All Questions

I am an electrical engineer and have been learning about quantum computing for the last year, and I can hardly believe what I read and hear. It is becoming clearer to me, but it's a very difficult ...

So starting with an up particle: $$ \lvert \uparrow \rangle = \begin{bmatrix} 1 \\ 0 \\ \end{bmatrix} $$ My understanding is that you can measure $\lvert \uparrow \rangle$ in $X$ and have ...

I knew that we usually use circuit instead of Turing machine in Quantum computation. In a deterministic Turing machine one has transition rules, $$ \delta: Q\times\Gamma\rightarrow Q\times\Gamma\...

I’m studying the paper Expressive power of tensor-network factorizations for probabilistic modeling by Glasser et al. In equation S6 (page 2 of supplementary material) it is claimed that a 2-local ...

I’m starting an engineering degree in computer systems and I’m starting to get really interested in quantum computing. First of all, I don’t know where or how to start and I would really like to learn ...

Used memory-profiler to check why I get memory spikes in what I though were small circuits. The circuit itself is constructed using ...

I am a Swiss student and have 2 years left at school. In these 2 years, I have to do a special piece of work on a specific subject. I decided to do it on quantum computers. For this, I have to find a ...

I'm trying to solve the following question: "Prove that one way to compute $\mathrm Tr_B$ is to assume that someone has measured system $B$ in any orthonormal basis but does not tell you the ...

I'm curious if there's any consensus on this question among actual practitioners, but please feel free to close it if it's hopelessly opinion-based (since we've only taken baby steps toward the ...

Take the Bell state $$\frac{1}{\sqrt{2}}\left(|00\rangle +|11\rangle\right) $$ and measure the first qubit with respect to some axis $\vec{n}_1$ on the Bloch sphere, i.e. measure the observable $$\vec{...

$\def\braket#1#2{\langle#1|#2\rangle}\def\bra#1{\langle#1|}\def\ket#1{|#1\rangle}$ When using Grover's algorithm to invert a function $f\colon \{0,1\}^m \rightarrow \{0,1\}$, an ancilla bit is used in ...

Say we had a Hadamard-like gate with the -1 in the first entry instead of the last. Let's call it $H^1$. $$H = \begin{bmatrix}1&1\\1&-1\end{bmatrix}$$ $$H^1 = \begin{bmatrix}-1&1\\1&...

In the answer to this question about random circuits, James Wootton states: One way to see how well we [fully explore the Hilbert space] is to focus on just randomly producing $n$ qubit states. ...

The Multiple-Control Toffoli (mct) gate takes as input: 1. a register containing the control qubits, 2. the target qubits and 3. a register containing ancilla qubits. I don't know how many ...

I really want to show something with others and try to do something for this

I used the following code. Can anyone say what that error is about? ...

IBM announced a 53 qubit chip. Will the advertised chip be available for non-paying users, or only to IBM clients?

I would like to prepare an initial state for variational quantum algorithms. The initial state should include the following states: $|000\rangle, |010\rangle, |100\rangle$, and $|001\rangle$. How ...

I am trying to implement 7 control toffoli gate in qiskit .

In almost all research on (universal) quantum computation the common models assumed from the outset are either the quantum circuit model with unitary gates, the measurement-based one-way model or the ...

We know that the Pauli matrices are: $$\sigma_x = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}, \sigma_y = \begin{bmatrix}0 & -i \\ i & 0\end{bmatrix}, \sigma_z = \begin{bmatrix}1 & ...

I cobbled together a few programs with Qiskit several months back which worked fine on both the BasicAer simulators and the actual IBMQ computers. However, when I tried to revisit them recently, ...

I am new to quantum computing and I am having trouble understanding the notation used for input/output qubits in quantum gates. I will use the CNOT gate as an example. In several (most) references I'...

I think there can't be a computer running software without having a clock signal. A fast classical computer has a clock rate between 4 to 5 GHz. If quantum computers are so much faster they must ...

What was the first paper/who was the first person to phrase anyon theory in terms of tensor categories? Going through Wilczek's book on fractional statistics, some of the reprinted papers anticipate ...

I am still confused when I am trying to use the IBM Q composer to reproduce some quantum circuits I found in different papers, and I am wondering if it is because there are two ways to represent a ...

Say, we have a $\require{mhchem}\ce{^87Rb}$ atom having an electric dipole transition on the $D_{1}$ line and we have two hyperfine ground states, one on $F = 1$ and one on $F = 2$ level. So, we take ...

Alice is sending a state to Bob via authenticated quantum channel. Can Eve apply a Unitary transform on the above state from Alice and send it back to Bob?

Construct a reversible operator that implements the unary gate 0-operator (an operator that acts on one bit and returns 0 independently of the input.). How many bits are necessary?

Show that it is impossible to implement a reversible OR operator with less than three bits

I know for instance I can derive a cccX gate using 2 Toffoli gates on 5 qubit wire or ccccX with 3 Toffoli gates and 7 qubits and so on. you will notice the depth is increasing as the number of ...

I was going through a paper in which protocol said that the party computes modulo 'd' sum of other party secrets directly. It was not mentioned that the computation is classical. Can I assume that it ...

I was skimming through the Google quantum supremacy paper but got stuck on this section: For a given circuit, we collect the measured bit-strings $\{x_i\}$ and compute the linear XEB fidelity [24-...

Are there quantum algorithms for Prolog (SLD resolution - unification and depth-first-search) or for automated theorem proving in general (negation, resolution, and SAT)? Usually automated theorem ...

I need to do some popularization of science for an event, and I would like to talk about the "best" applications of quantum computing. I know there is code-breaking (Shor algorithm), simulation of ...

It is known that every state $\rho$ of a $d$-level system (or if you prefer, qudits living in a $d$-dimensional Hilbert space) can be mapped into elements of $\mathbb R^{d^2-1}$ through the mapping ...

I'm told that the input register is in little-endian format. But the vscode gives me error telling me that it is wrong argument for QFT even after using a suitable converter. Am I missing something ...

I know just the basics of quantum computer i.e. superposition, entanglement, gates and few other kinds of stuff. Now the question is it possible to transfer a trained machine learning model from IBM ...

...

What is the cost of implementing the Quantum Fourier transform (QFT) in a classical computer? We know we require at least $\log{n}$ depth quantum circuits to do a QFT in a quantum computer, with $n$ ...

A source constantly produces a stream of photons in one of the following states $$|\varphi_1\rangle=\dfrac{1}{\sqrt2}(a|00\rangle+ b|01\rangle+c|10\rangle+d|11\rangle)$$ $$|\varphi_2\rangle=\dfrac{1}...

I'm prepared to explore quantum computing which is completely new to me. Searching for a while on the Internet, I found IBM Qiskit which is an Open Source software necessitated for Quantum Computing. ...

A Pauli channel is defined as a convex combination of Pauli operators, i.e. $\epsilon_{\text{Pauli}} (\rho)=\sum_{j} q_j\sigma_j\rho \sigma_j$, where $0 \leq q_j \leq 1$ and $\sum_j q_j=1$. Now, I ...

I'm trying to show/convince myself the following statement is correct (I haven't been able to find any similar posts): "There is no reversible quantum operation that transforms any input state to a ...

Let's say 1000 years from now powerful quantum computers are still a matter of fiction and no useful calculations can be carried out using them. Would this mean that the entire industry of quantum ...

I found this explanation. "The Hadamard gate can also be expressed as a 90º rotation around the Y-axis, followed by a 180º rotation around the X-axis. So $H=XY^{1/2}H = X Y^{1/2}H=XY^{1/2}$." Can ...

Given that classical physics emerges from quantum physics on a macroscopic scale, and all quantum operators are unitary, how are we able to perform non-unitary operations (such as setting a register ...

I'm studying Quantum Computing: A Gentle Introduction. On page 33, Section 3.1.2, after defining tensor product with 3 properties (distribution over addition on both left and right, scalar on both ...

I am having trouble understanding the following step. From: $$\operatorname{trace}\left(\sum_z |z\rangle\langle z| \rho_A |z\rangle\langle z| * \log( \sum_z |z\rangle\langle z| \sum_x |\langle x|z \...

I'm trying to understand if there is some sort of formula or procedural way to determine if a vector is separable or entangled – aka whether or not a vector of size $m$ could be represented by the ...