Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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Why is the size of the top register for Shor's algorithm chosen as it is?

Let $N$ be the number we're trying to factor. In Shor's algorithm, the top register then has $2 \lceil\log_2(N)\rceil+1$ qubits, while the bottom register (the ancilla qubits) has $\lceil\log_2(N)\rceil$ qubits. This is stated in my lecture notes on…
David Cian
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Is there anything practical that can be done with a single qubit?

Is there anything practical that can be done with a single qubit? And by "practical," I mean a problem that can be solved or information that can be stored. I realize that one practical thing that you can do with a single qubit is to write a grant…
vy32
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Problem 2.2 in Nielsen & Chuang - Properties of the Schmidt number

This question has been asked here: "Problem 2.2 in Nielsen & Chuang - Properties of the Schmidt number", but no answer has been provided there yet, thus I move it here. The problem is stated below. This is problem 2.2 (not exercise 2.2) in Nielsen &…
fagd
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What are quantum inspired algorithms?

I am starting to see press about quantum inspired algorithms. Are these algorithms that solve problems faster by looking at things from a quantum computing perspective?
LeWoody
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Why are POVMs useful? Are they just an axiomatic way to define measurement?

I know the definition of projective measurement, generalized measurement, POVM. I understand the usage of generalized measurement for the reason that it can model experiments "easier" (for example measurement of a photon that will be destructive so…
Marco Fellous-Asiani
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How to implement the CCH gate in quantum computers available in clouds?

How to implement CCH gate in quantum computers available in clouds? If there is not any gate directly available for it, what are the possible ways to represent CCH?
Ankit Raj
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What is the state of the art on Quantum Random Access Memories?

I realized that Quantum Random Access Memory (qRAM) was proposed to make quantum computers more similar to classical one. Currently quantum computers have very constrained memory, given only quantum registers on quantum processors can be used for an…
Martin Vesely
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What is the practical interest of superdense coding?

When you enter the field of quantum communications, you run at some point into the concept of superdense coding. Basically it is a way to encode classical bits on the qubits of a quantum channel, which sounds interesting in the first place to…
Mathias
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Could quantum computers be useful for sending encrypted information over a classical channel?

A quantum computer running Shor's algorithm would be famously useful for decrypting information encrypted by many classical public-key cryptography algorithms. Is there any reason (either a specific proposed protocol or a general heuristic argument)…
tparker
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Is a qubit always in superposition?

I am introduced to ancilla qubits which are usually initialized to $\vert 0 \rangle$. It seems that an ancilla qubit is equivalent to the $0$ bit in classical computing as it will evaluate to $\vert 0 \rangle$ 100% of the time. My question is that…
M. Al Jumaily
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Reversal of time arrow on IBM Q

It is well known that a quantum computer is reversible. This means that it is possible to derive an input quantum state $|\psi_0\rangle$ from an output $|\psi_1\rangle$ of an algorithm described by a unitary matrix $U$ simply by applying transpose…
Martin Vesely
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How powerful would quantum computers be if we had direct access to the full state vector?

The state vector is exponential in size, so we can manipulate an exponential quantity of information with a linear quantity of gates. However, this doesn't give us general exponential speedup because we can only extract $n$ bits of information from…
ahelwer
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Custom gates on IBM Q

I realized that QASM supports custom gates. However, when I tried to create the gate, transpiling error appeared both on simulator and real quantum processor. I suspect that IBM has not implemented this functionality fully yet. Does anybody (maybe…
Martin Vesely
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Why, in Grover's algorithm, $H^{\otimes n}(2|0\rangle\! \langle0| - \mathcal{I})H^{\otimes n}=2|\psi\rangle \!\langle\psi| - \mathcal{I}$?

I've been working through Grovers algorithm. I've read many times that $*^1H^{\otimes n}(2|0\rangle \langle0| - \mathcal{I})H^{\otimes n}$ is equivalent to $*^22|\psi\rangle \langle\psi| - \mathcal{I}$. I did verify that $*^2$ turns $\sum_x…
Leander Behr
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What does the error rate on the IBMQ website mean？

How is the error rate pointed by the arrow defined? How did you get it? thanks!
wei zi
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