All Questions

For example in grover search algorithm, assuming that the amplified amplitude is $\alpha$ , is it possible to perform this operation : $\alpha |0...\rangle + \beta |1...\rangle \longmapsto \beta|0...\...

I just got started with Qiskit. When I tried to save my account with the API token from IBMQ website, I got the error: ...

I don't understand it. But suppose you have a state of two qubits in superposition and it looks like $|10\rangle-|11\rangle$. Now you have in your circuits two gates one is a controlled-NOT from the ...

I started working in Qiskit, and here is an example of how gates of a circuit are represented graphically in LaTeX format: Obviously, $R_y(\theta)$, is a y rotation by a certain angle. But all the ...

In designing reversible circuits one of the useful circuits is the decoder. The operation of a decoder is naturally reversible, so it makes sense to be able to create one with no garbage outputs. ...

Recently, a series of research papers have been released (this, this and this, also this) that provide classical algorithms with the same runtime as quantum machine learning algorithms for the same ...

My question is very simple. I know there is a method to add a control to previously defined gates. I saw in the API of cirq that there is a command Controlled gate (here). I'm not understanding though ...

Bell’s inequality is $$S = P(a,b)-P(a,d)+P(c,b)+P(c,d) \leq 2,$$ which is calculated as $$S = ab – ad + cb + cd \leq 2.$$ The CHSH version is: $$E = \frac{N_{11} + N_{00} - N_{10} -N_{01}} {N_{11} + ...

Question: For 2x2 and 2x3 systems, is the partial transpose the only positive but not completely positive operation that is possible? Why this came up: The criteria for detecting if a state $\rho$ is ...

The concurrence for a state $\rho$ as defined here is \begin{equation} C(\rho) = {\rm max}\{0, \lambda_1-\lambda_2-\lambda_3-\lambda_4\}. \end{equation} Where $\lambda_i$ are the eigenvalues of matrix ...

What are the main pros of using this book and why does nearly every paper cite it? What is so special about it? It also has a tag solely devoted to it on this site. This tag is also quite popular ...

Can one replace Nitrogen with Phosphorus and Carbon with Silicon and so on? What would be the conditions that would preclude such a realisation? Are there any implemenations so far?

I am attempting to run the following on a remote backend through QISkit: ...

In the book by Chuang and Nielsen they prove that controlled U operations can be made out of CNOTs and single qubit gates. But then they go on to prove that they are universal by showing that every n ...

Craig Gidney's blog has some .gifs which directly link to the corresponding simulation on Quirk. For example: Grover Search Delayed Eraser Is it possible to create these .gifs from within Quirk? Or ...

I understand in Shor's algorithm we use quantum computers to find the period of a function which can then be used to find N, and we increase the probability of observing the state with the correct ...

Suppose $x \in \{0,1\}^n$. The standard way to make a query is with an oracle $O_x$ that given an input $|i,b \rangle $ returns $|i,b \oplus x_i \rangle$. Via the phase kick-back trick, this can be ...

What does quantum teleportation mean? Is it something that will allow us to send information faster than the light? Can we teleport a human with it?

When an RF pulse is interacting on resonance with a transmon qubit, it leads to rotation of the qubit around an axis in the XY plane (in a reference frame rotating in the transition frequency of the ...

I'm learning how to use the cirq library. Every time I set up a circuit the starting state of the qubits is $|0000..0\rangle$. Is there any way to make the starting state different? I'm thinking of ...

How can a pure two-qubit state $|\psi\rangle = a |00\rangle + b|01\rangle + c|10\rangle + d|11\rangle$, be written in the following form \begin{equation} |\psi_{\alpha}\rangle = \sqrt{\alpha}|01\...

I'm just wondering how one should go about using parametrised values and the Symbol object that gets resolved at runtime? For example, if I would like to implement the gate $R_x(\theta) = e^{-i\theta/...

I'm trying to figure out how to simulate the evolution of qubits under the interaction of Hamiltonians with terms written as a tensor product of Pauli matrices in a quantum computer. I have found the ...

I ran the Grover's Algorithm for 3 Qubits on the IBM Q platform (ibmqx4) and the results of the simulation and the actual computer differ a lot. The screenshots of the circuit and the results are ...

We often seek to decompose multi-qubit unitaries into single-qubit rotations and controlled-rotations, minimising the latter or restricting to gates like CNOTs. I'm interested in expressing a general ...

I've been trying to decompose the ProjectQ objects and I could manage to decompose non-controlled gates and daggered gates. But I noticed that the object of a controlled version of a gate is the ...

For example, we can create a single qubit state with a polar angle of $\pi/2$ with the Hadamard gate. But, can we create a state such as this, $$\Psi = \cos(\pi/8)|0\rangle + \sin(\pi/8)|1\rangle$$ ...

In QC and QI by Chuang and Nielsen, they state that the $P_U$ of operation $U$ acting on $\psi$ can be reached by $\langle \psi |U^{\dagger} M U |\psi\rangle$. Where $P_U$ (or $P_V$) is the ...

I just started programming in Q# and I wonder if the coding for Q# in classical computer would be the same as coding in a quantum computer. Obviously, these 2 kinds of computers work differently, so I ...

In Wiseman et al. (2007), in the process of deriving necessary and sufficient conditions for the steerability of some classes of states, the authors show (lemma 1, page 3) how to construct an optimal ...

Assume that we know a quantum state and the result of applying an unknown unitary $U$ on it. For example, if the quantum states are pure qubits, we know $|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$ ...

When faced with exercises like these, I find it hard to know how to construct the circuits due to the amount of input one needs to account for. I have seen the solution provided here however, I don't ...

I don't really know the difference between projective measurement and regular measurement or POVM. Until now, wherever I read about the subject I saw that the amplitude describes the probability of ...

Since quantum computer with $n$ qubits is described by a $2^{n}\times2^{n}$ unitary matrix is it equivalent to an oracle that can do multiplication of large matrix and return $n$ numbers computed ...

I'm looking for fast code, or a fast algorithm, for checking if a given state vector $A$ can be transformed into another state vector $B$ using only the Pauli operations $X$, $Y$, $Z$. The naive ...

In other words, will factoring research remain solely in the classical world or are there interesting research on-going in the quantum world related to factoring?

I have questions regarding quantum teleportation, which keep confusing me. Suppose Alice and Bob are in the same inertial frame $K$, and at time $t$ (in $K$) Alice teleports a quantum state to Bob. ...

Is there a way to create a rotation gate which has half the angle of some implementable gate? I am looking to implement a gate on Quirk which allows for standard time-dependent rotations $$R_x(\...

There is a vast amount of new notations which would be new even to Ph.D. in math. How on Earth can I catch up with all of this? Is there a place online which is devoted to the QC syntax? I would ...

I have updated qiskit module but unfortunately, it doesn't work it says ...

I was wondering why till date Grover search has been implemented only till 3 qubits (corresponding to size of database = 8). Refer this paper The reason why I ask is that we have much larger sized ...

Consider the modular exponentiation part of Shor's algorithm which in many works is just referred to as $$U_{f}\sum^{N-1}_{x = 0}\vert x\rangle\vert 0\rangle = \vert x\rangle\vert a^{x}\text{ mod }N\...

In this paper Quantum Circuit Learning they say that the ability of a quantum circuit to approximate a function can be enhanced by terms like $x\sqrt{1-x^2}$ ($x\in[-1,1])$. Given inputs $\{x,f(x)\}$, ...

I'm using the SWAP test circuit for implementing a qubit registers comparison From the documentation I could find I've understood it can be applied to input qubits |$\alpha\rangle$ and |$\beta\...

I saw an example which takes a 2 level matrix. Which is a $8\times8$ matrix that acts non trivially only on 2 levels of only states $|000\rangle$ and $|111\rangle$. The way they do it is by using a ...

I'm curious about how to form arbitrary-sized uniform superpositions, i.e., $$\frac{1}{\sqrt{N}}\sum_{x=0}^{N-1}\vert x\rangle$$ for $N$ that is not a power of 2. If this is possible, then one can ...

I am able to apply multiple measurements (2) to the same qubit system. However, I would like to get the counts right after each measurement is executed. I realize that the counts should be the same ...

Is there a polynomial time and polynomial space quantum algorithm for finding a 4 colouring of any loopless planar graph?

After reading through Shor's algorithm, I have a few questions about the probability of factoring semiprime number out. Here is some background of the question. To factor a semiprime number $N$ such ...

I am new to quantum computing and saw this argument on this site but I don't understand it. First of all, I don't understand what is exactly meant by 'reversible'. Because even if you had a unitary ...