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2 answers

Density matrices for pure states and mixed states

What is the motivation behind density matrices? And, what is the difference between the density matrices of pure states and density matrices of mixed states? This is a self-answered sequel to What's the difference between a pure and mixed quantum…
Sanchayan Dutta
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22
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How can I build a circuit to generate an equal superposition of 3 outcomes for 2 qubits?

Given a $2$ qubit-system and thus $4$ possible measurements results in the basis $\{|00\rangle$, $|01\rangle$, $|10\rangle$, $|11\rangle\}$, how can I prepare the state, where: only $3$ of these $4$ measurement results are possible (say,…
22
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Is it possible to "calculate" the absolute value of a permanent using Boson Sampling?

In boson sampling, if we start with 1 photon in each of the first $M$ modes of an interferometer, the probability of detecting 1 photon in each output mode is: $|\textrm{Perm}(A)|^2$, where the columns and rows of $A$ are the first $M$ columns of…
22
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3 answers

What integers have been factored with Shor's algorithm?

Shor's algorithm is expected to enable us to factor integers far larger than could be feasibly done on modern classical computers. At current, only smaller integers have been factored. For example, this paper discusses factorizing…
Lying Dancer
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22
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4 answers

Why are quantum gates unitary and not special unitary?

Given that the global phases of states cannot be physically discerned, why is it that quantum circuits are phrased in terms of unitaries and not special unitaries? One answer I got was that it is just for convenience but I'm still unsure. A related…
wdc
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22
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1 answer

What is the use of categorical quantum mechanics?

I recently noticed that Oxford's computer science department has started offering a grad course on categorical quantum mechanics. Apparently they say that it is relevant for the study of quantum foundations and quantum information, and that it uses…
Sanchayan Dutta
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22
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3 answers

Is Quantum Biocomputing ahead of us?

Now that we know of bio/molecular tools that allow living organisms to deal with quantum computations e.g. the fancy proteins that allow birds to handle quantum coherence (e.g. The quantum needle of the avian magnetic compass or Double-Cone…
AG-M
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22
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3 answers

Advantage of quantum key distribution over post-quantum cryptography

Post-quantum cryptography like lattice-based cryptography is designed to be secure even if quantum computers are available. It resembles currently employed encryptions, but is based on problems which are most likely not efficiently solvable by a…
M. Stern
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22
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1 answer

Quantum Bitcoin Subdivision

Background Recently I was reading the article "Quantum Bitcoin: An Anonymous and Distributed Currency Secured by the No-Cloning Theorem of Quantum Mechanics" which demonstrates how a quantum bitcoin could function. The article's conclusion states…
22
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1 answer

What is the difference between a qubit and classical bit?

As I understand it, the main difference between quantum and non-quantum computers is that quantum computers use qubits while non-quantum computers use (classical) bits. What is the difference between qubits and classical bits?
User that hates AI
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How is quantum cryptography different from cryptography used nowadays?

Recent researches indicate that quantum algorithms are able to solve typical cryptology problems much faster than classic algorithms. Have any quantum algorithms for encryption been developed? I'm aware about BB84, but it only seems to be a partial…
21
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1 answer

What cryogenic systems are suitable for superconducting qubits?

Is a dilution refrigerator the only way to cool superconducting qubits down to 10 millikelvin? If not, what other methods are there, and why is dilution refrigeration the primary method?
21
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2 answers

Did D-Wave show quantum advantage in 2023?

I would like to know your thoughts on whether or not D-Wave has shown a a smoking-gun example of quantum advantage this year. I am genuinely not quite sure what to think, but I believe the answer to this question is important in understanding the…
21
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1 answer

Quantum phase estimation and HHL algorithm - knowledge of eigenvalues required?

The quantum phase estimation algorithm (QPE) computes an approximation of the eigenvalue associated to a given eigenvector of a quantum gate $U$. Formally, let $\left|\psi\right>$ be an eigenvector of $U$, QPE allows us to find…
21
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1 answer

Is "probabilitistic,universal, fault tolerant quantum computation" possible with continuous values?

It seems to be a widely held belief within the scientific community that it is possible to do "universal, fault-tolerant" quantum computation using optical means by following what is called "linear optical quantum computing (LOQC)" pioneered by KLM…