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Why does not Shannon Chain Rule work in Quantum Mechanics

Shannon Entropy conditional variant is H(A/B)=H(AB)-H(B). Its chain rule implies: H(A/BC)=H(AB/C)-H(B/C). The Quantum ...
Avi's user avatar
  • 153
4 votes
0 answers
12 views

Kraus operator identity question

Let a channel $N$ be given in terms of its Kraus operators $K_i$. That is $$N(\rho) = \sum_i K_i\rho K_i^\dagger$$ Is the sum $\sum_i K_iK_i^\dagger$ a meaningful quantity? I know that $\sum_i K_i^\...
Pluto's user avatar
  • 41
1 vote
0 answers
12 views

How does the surface code detect errors on its boundary?

In the image below, we have a distance $3$ surface code. This should detect if there are $d-1 = 2$ or fewer errors. Suppose I have a $Z$ error on both $D8$ and $D9$. This is not detected by any of ...
user1936752's user avatar
  • 2,935
0 votes
1 answer
7 views

Sinter, decode_to_edges_array

Does anyone know if sinter has the capability of decoding to edges array? It's a method in the pymatching. Thanks.
edp23's user avatar
  • 11
0 votes
0 answers
8 views

Efficient Clifford simulation of reduced density matrices and entropy

Suppose I have a Clifford circuit $C$ and I want to estimate the entanglement entropy of a subset of two qubits, say, $\{q_0, q_1\}$, i.e. the quantity $$S(\rho_{q_0 q_1}) = - \text{Tr}[\rho_{q_0 q_1} ...
T.H's user avatar
  • 326
1 vote
1 answer
23 views

How to represent unitary evolution in Python?

How to represent $U(t)$ (a unitary operator) in a code? Is there any package available for that in Python?
saaru darshini's user avatar
2 votes
0 answers
71 views

Why does the Bloch sphere have a radius of 1?

Why does the Bloch sphere have a radius of 1? Thank you so much! I am a quantum newbie, so forgive me if this is basic.
Isha Bhadauria's user avatar
1 vote
1 answer
63 views

Does measurement at the end of all transformations in quantum computing have a specified time?

The concept of measurement in quantum mechanics is usually discussed without specifying how much time such measurement might take. In principle, one can imagine that the time needed to perform ...
quantum novice's user avatar
0 votes
0 answers
8 views

Using Orbital Optimization VQE

How can I use the OrbitalOptimuzationVQE class in qiskit? I want to find the ground state energy if different molecules using OOVQE but I cannot import the orbital optimization vqe class from qiskit. ...
Cheshta Joshi's user avatar
0 votes
0 answers
6 views

Modeling a chemical reaction when there is a catalyst

I'd like to construct potential energy surfaces (PES) for chemical reactions with and without the presence of a catalyst. Something like this The closest paper that is https://arxiv.org/pdf/2007....
Minh Triet's user avatar
0 votes
1 answer
25 views

How to use the classical expressions for qiskit for real backends?

I would like to build a quantum circuit that executes a gate based on mid-circuit measurements. In particular I want to create a $n$ qubit GHZ state using the scheme formulated to this question:https:/...
ty.'s user avatar
  • 143
1 vote
2 answers
61 views

Construct operator for controlled gate with qubits in-between

How can I construct the operator of a circuit with a controlled quantum gate where between the control and target qubits are other untouched qubits. Given a controlled quantum gate $C(U) = I\oplus U$ ...
upe's user avatar
  • 237
3 votes
1 answer
600 views

Expressing a quantum state as a polynomial

Let us consider the state $\left|\psi\right>$ obtained by applying $m$ 1- and 2-qubit gates to $n$ qubits, starting from the state $\left|0,0,\dots\right>$. Let us express it as: $$ \left|\psi\...
Doriano Brogioli's user avatar
1 vote
1 answer
51 views

What is the input when simulating a quantum state?

Currently I am simulating a quantum gate using verilog. I learned that: $$ |\psi\rangle = \alpha|0\rangle + \beta|1\rangle $$ I want to ask: when simulating, should I let alpha and beta be complex ...
Bakeu's user avatar
  • 11
2 votes
0 answers
46 views

Is BQP contained in BPP with Quantum Phase Estimation (QPE) oracle?

I am trying to see if the below proposition holds: Proposition-1: $BQP\subseteq BPP^{QPE}$. Here, QPE is the Quantum Phase estimation algorithm. QPE takes an eigenstate and the unitary matrix as ...
Manish Kumar's user avatar
0 votes
0 answers
17 views

coding a hamiltonian for an ion trap system

How do I represent $$a_k ∣n_1 n_2 n_3 ,,,,n_n⟩ = √nk-1 ∣n_1 n_2 n_3 ,,,,n_n⟩$$ and $$a_k^\dagger ∣n_1 n_2 n_3 ,,,,n_n⟩= √nk-1 ∣n_1 n_2 n_3 ,,,,n_n⟩$$ in python(qutip or qiskit preferably) and where ...
saaru darshini's user avatar
3 votes
0 answers
18 views

Gradient-free optimization in Qiskit without using pre-defined classes

Basically I want to build a gradient-free optimizer that classifies a very simple dataset (e.g. the sklearn make_moons) using scipy.optimize (Nelder-Mead or Powell ...
Kian's user avatar
  • 31
2 votes
1 answer
47 views

Quantum Error Correction Difficulties: "Measurements destroy quantum information" Intuition

Context: In section 10.1.1, Nelson and Chuang describe the difficulties QEC faces compared to classical error correction. Particularly that Measurements destroy quantum information. Shor states in ...
vollautomatthi's user avatar
0 votes
0 answers
15 views

Config (setting) file choices for Python

Before raising my questions, I am aware there are similar questions on other websites that have been answered pretty much in very good detail, but I am interested in asking my questions from a quantum ...
Rex's user avatar
  • 25
4 votes
1 answer
207 views

Quantum error correction references

I would like to understand more about QEC, such as surface codes, error codes, and qLDPC codes. For quantum algorithms beyond the Nielsen and Chuang book the lecture notes by Andrew Childs are a very ...
NYG's user avatar
  • 389
1 vote
0 answers
59 views

Generating Equal Amplitude Superposition States from Another Equal Amplitude Superposition State

Can we prepare a state regarding a transformation in quantum computing that seems to generate another equal amplitude superposition state when applying a Hadamard gate? Specifically, I observed that ...
Aman's user avatar
  • 493
0 votes
1 answer
30 views

How to use stim to implement a specific circuit

I'm doing a QEC job, and I want to apply an error like $U_{err}(\theta) = \prod_j e^{-i\frac{\theta_j}{2}P_j} = \prod_j (I\cos(\frac{\theta_j}{2}) - iP_j\sin(\frac{\theta_j}{2}))$, where $\theta_j$ is ...
Yule Su's user avatar
0 votes
1 answer
58 views

How to introduce non-linearity into a quantum circuit?

What are the known ways to encode or introduce non-linear functions/operators into a quantum circuit?
ty.'s user avatar
  • 143
0 votes
0 answers
12 views

relationship between helstrom operators acting on different pairs of quantum states

Let $\rho_1, \rho_2, \rho_3, \rho_4$ be arbitrary single-qubit density matrices. Let $A$ be an Hermitian operator and its spectral decomposition as $A = \sum_i \lambda_i \lvert i \rangle \langle i \...
user185671631's user avatar
0 votes
0 answers
21 views

Is there value in developing a 'physical/relativstic' QIT (discussion)?

My motivation for asking this question is that I've recently been captivated by representation theory and I am incredibly interested in studying the symmetries behind different the operators in QIT. ...
HugeGroupGuy's user avatar
3 votes
1 answer
33 views

What is the general form for GHZ and W class states?

I am reading the following paper on mixed three-qubit states. It states that any three–qubit pure state can be written as (equation 1 of the paper) $|\psi_{GHZ}\rangle=\lambda_0 |000\rangle+\lambda_1 ...
Anindita Sarkar's user avatar
1 vote
1 answer
62 views

How cat state is constructed?

Context: On Wikipedia, a cat state (2-component) is defined as $$ |\text{cat}_+\rangle = C_+(|\alpha\rangle + |-\alpha\rangle) $$ $$ |\text{cat}_-\rangle = C_-(|\alpha\rangle - |-\alpha\rangle), $$ ...
Martin Vesely's user avatar
2 votes
1 answer
190 views

Classical computation required in Shor's algorithm: are they heavy?

A quantum computer also requires to perform classical computations. I would like to know if to implement Shor's algorithm, there is a heavy classical computation cost (i.e. that would require a ...
HelloMan's user avatar
  • 123
1 vote
1 answer
32 views

How to suppress long parameters list that appears in the initialize gate?

Below is a simplified code which I am using for a quantum circuit. ...
Shravan Patel's user avatar
0 votes
0 answers
20 views

BQSkit Selecting Starting Circuit Structure

Background On the BQSKit repository, there is a nice example of using the qfactor algorithm to instantiate a 3-qubit Toffoli circuit. For this to work, however, it is first necessary to specify an ...
Shadow43375's user avatar
1 vote
0 answers
44 views

Doubt in Shor-Preskill's proof of security proof of BB84

I was going through the proof of security of the modified Lo-Chau protocol, which eventually leads to the proof of security of BB84. In the error correction step, Nielson-Chuang mention that any ...
Schroedinger'sStupid's user avatar
4 votes
0 answers
77 views

Where does this upper bound relating the $T$ count and $H$ count come from?

I am reading this paper on optimisation of the Hadamard gate count (Optimal Hadamard Gate count for Clifford + $T$ synthesis of Pauli rotations sequences). The idea of the paper is to optimise the ...
Callum's user avatar
  • 1,015
0 votes
0 answers
21 views

Better optimization of bounds on sums of Pauli strings?

I'm trying to bound a quantity $||\sum_i \alpha_i P_i ||$ where the $P_i$ are arbitrary Pauli strings, $||.||$ is the operator norm (max eigenvalue) and $\alpha_i$ are arbitrary real coefficients. If ...
Hans Schmuber's user avatar
3 votes
5 answers
3k views

The heart of all of quantum physics is superposition

I am going to teach an introductory course on quantum information and I thought about this statement that I want to give at the very beginning. Would you agree on that? From my perspective, every ...
relativeentropy's user avatar
0 votes
2 answers
27 views

Does $\frac{I + K}{2}\otimes\frac{I+L}{2} = \frac{I+K\otimes L}{2}$ hold for operators $K,L$ acting on different subsystems?

Let's index $i= 1, 2$ be the index representing different systems. A $Z_i$ projective measurement has projectors $P_i = \{ \frac{I+Z_i}{2}, \frac{I-Z_i}{2} \}$. One can verify that the measurement $...
user1936752's user avatar
  • 2,935
0 votes
2 answers
27 views

Quantum Computing - via Qiskit - error 403

A year ago, I registered in the IBM Quantum Computing app, which provides access to quantum computers and to simulators. I got an API key, and was able to run some programs. However, lately, I try to ...
JDias's user avatar
  • 11
6 votes
1 answer
399 views

Happy 30th Anniversary to Shor's Algorithm! How challenging was the review process when it was first announced?

Shor's algorithm dropped 30 years ago sometime in April, 1994. Peter Shor has given many wonderful accounts of the early history of the field and of what sparked his particular interest. Shor has been ...
Mark Spinelli's user avatar
1 vote
1 answer
47 views

How are qubits actually implemented in terms of hardware?

I am new to quantum computing and just have a beginner question. I am fascinated by the subject. Say I have the qubit \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{bmatrix} I ...
Fraser's user avatar
  • 11
1 vote
1 answer
76 views

Are there standard forms for non-additive quantum codes?

Stabilizer codes have a well known standard form for the stabilizers, logicals and destabilizers. Are there any counterparts for non-additive codes? In particular I'd like to get a standard form ...
unknown's user avatar
  • 2,148
1 vote
0 answers
9 views

Can dimensionality reduction be used to simplify data before using an optimization algorithm?

I am attempting to use a quantum algorithm, like a QAOA, to solve an optimization problem. I saw that qPCA can be used to simplify datasets and make them easier to analyze. Can quantum optimization be ...
Mihir Macwan's user avatar
2 votes
0 answers
52 views

Does no-cloning imply zero capacity of antidegradable channels?

I read that (paraphrasing, see below) "antidegradable channels have zero capacity because of the no-cloning theorem". Is there a formal derivation of the capacity of an antidegradable ...
forky40's user avatar
  • 6,878
2 votes
1 answer
98 views

Non-linear quantum mechanics and NP-complete problems

Thanks to user Cuhrazatee (comments to my other question here) I came accross article Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems by D. Abrams and S. ...
Martin Vesely's user avatar
3 votes
0 answers
37 views

Proof that the relative entropy satisfies $S(\rho\|\sigma)=S(T\rho\|T\sigma)$ iff $\hat TT\rho=\rho$, $\hat TT\sigma=\sigma$ for some $\hat T$

To prove the saturation condition for the strong subadditivity of the von Neumann entropy, the authors of [HJPW2004] make use of the following characterisation of when the monotonicity of the ...
glS's user avatar
  • 25k
3 votes
0 answers
20 views

What are examples of states saturating the strong subadditivity of the von Neumann entropy?

A well-known property of classical distribution is that they satisfy strong subadditivity, meaning that for any tripartite joint probability distribution $p(x,y,z)$, we have the inequality $$H(AB)+H(...
glS's user avatar
  • 25k
1 vote
0 answers
58 views

How to express a traceless matrix in Pauli basis

This question is probably too obvious, so sorry beforehand. We know that the generalized Pauli elements $P\in \mathcal{P}_d \setminus {\mathrm{Id}_d}$ in Sylvesters representation, hence not Hermitian,...
relativeentropy's user avatar
1 vote
0 answers
26 views

Adding an Extra Qubit into a Quantum Circuit

I am a beginner in quantum computing and am learning about parameterised quantum circuits (in the context of quantum neural networks). What effect does adding an extra qubit into a quantum circuit ...
Rij's user avatar
  • 23
4 votes
1 answer
99 views

Can we find a product of single-qubit states that is orthogonal to a stabilizer codespace?

Let's consider a single-qubit pure state $$\rho=\rho(x, y,z)=\frac{1}{2}(I+xX+yY+zZ)$$ with $x^2+y^2+z^2=1$. Can we show the following statement is true: For any $n$-qubit tensor product states $\rho^{...
Yunzhe's user avatar
  • 671
3 votes
0 answers
29 views

How to create a quantum algorithm to determine unknown coefficients in a linear function

I am trying to solve the following practice question shown below. I am stuck on part (c) where I must design a quantum algorithm to solve the stated problem. I can tell that the solution is probably ...
Featherball's user avatar
1 vote
0 answers
9 views

Feedback control with feedback Hamiltonian vs quantum error correction

I stumbled upon a pretty old paper from 2003 by C. Ahn, H.M. Wiseman and G.J. Milburn. They use quantum control with feedback Hamiltonian to perform error correction. The paper proposes to encode $n-1$...
MonteNero's user avatar
  • 2,561
2 votes
1 answer
308 views

How can the depolarizing channel be a quantum operation?

In Quantum Computing: From Linear Algebra to Physical Realizations it states that A quantum operation maps a density matrix to another density matrix linearly But let $\rho\in M_2$ be a density ...
John Hippisley's user avatar

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