Quantum Computing Stack Exchange Community Digest

Top new questions this week:

Why do we care about the number of $T$ gates in a quantum circuit?

When reading this question and quickly reading some of the linked papers, I wondered why was the number of $T$ gates specified along the number of controlled-$X$ gates. I've often read that ...

circuit-construction quantum-circuit clifford-group  
asked by Tristan Nemoz 5 votes
answered by DaftWullie 6 votes

What is the meaning of "shots" and "rounds" in Stim?

I'm running simulations using Stim to get logical error rate vs. physical error rates of some quantum error correcting codes (QECC). I looked into the documentation, but I'm confused about the meaning ...

programming error-correction stim  
asked by unknown 3 votes
answered by Craig Gidney 5 votes

Are there direct usefull applications of the quantum Fourier transform not requiring heavy other subroutine

I know that the quantum Fourier transform has many applications such as order finding (which is used in Shor algorithm), phase estimation, etc. However those algorithms require extra subroutines which ...

asked by StarBucK 3 votes

At what depth and for what architecture are random quantum circuits $1$-designs?

I was confused about something related to quantum $1$ designs. Let us recap two facts we know about random circuit ensembles that form a $1$ design. $1$ design, for a quantum circuit over $n$ qubits, ...

quantum-gate quantum-advantage random-quantum-circuit haar-distribution t-designs  
asked by BlackHat18 2 votes
answered by Markus Heinrich 4 votes

How to calculate the threshold for gate fidelity?

I've been interested in gate fidelity lately. In the meantime, I came up with a specific example. Let's think about the encoding of situation $\alpha_0 |0\rangle + \alpha_1 |1\rangle \rightarrow \...

error-correction fidelity  
asked by cryptcipher 2 votes
answered by DaftWullie 2 votes

Doubt in Simple proof of Security of the BB84 QKD

I am not able to understand an argument from Simple proof of Security of the BB84 QKD; I need your help. In page 2 it is mentioned that "Alice can measure her half of the encoded EPR pairs before ...

error-correction cryptography key-distribution bb84 qkd  
asked by IamKnull 2 votes
answered by DaftWullie 1 vote

Does ${\rm tr}(\Pi_z\rho\Pi_z)\le p$ imply $\cal E(\rho)$ and $\cal E(\Pi_{-z}\rho\Pi_{-z})$ are close in trace distance?

Suppose I have a quantum operation $\mathcal{E}$ and a state $\rho$ such that: $$ \operatorname{tr}(\Pi_z \rho \Pi_z) \le p $$ for some probability $p$ and some projection $\Pi_z$ onto some subspace ...

quantum-operation information-theory trace-distance projection-operator  
asked by NoImaginationGuy 2 votes
answered by Quantum Mechanic 1 vote

Greatest hits from previous weeks:

How can quantum computing win 97% of times in coin flipping experiment?

I'm new to this field of science. I'm curious about how quantum computing can win 97% of times in a coin flipping experiment? Refer this link: Ted Talk by Shohini Ghose To give an idea about how ...

asked by Saddam Pojee 5 votes
answered by ahelwer 6 votes

How can I build a circuit to generate an equal superposition of 3 outcomes for 2 qubits?

Given a $2$ qubit-system and thus $4$ possible measurements results in the basis $\{|00\rangle$, $|01\rangle$, $|10\rangle$, $|11\rangle\}$, how can I prepare the state, where: only $3$ of these $4$ ...

quantum-state measurement circuit-construction superposition  
asked by weekens 20 votes
answered by AHusain 11 votes

Building a quantum computer in simulation

If one wants to start building a quantum computer from scratch inside simulations (like how people get to build a classical computer from scratch in the Nand2Tetris course), is it possible? If yes, ...

simulation performance  
asked by ak_nama 14 votes
answered by Sanchayan Dutta 6 votes

What integers have been factored with Shor's algorithm?

Shor's algorithm is expected to enable us to factor integers far larger than could be feasibly done on modern classical computers. At current, only smaller integers have been factored. For example, ...

asked by Lying Dancer 20 votes
answered by Auden Young 16 votes

How do you implement the Toffoli gate using only single-qubit and CNOT gates?

I've been reading through "Quantum Computing: A Gentle Introduction", and I've been struggling with this particular problem. How would you create the circuit diagram, and what kind of reasoning would ...

algorithm quantum-gate gate-synthesis  
asked by Lucas Myers 11 votes
answered by Dripto Debroy 13 votes

Why isn't there a contradiction between the existence of CNOT gate/entanglement and the no-cloning theorem?

Of course I am not implying that I am right and the no cloning theorem is wrong, but I am trying to figure out what is wrong with my reasoning and yet I couldn't find the mistake. Based on Wikipedia ...

entanglement mathematics no-cloning-theorem  
asked by oddcoder 11 votes
answered by Mariia Mykhailova 15 votes

Is there proof that the D-wave (one) is a quantum computer and is effective?

I'm admittedly a novice in this field, but I have read that, while the D-wave (one) is an interesting device, there is some skepticism regarding it being 1) useful and 2) actually a 'quantum computer'....

performance annealing d-wave classical-computing experiment  
asked by Discrete lizard 43 votes
answered by Andrew O 28 votes

Can you answer these questions?

unsymmetric observable estimation by Qiskit

Assume $|i\rangle,i\in[1,m]$ is a set of state, like the Fock states for Fermions. The question is how to compute the quantity ,$\langle i|H|j\rangle,i,j\in[1,m]$, in qiskit. The $H$ here is the qubit ...

asked by ironmanaudi 1 vote
answered by jecado 0 votes

Question regarding the notation of QFT

I have a question about the notation of QFT. I would like to present briefly what my problem is. So given is the QFT as a mapping with: $$|j_1,...,j_n\rangle \rightarrow \frac{(|0\rangle + e^{2\pi i 0....

quantum-fourier-transform notation  
asked by P_Gate 1 vote
answered by Jaimin 0 votes

How many single and double qubit gates are required to create a uniform superposition of vertices of a Johnson Graph J(n,r)?

Can I in $\tilde{O}(r)$ number of gates (single and double qubit) create a uniform superposition of vertices of Johnson Graph $J(n,r)$? I would like to create a state $|\psi\rangle = \frac{1}{\sqrt{n \...

quantum-gate quantum-state circuit-construction  
asked by Subhasree Patro 1 vote
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