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A better name for "weakly self-dual CSS codes"

Does anyone know a better name than "weakly self-dual"/"self-orthogonal" for CSS codes where $H_X=H_Z$, for example the Steane code, and the color codes? Details In the discussion in the comments of Example CSS codes and the properties "doubly even"…
Balint Pato
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1 answer

Generalized version of the Hadamard test for $\text{Re} \langle \phi | U | \psi \rangle$

I am wondering if it is possible to generalize the Hadamard test for computing $\text{Re} \langle \phi | U | \psi \rangle$ (different states for left and right operands).
francler
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Upper bound on $\Vert U_1 \otimes U_2 \otimes \cdots \otimes U_k - V_1 \otimes V_2 \otimes \cdots \otimes V_k \Vert$

Let $U_i$ and $V_i$ be unitaries that act on the same subsystems. Can we upper bound the difference between the tensor products of these unitaries, i.e. $\Vert U_1 \otimes U_2 \otimes \cdots \otimes U_k - V_1 \otimes V_2 \otimes \cdots \otimes V_k…
Mohan
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Smallest stabilizer codes with transversal CCZ or CS gates?

It has been shown that $[[15,1,3]]$ quantum Reed-Muller code is the smallest quantum error correcting stabilizer code with a transversal T gate. What are the smallest codes with transversal CCZ or CS gates (which are the other examples of level 3…
tomek
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2 answers

Decomposition of a $4 \times 4$ unitary matrix

I am currently studying the paper "Decomposition of unitary matrices and quantum gates (2012)" and referring to the textbook Quantum Computation and Quantum Information. Among the topics, I am particularly focused on understanding the decomposition…
junghyunHa
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How to characterize the extreme points of the set of CPTP maps?

The set of CPTP maps is convex, therefore, it is enough to perform the needed optimizations over the set of extreme points. Is there any way of characterizing the said extreme points that would lend itself to optimization in general? As I write…
Cain
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Question about Nielson & Chuang Problem 9.2

I am working on the following problem from the book "Quantum Computation and Quantum Information" by Nielsen and Chuang. Problem 9.2: Let $\mathcal{E}$ be a trace-preserving quantum operation. Show that for each $\rho$ there is a set of…
DJD
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Are there tools I can use to test OpenQASM 3 circuits?

I recently added a to_qasm method to stim. An issue I'm having is how to test that the outputs are correct. I can test OpenQASM 2 outputs by giving the output to qiskit, which can parse OpenQASM 2 and execute the result. But it seems that qiskit…
Craig Gidney
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Qutrit Steane Code

There is a well known 5 qubit code $ [[5,1,3]] $ with stabilizer generators $$ XZZXI \\ IXZZX \\ XIXZZ \\ ZXIXZ $$ There is a corresponding $ [[5,1,3]]_3 $ code for qutrits given by \begin{align*} & XZZ^\dagger X^\dagger I \\ & IXZZ^\dagger…
Ian Gershon Teixeira
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Why do current large-scale QCs fail to run Shor's algorithm?

Quantum noob here. Apologies if my question is trivial. According to google, IBM has a quantum computer with 433 qubits. Based on this (How many logical qubits are needed to run Shor's algorithm efficiently on large integers ($n > 2^{1024}$)?) post,…
Adelhart
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Smallest distance 9 self-dual CSS code?

The level-2 concatenated [[7,1,3]] Steane code, and the 4.8.8 color code are both self-dual [[49,1,9]] codes from the CSS family. Is there a distance 9 self-dual CSS code that has less than 49 qubits?
Balint Pato
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2 answers

Validity of quantum channel given pairs of inputs and outputs

Given finitely many pairs of pure states $|x_1\rangle,|y_1\rangle,\ldots,|x_k\rangle,|y_k\rangle\in\mathcal{H}_n$, we can decide if there exists a unitary operator $U$ such that $U|x_i\rangle=|y_i\rangle$ for all $i$ by verifying the…
Wei Zhan
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What is a Hadamard test?

What is a Hadamard test? I have seen this term at many places in video lectures and on various weblinks. A detailed answer on this would be a great help. This is what Wikipedia says, but I really could not understand anything. Edit I have some…
Manu
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Is there a known deterministic counterexample for non-additivity of minimal output entropy?

Hastings has proved that the minimal output entropy is not additive: it may happen that $S_{\mathrm{min}}(\Phi_1 \otimes \Phi_2) < S_{\mathrm{min}}(\Phi_1)+S_{\mathrm{min}}(\Phi_2) $ for quantum channels $\Phi_1, \Phi_2$. His construction is…
Blazej
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Getting intuition on the state-injection relations for the generalized $\exp(-iP \pi/8)$ $T$-gates (ideally using ZX calculus)

In Litinsky's paper, there are many circuits relations, like the one below. The left handside represents the "rotation" $\exp(-i P \phi)$ with $\phi=\pi/8$ with similar definitions for the orange ($\phi=\pi/4$) and gray box ($\phi=\pi/2$) on the…
Marco Fellous-Asiani
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