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Can Shor's algorithm be done with the same efficiency on an adiabatic quantum computer as on a circuit-based one?

Unfortunately, I cannot find any information on this, so I am asking in this forum if anyone knows, and if so, why this is the case?
BootBootBoot
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Do no-cloning and no-deletion theorems follow one from the other?

I am very new to Quantum Information. I had the following question on two no-go theorems: The No cloning theorem states there is no unitary operator $U$ such that $U|\psi\rangle|0\rangle=|\psi\rangle|\psi\rangle$ for all state $|\psi\rangle$. The No…
solaris_knight
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Is the Deutsch-Jozsa problem in NP?

The Deutsch-Jozsa problem is a problem that quantum computers can solve deterministically, while classical computers cannot. However, there are classical algorithms that can solve it probabilistically. A simple example of such an algorithm…
Andrew Baker
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How to derive the state of a qubit after a partial measurement?

I am trying to solve a problem from the course "Quantum Information Science I" of MIT Open Learning Library, but I get stuck. Here is the problem. Consider the below circuit where the meter sign denotes the measurement with $\{|0\rangle,|1\rangle\}$…
Stéphane
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Equivalence between Quantum Error Correcting codes and uniqueness of the $[\![5,1,3]\!]$ code

In quantum error correction, two stabilizer codes are considered to be equivalent if they differ by a local Clifford transformation or a qubit permutation. Represented as a tableau, these set of transformations establish an equivalence class between…
Jan Olle
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Is it possible to obtain a closed-form expression of the diamond distance between two single-qubit channels?

I would like to compute the diamond norm of the difference of two single-qubit channels $\Phi_1$ and $\Phi_2$. This difference is equal to, for any $2\times2$ complex matrix…
Tristan Nemoz
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Can $2^n$ bits be sent with $n$ instances of quantum teleportation?

So, right now these are two pieces of information I've been told are correct: Quantum teleportation can send a single qubit from Alice to Bob, with two classical bits $n$ qubits can store $2^n$ classical bits of information If both of these are…
Radvylf Programs
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What is a POVM?

I am having a hard time understanding what exactly a Measurement is by its definition? What I read is that a POVM $M$ is defined by its set of elements $M_i$. So is $M$ itself an operator? In circuit diagrams its a little "Measure" box, but I've…
TTa
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Is the Clifford hierarchy finite?

This question is inspired by Is the Clifford group finite? Which shows that that the Clifford group (the second level of the Clifford hierarchy) is finite. (finite meaning finite mod global phases) The Pauli group, which is the first level of the…
Ian Gershon Teixeira
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Why is combined amplitude and phase damping considered sufficient for noise modeling?

In QECC literature, I often come across the "combined amplitude and phase damping channel" as being representative of a realistic noise model which makes sense (as amplitude damping and de-phasing are the two fundamental error processes for a…
Sam
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Why can't we implement fault-tolerant single qubit rotations continuously?

My understanding is that in order to implement single-qubit rotations on logical fault-tolerant qubits one has to do smth like discretizing rotations and using $T$ gates. So, is it the case that given perfect single-qubit rotations of physical…
mavzolej
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Why do black box separations imply oracle separations?

Why does Simon's algorithm show that there exists an oracle $O$ such that $\mathsf{BPP}^O$ is not equal to $\mathsf{BQP}^O$? To show that $\mathsf{BQP}^O$ is larger than $\mathsf{BPP}^O$, one needs to find a language $L$ in $\mathsf{BQP}^O$ that is…
xutinal
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What are the relations between the permutation group and the Clifford group?

I'm trying to understand the relation between the permutation group on all the $2^n$ bitstrings and the Clifford group. My question arises from the fact that the Toffoli gate (which can be thought of as a permutation) cannot be decomposed in terms…
mavzolej
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Is there a non-Clifford gate preserving both $X$ and $Z$ errors?

I would like to know if there exists an $n$-qubit (for $n \geq 2$) quantum gate $G_n$ that preserves both $X$ and $Z$ errors and that is additionnally non-Clifford. In other words, I would like that $G_n$ satisfy $$ \forall P^X_n, \exists E^X_n | \…
Marco Fellous-Asiani
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Thermodynamic Speed Limit to Quantum Computing

There's a lot of mystifying jargon in the field of quantum computation, so I would like to examine some elementary physics to maybe help clarify the assumptions being made. Is it not true that the speed of a real-world reversible computer scales…
user22003
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