Questions tagged [classical-quantum]

For questions about classical-quantum (CQ) states and channels.

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What's the map from any linear classical codes to entanglement-assisted stabilizers codes

When a linear code is self-dual, its parity check matrix can be used to easily define a stabilizer code. From my understanding, thanks to entanglement-assisted stabilizer codes, it is possible to ...
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1 answer
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How does qiskit's CircuitQNN calculate the gradients of circuits?

I'm trying to understand how the gradients are calculated for any given circuit using qiskits CircuitQNN and ...
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Can error correction for a classical algorithm with bit flips be easier than for a general quantum circuit?

Assume one runs a purely classical algorithm on $n$ logical qubits on a physical device with some bit flip probability. Can implementing error correction in this case be any easier than in the case of ...
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Showing that $S(\rho_{XB}||\sigma_{XB})=\sum_{x}p(x)D(\rho_{B}^{x}||\sigma_{B}^{x})$ for classical-quantum states

Having some trouble showing that $S(\rho_{XB}||\sigma_{XB})=\sum_{x}p(x)D(\rho_{B}^{x}||\sigma_{B}^{x})$ for $\rho_{XB}=\sum_{x}p(x)|x\rangle\langle x|\otimes\rho_{B}^{x}$ and $\sigma_{XB}=\sum_{x}p(x)...
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Understanding the association rule between classical to quantum data $|x\rangle=\frac{1}{|\vec x|_2}\sum_{i=1}^d x_i|i\rangle$

I've been reading the paper on Quantum Hopfield Networks by Rebentrost et al. and I'm not sure to quite understand the association rule they mention on page 2. Here's what they say : Consider any $d$-...
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3 votes
2 answers
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Bounding diamond norm distance using probability of error in transmission of classical information

Let us consider an encode, noisy channel and a decoder such that classical messages $m\in\mathcal{M}$ can be transmitted with some small error. That is, for a message $m$ that is sent by Alice, Bob ...
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Efficient simulation of linearly assembled Quantum States

In this paper section 4.2 the author describes how to efficiently simulate linearly assembled quantum states. When describing the procedure to do so the author shows the following circuit: The ...
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2 votes
1 answer
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Prove that for a pure tripartite state $\rho_{ABE}$, $H(RB) = H(RE)$

Let's say we have a pure tripartite state $\rho_{ABE}$ and a completely positive map $\mathcal{R}$, which is defined as: $$ \mathcal{R} : \rho \rightarrow \sum_j \langle\psi_j|\rho |\psi_j \rangle |\...
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8 votes
3 answers
420 views

Why are diagonal Hamiltonians considered classical?

I've been following UT QML course (http://localhost:8888/tree/UNI/PHD/UT-QML) and during their lecture on the Ising hamiltonian, they point out that the hamiltonian of an Ising model without a ...
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4 votes
1 answer
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What is the general form of a classical-quantum state?

In the literature, one comes across the following situation: Alice holds two registers $X$ and $A$ and it is given that $X$ is a classical register. What is the most general way to write down Alice's ...
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Prove that the conditional entropy of a classical-quantum state is non-negative

Let $\rho_{XA}$ be a classical-quantum state, i.e., $\rho_{XA} = \sum_{x} p(x) |x\rangle \langle x| \otimes \rho_A^x$. How to prove that the conditional von Neumann entropy $S(X|A) = S(\rho_{XA}) - ...
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2 answers
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Given averages of powers of position and momentum in quantum mechanics what information can be secured about the wave-function?

Question If I tell you all the averages of powers of position and momentum in quantum mechanics can you tell me the value of the wave-function? What can you tell me about the wavefunction? Is there ...
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1 vote
1 answer
95 views

Trace distance of two classical-quantum state with hashing

Let's say I have a classical-quantum(cq) state $\rho_{XE}$, where the classical part $(X)$ is orthogonal. It's trace distance from another uniform density operator is defined to be: $$ \frac{1}{2}||\...
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1 answer
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Does the quantum Jensen-Shannon divergence appear in any quantum algorithms or texts on quantum computing?

The generalization of probability distributions on density matrices allows to define quantum Jensen–Shannon divergence (QJSD), which uses von Neumann entropy. Does QJSD appear in any quantum ...
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What is the relation between density matrices and phase-space probability distributions?

According to its tag description, a density matrix is the quantum-mechanical analogue to a phase-space probability measure (probability distribution of position and momentum) in classical statistical ...
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Quantum analogues of information theoretic measures: are log probabilities replaced with the density matrix?

Below is a question and an answer. How does quantum information relate to, diverge from or reduce to Shannon information, which used log probabilities? What people are more often interested in are ...
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2 votes
1 answer
108 views

Relating quantum max-relative entropy to classical maximum entropy

The quantum max-relative entropy between two states is defined as $$D_{\max }(\rho \| \sigma):=\log \min \{\lambda: \rho \leq \lambda \sigma\},$$ where $\rho\leq \sigma$ should be read as $\sigma - \...
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2 votes
1 answer
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Is "classical information" the same as "Shannon information"?

does Shannon meet Feynman? Bits underlie classical information measurements in information theory, while qubits underlie quantum information measurements in, what I can only assume to be called, ...
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2 votes
1 answer
49 views

Counting Achievable Operations

I'm struggling to find an analytic way to solve this problem. There are $4! = 24$ possible classical operations on the four 2-Cbit basis states. How many of these are achievable via the classical ...
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3 votes
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What is known about the quantum version of Schoening's algorithm for 3SAT?

Schoening's algorithm for 3SAT can be converted to a quantum algorithm.  The classical circuit representing a 3SAT expression in CNF form can be converted to a quantum version involving reversible ...
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2 votes
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Question about the practical use of super dense coding in information transmission [duplicate]

Question about the practical use of super dense coding in information transmission: We know that by using super dense coding it is possible to transmit 2n classical bits transmitting n qubits, ...
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4 votes
2 answers
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Example of a quantum algorithm better than its classical counterpart which involves only $1$ qubit?

I was reading over the proof of the Deutsch-Jozsa algorithm, which in its simplest case, involves at least 2 qubits. Is there an example of a quantum algorithm that is better than it's classical ...
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2 votes
1 answer
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The effect of available information on random quantum channels

This question is about the effect of available information on random quantum channels. Suppose there are two black box devices. Device 1. We have a black box device with a single qubit in it. Once ...
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3 votes
1 answer
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What does superposition do for quantum probabilistic sampling?

The idea of a qubit being able to exist for several values between 0 and 1 (superposition) makes it sound like it can do alot for probabilistic math problems, but for one task that comes instantly to ...
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2 votes
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Quantum Optimization algorithms

The Harrow-Hassidim-Lloyd (HHL) algorithm for quantum matrix inversion (linear algebra) bridges classical math to quantum math and has been adopted for quantumizing many classical applications, such ...
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2 votes
2 answers
183 views

Translating classical math and code, to quantum math and code

I am starting to see alot of classical quantitative problems such as linear regression being represented in quantum math, which suggests that almost anything based on frequentist statistics could be ...
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1 vote
3 answers
2k views

How to initialize classical register in Qiskit?

I'm working on a Hybrid classical-quantum linear solver. For this, they make a loop on a quantum circuit (ie. below), and each time they change the value of the classical register and apply a X gate ...
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3 votes
1 answer
100 views

Classical and quantum limits to classical copying?

The no-cloning theorem can be sharpened to give quantitative bounds on the fidelity with which an arbitrary quantum state can be copied. Is there a similar picture available for classical copying? ...
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3 votes
1 answer
839 views

Can a quantum computer run classical algorithms?

I realize that fundamentally speaking quantum and classical computers might as well be apples and oranges, and that for very specific problems such as integer factorization with Shor's algorithm ...
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3 votes
1 answer
204 views

Trace distance of two classical-quantum states

I have these two classical-quantum states: $$\rho = \sum_{a} \lvert a\rangle \langle a\lvert \otimes q^a \\ \mu = \sum_{a} \lvert a\rangle \langle a\lvert \otimes r^a $$ Where $a$ are the classical ...
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1 vote
1 answer
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Better Way Of Separating Two CQ-States

I have this cq-state: $$\frac{1}{2} \times (|0\rangle \langle0|_A \otimes \rho^0_E + |1\rangle \langle1|_A \otimes \rho^1_E)$$ Where Alice (A) is classical and an adversary Eve (E) has some ...
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5 votes
0 answers
474 views

Real-life examples of classical-quantum channels

In quantum information theory, classical-quantum channels are considered to be channels whose input is the realizations $x\in\mathcal{X}$ of a classical random variable to a quantum state $\rho_x^B$, ...
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6 votes
1 answer
393 views

Is the set of classical-quantum states convex?

I read about the classical-quantum states in the textbook by Mark Wilde and there is an exercise that asks to show the set of classical-quantum states is not a convex set. But I have an argument to ...
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