All Questions

1
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1answer
27 views

Is there a way to reverse the amplitudes of a quantum system?

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...\...
1
vote
1answer
18 views

Cannot load account with Qiskit

I just got started with Qiskit. When I tried to save my account with the API token from IBMQ website, I got the error: ...
0
votes
1answer
63 views

What is the meaning of the state $|1\rangle-|1\rangle$?

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 ...
1
vote
0answers
17 views

Qiskit gates in LaTeX representation: notation meaning [duplicate]

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 ...
3
votes
1answer
43 views

Garbage-Free Reversible Binary-To-Unary Decoder Construction

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. ...
9
votes
0answers
71 views

Quantum machine learning after Ewin Tang

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 ...
3
votes
1answer
28 views

How to add control to gates in Cirq?

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 ...
6
votes
0answers
66 views

How is Bell’s Inequality converted to the CHSH inequality?

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} + ...
3
votes
1answer
34 views

Partial Transpose and Positive Operators

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 ...
2
votes
1answer
47 views

Concurrence for a two qubit state

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 ...
0
votes
0answers
50 views

Why is Nielsen and Chuang book so popular in this field? [on hold]

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 ...
2
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0answers
15 views

Can one make NV centred type qubits from analogus materials in the periodic table?

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?
2
votes
1answer
27 views

Consistent QISkit error: “All devices are currently unavailable”

I am attempting to run the following on a remote backend through QISkit: ...
2
votes
1answer
60 views

If CNOTs and single qubit gates are universal then why do we need to prove that controlled U operations can be composed by them as well?

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 ...
4
votes
1answer
37 views

Creating .gifs corresponding to Quirk simulations

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 ...
4
votes
1answer
62 views

Why do we use the quantum superposition for a period instead of factors in Shor's algorithm?

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 ...
7
votes
2answers
82 views

Equivalent unitary transformations

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 ...
1
vote
1answer
73 views

Can we teleport a human or send information faster than light using quantum teleportation?

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?
4
votes
1answer
53 views

Interaction of an RF pulse with transmon qubit

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 ...
3
votes
1answer
22 views

How to set a starting state in cirq?

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 ...
6
votes
2answers
87 views

A two qubit state in a special form

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\...
3
votes
1answer
24 views

Using parametrised values and 'Symbols' in Cirq

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/...
7
votes
2answers
74 views

Simulate hamiltonian evolution

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 ...
4
votes
3answers
75 views

Why is there a difference between the simulation results and the actual quantum computer results?

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 ...
2
votes
1answer
83 views

Decompose a general two-qubit gate into general controlled-qubit gates

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 ...
2
votes
0answers
49 views

ProjectQ - In which part of the controlled gate object are the control bits scored

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 ...
3
votes
1answer
49 views

Is it possible to create a superposition in IBMQ QISkit which has probability amplitudes $|a|\neq |b|$?

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, $$\Psi = \cos(\pi/8)|0\rangle + \sin(\pi/8)|1\rangle$$ ...
0
votes
1answer
69 views

Why does $|P_U − P_V |$ equal $\langle \psi |U^{\dagger} M U|\psi\rangle −\langle \psi |V^{\dagger} M V |\psi\rangle$?

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 ...
1
vote
2answers
66 views

Is programming in quantum computer same as programming in quantum simulator in classical computer?

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 ...
4
votes
0answers
19 views

Construction of optimal ensemble to show quantum steerability

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 ...
6
votes
1answer
28 views

If $|\psi\rangle, U|\psi\rangle$ are known, how many pairs of such qubits are required to find the operator $U$?

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 $|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$ ...
5
votes
2answers
63 views

Constructing a circuit which performs the transformation $|x,y\rangle$ $\rightarrow$ $|x, x + y\text{ mod } 4\rangle$

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 ...
3
votes
1answer
50 views

Do the probability amplitudes describe the probability of projective measurement?

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 ...
6
votes
1answer
90 views

Is quantum computer equivalent to Turing machine with matrix multiplication oracle?

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 ...
8
votes
2answers
105 views

Fast way to check if two state vectors are equivalent up to Pauli operations

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 ...
4
votes
0answers
59 views

Does Shor's algorithm end the search for factoring algorithms in the quantum world of computation?

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?
5
votes
0answers
64 views

Quantum teleportation with moving Alice and Bob

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. ...
2
votes
1answer
51 views

How to implement a $\frac{\theta}{2}$ rotation from $\theta$ rotation?

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(\...
2
votes
1answer
56 views

Is there a place online where I can catch up with all the notational syntax associated with quantum computing?

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 ...
1
vote
1answer
68 views

QISKit warrning on marshmallow

I have updated qiskit module but unfortunately, it doesn't work it says ...
8
votes
1answer
77 views

Current limits on Grover search space

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 ...
4
votes
0answers
33 views

How exactly does modular exponentiation in Shor's algorithm work?

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\...
3
votes
0answers
25 views

Why does $x\sqrt{1-x^2}$ enhance the ability to approximate analytical functions in quantum circuit learning?

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 $\{x,f(x)\}$, ...
3
votes
2answers
92 views

SWAP test inputs

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\...
3
votes
0answers
24 views

Decomposition of any 2-level matrix into single qubit and CNOT gates

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 ...
2
votes
1answer
43 views

Forming states of the form $\sqrt{p}\vert 0\rangle+\sqrt{1-p}\vert 1\rangle$

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 ...
4
votes
1answer
40 views

Qiskit - How do we measure the same single qubit system multiple times while also getting the counts/results after each measurement?

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 ...
3
votes
1answer
125 views

Is there a polynomial quantum algorithm for graph coloring?

Is there a polynomial time and polynomial space quantum algorithm for finding a 4 colouring of any loopless planar graph?
2
votes
0answers
47 views

Possible results from Shor's algorithm in practice

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 ...
1
vote
3answers
71 views

Is it correct to say that we need controlled gates because unitary matrices are reversible?

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 ...

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