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Is the Solovay-Kitaev theorem relevant for modern hardware?

The Solovay-Kitaev theorem (and more recent improvements) explains how to efficiently compile any 2-qubit unitary into any universal (dense) finite set of gates. My question is if this theorem is relevant for modern hardware? Take, for example,…
Nikita Nemkov
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Is Toffoli a fault tolerant transversal gate of the repetition code on bit-flip-error-only qubits?

Suppose you have physical qubits that only have bit flip noise (no phase flip noise, no unwanted measurements, no leakage, no amplitude decay, etc; just unwanted X rotations). Such qubits can be kept alive, protected from the bit flip noise, using…
Craig Gidney
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Reference on MITxPRO Applications of Quantum Computing Professional Certificate Program

Recently I found out the Applications of Quantum Computing Professional Certificate Program that MITxPRO is offering for people interested in quantum computing. I saw that it is consisted of four courses that can be done independently or as a whole…
Josu Etxezarreta Martinez
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$T_2>2T_1$ qubits on the ibm_washington quantum processor

I have been checking out the parameters of the new ibm_washington processor and I have the following doubt about the calibration data provided by them. Checking out the relaxation and dephasing times I found out that some of their qubits are said to…
Josu Etxezarreta Martinez
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Does conjugation by a Clifford send each non-identity Pauli to every other non-identity Pauli with equal frequency?

I see here in Olivia DeMatteo's notes, she states: When we consider the action of the entire Clifford group on a single non-identity Pauli, it maps that Pauli to each of the $d^2 − 1$ other possible Paulis an equal number of times. Since we have…
Quantum Guy 123
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Visualization of Quantum Circuits when using IBM QISKit

I have followed the installation steps, regarding QISKit working environment. For circuit visualization, I've installed latex as in addition to poppler to convert from PDF to images. Afterwards, I followed the example given here. I wrote the code…
user2519
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Why isn't $Ry(\pi/2)$ gate equivalent to Hadamard gate?

I've been experimenting with quantum circuits and can't quite fathom how the difference between states comes together. Speaking in terms of simulations using qiskit, the following code yelds the same results: circuit =…
Ricardo
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Why does a quantum operation being trace-preserving imply that $\sum_k E_k^\dagger E_k=I$?

I am reading Nielsen Chuang Chapter 8. They say that if a quantum operation is trace-preserving, then \begin{equation} Tr\left(\sum_k E_k^{\dagger}E_k \rho\right) = 1 \end{equation} which I understand. They however then claim that as this is true…
alpha
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Maximum number of Stabilizer Generators?

The Pauli group, $P_n$, is given by $$P_n=\{ \pm 1, \pm i\}\otimes \{ I,\sigma_x,\sigma_y,\sigma_z\}^{\otimes n}$$ Abelian subgroups of this which do not contain the element $(-1)*I$ correspond to a stabilizer group. If there are $r$ generators of…
Quantum spaghettification
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Using Classical Shadow to predict quantum state's fidelity has nothing to do with the dimension of the density matrix?

Using classical shadow(or refer to this post for basic things about classical shadow), we can predict linear functions like $Tr(O\hat{\rho})$ with number of copies(referred…
narip
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What quantum channels are considered in quantum communication, and how does this choice affect the construction of error correction codes?

The so-called depolarizing channel is the channel model that is mostly used when constructing quantum error correction codes. The action of such channel over a quantum state $\rho$ is $$\rho\rightarrow(1-p_x-p_y-p_z)\rho+p_xX\rho X+p_yY\rho…
Josu Etxezarreta Martinez
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Enforcing a particular layout mapping in Qiskit

I would like to ask how to set a particular layout during transpiling. I guess that the layout can be set by the initial_layout parameter in the transpiler. However, there are several options that may conflict, namely: layout_method, and…
soara
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Clarification needed regarding quantum "black-box" circuits

$\newcommand{\Ket}[1]{\left|#1\right>}$ I understand that in general quantum black box algorithms (such as the ones which play a part in Simon's & Deutsch's algorithm) implement a quantum circuit to compute some function $f\left(x\right)$ in such a…
Amit
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Why are there eight $T$ magic state and twelve $H$ magic states?

I am learning magic state distillation. We can define the following two states: $$ |T\rangle \langle T | = \frac{1}{2}(I+\frac{1}{\sqrt{3}}(\sigma_x+\sigma_y+\sigma_z))$$ $$ |H\rangle \langle H | =…
Marco Fellous-Asiani
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What is the rank of a quantum channel?

I read the following sentence in a paper: We consider a quantum channel $\mathcal{E}_{\omega}(\rho)=\sum_{i=1}^{r} K_{i} \rho K_{i}^{\dagger}$ where $r$ is the rank of the channel. I didn't find the definition of the rank of the quantum channel…
Sherlock
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