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What is the difference between quantum gates and quantum channels?
I'm not sure if this is a dumb question, since they seem to be very basic building blocks of quantum information theory; however, I can't seem to wrap my head around the difference between the two. As I understand it, both quantum gates and quantum…
learner1234
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Any simple description of a circuit for Yamakawa-Zhandry algorithm?
Recently, popular sources (including Aaranson's blog and Quanta Magazine) have made it look like the recent Yamakawa-Zhandry algorithm is akin to Shor's algorithm, in the sense that it could demonstrate quantum advantage soon if done with sufficient…
Mauricio
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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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Advances in Quantum Channel Capacity
I have been reading about the Quantum Channel Capacity and it seems to be an open problem to find such capacity in general. Quantum capacity is the highest rate at which quantum information can be communicated over many independent uses of a noisy…
Josu Etxezarreta Martinez
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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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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 use cases are there for 127 qubit QPUs?
IBM have recently announced their 127 qubit Eagle processor. Other approaches, such as Rydberg arrays, have now 256 qubits, as for example in QuEra's QPU QPU.
While these are without a doubt outstanding techical acheivements, I am wondering what is…
Lior
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What is a "maximally mixed state"?
What is meant by maximally mixed states? Does this mean that there are partially mixed states?
For example, consider $\rho_{GHZ} = \left| {GHZ} \right\rangle \left\langle {GHZ} \right|$ and $\rho_W = \left| {W} \right\rangle \left\langle {W}…
Bekaso
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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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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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