix?
What conditions must a matrix hold to be considered a valid density matrix?
Archil Zhvania
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Barren plateaus in quantum neural network training landscapes
Here the authors argue that the efforts of creating a scalable quantum neural network using a set of parameterized gates are deemed to fail for a large number of qubits. This is due to the fact that, due to the Levy's Lemma, the gradient of a…
asdf
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