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CSS codes are the only stabilizer codes with transversal CNOT?

Given a stabilizer code $\mathcal{C}$ then $$ \mathcal{C} \text{ is CSS} \iff \text{CNOT} \text{ is transversal}. $$ The forward implication is well known, see for example Transversal logical gate for Stabilizer (or at least Steane code). On the…
Eric Kubischta
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Can you programatically check whether a given set of gates is universal?

I am wondering if there is an automated way to determine whether a given set of quantum operations is universal. More precisely given a set of 1 and 2 qubit gates can we write a program to determine whether this constitutes a universal gateset? If…
Callum
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Polynomial time reductions vs. Quantum Polynomial time reductions

In computer science, a language $A$ reduces to a language $B$ if there exists a computable function (one that can be computed by a Turing machine) $f_{AB} \colon \Sigma^* \mapsto \Sigma^*$ such that $x \in A \iff f_{AB}(x) \in B$. We call the…
Andrew Baker
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Optimal estimation of quantum state overlap - Circuit implementation?

I've been reading this paper, but don't understand what their optimal method really is, and how it can be realized as a quantum circuit. The paper mentions the "Schur transform" which has a circuit provided in this paper. But is this Schur transform…
Loic Stoic
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Is it known that BQP is not contained within NP?

I recently stumbled upon this paper here and here on the "deep ai" website that claims "BQP is not in NP." I thought that this result would be huge (as a corollary would be that $BQP \neq P$), so I find it strange that I haven't heard about the…
wavosa
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Parametrization of a two-qubit state

A single-qubit state can be parametrized with real $\theta$ and $\phi$ as follows: $$|\psi(\theta, \phi)\rangle = \cos\frac{\theta}{2}|0\rangle + e^{i \phi} \sin\frac{\theta}{2}|1\rangle.$$ I would like to know how to parameterize an arbitrary…
MonteNero
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How accurate is this figure by TIME magazine?

Below is a figure from a TIME magazine edition. I have a few questions regarding this representation of quantum computing: Is saying "0 and 1 at the same time" a correct statement? Isn't the qubit just in a superposition of both states, not "both…
Rydberg
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Is LOCC equivalence the same as LU equivalence?

I'm currently learning on LOCC transformations. In the Dur, 2000 paper, there is a statement that (...) two pure states $|\psi\rangle$ and $|\phi\rangle$ can be obtained with certainty from each other by means of LOCC if and only if they are…
Steve J.
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Inverses and the Clifford Hierarchy

Elements of the (qubit) Clifford Hierarchy are unitary matrices. For a good definition of the Clifford Hierarchy see: Is there a closure property for the entire Clifford hierarchy? While a complete structure theorem for the Clifford Hierarchy,…
Jonas Anderson
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What is a gate-level circuit used in the 2022 Jafferis et al. experiment on Sycamore?

A recently published Nature paper of Jafferis et al. describes an experiment with a handful of qubits performed on Google's Sycamore processor to explore the SYK model in the context of AdS/CFT and quantum gravity, and states that the experiment…
Mark Spinelli
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Is there a CPTP map that takes $\rho_{AB}$ to $\rho_A\otimes\rho_B$?

Given some joint state $\rho_{AB}$, one can find either the marginal state $\rho_A$ or the marginal state $\rho_B$ through a CPTP map. The proof being that partial tracing is indeed CPTP. Is a CPTP map that outputs $\rho_A\otimes\rho_B$ possible?
user1936752
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What is the minimum number of non-Clifford gates does it take to prepare a superposition over all "two-hot" basis vectors?

The generalized W state: $$W_n=\frac{1}{\sqrt{n}}(|100\cdots 0\rangle + |010\cdots 0\rangle + \ldots + |00\cdots 01\rangle)$$ is often thought of as the uniform superposition over all "one-hot" basis vectors, as each such vector has a single qubit…
Mark Spinelli
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Is quantum computer without entanglement no better than anything classically achievable?

Today I saw a tweet by Tom Wong which writes: "Did you know? Without quantum entanglement, quantum computers would be no better than traditional computers." But I remember I came up with papers like this one, which says in the abstract: "We present…
user777
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Prove that a channel is close to acting on only one system

Background Suppose I have a quantum channel $\Phi:B(\mathcal{H}_1)\rightarrow B(\mathcal{H}_1)\otimes B(\mathcal{H}_2)$, such that there is some small $\epsilon$ such that for any two input states $\rho$ and $\sigma$ $$ \Vert \rho - \sigma\Vert_1…
Sam Jaques
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Additive Codes: What are they? And how are they related to stabilizer codes?

I recently encountered the term "additive code" in the answer to my question here What are nontrivial examples of stabilizer codes whose codewords have some $\pm i$ coefficients? Implicit in the answer seems to be the claim that additive codes are…
Ian Gershon Teixeira
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