All Questions

1
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1answer
20 views

Simple proof that $(U \otimes V)(|x\rangle \otimes |y\rangle) = U|x\rangle \otimes V|y\rangle$?

This transformation comes up a lot during symbolic manipulation of quantum operations on state vectors. It's the reason why, for instance, $(X\otimes \mathbb{I}_2)|00\rangle = |10\rangle$ - it lets us ...
1
vote
1answer
11 views

Q# How to use a namespace in another project?

I have some utility operations that I'd like to use across projects. How can I import its namespace using Q# in Visual Studio 2017 in other projects?
3
votes
0answers
13 views

Can we use quantum machines to reduce space complexity of deterministic turing machines?

Can we convert every algorithm in $\text{P}$ (polynomial time complexity for deterministic machines) into a quantum algorithm with polynomial time and $O(\log n)$ quantum bit?
5
votes
0answers
22 views

Does the GLOA have any advantage over the Solovay-Kitaev algorithm?

The Solvay Kitaev algorithm was discovered long before the Group Leaders Optimization algorithm and it has some nice theoretical properties. As far as I understand, both have exactly the same goals: ...
3
votes
0answers
31 views

When and where was the first use of the term Chimera?

This is along the same lines as the earlier question: When was the first use of the word Entanglement? I was surprised to discover that when searching for "chimera" in both of Vicky Choi's minor-...
1
vote
1answer
30 views

How to construct a quantum gate producing 1 if r divides x, 0 otherwise?

If you have two registers in the state $\frac{1}{2^{n/2}} \sum_{x = 0}^{2^{n/2} - 1} |x\rangle |0\rangle$, how could you construct a gate that produces a superposition of states $|x\rangle|1\rangle$ ...
1
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0answers
35 views

Why do we need Shor's algorithm to find the period of a function?

I am not getting the point why we need Shor's algorithm to find the period of a function when we could use Simon's algorithm for it.
2
votes
1answer
28 views

What's the meaning of applying $U_{\text{div}}$ to a register in superposition?

$\newcommand{\qr}[1]{|#1\rangle}$Say I begin with $10$ q-bits $\qr{+}\qr{+}\qr{+}\qr{+}\qr{+}\qr{+}\qr{+}\qr{+}\qr{+}\qr{+}$ forming a register $B$. Name these q-bits as $b_9, ..., b_2, b_1, b_0$. ...
4
votes
1answer
43 views

Does entanglement correlate qubits a $100\%$ of the time?

$\newcommand{\qr}[1]{|#1\rangle}$Say I begin with $4$ qubits $\qr{+}\qr{+}\qr{+}\qr{+}$ forming a register $B$. Name these qubits as $b_3, b_2, b_1, b_0$. Also, let $C$ be another register $\qr0\qr0\...
4
votes
2answers
60 views

What happens when I input two qubits starting at state $|00\rangle$ into a hadamard gate

I was watching the following video https://www.youtube.com/watch?v=IrbJYsep45E And around 3 minutes in, they do an example computation with two qubits. The qubits started off in the state $|00\rangle$...
0
votes
1answer
27 views

Solving a circuit implementing a two-level unitary operation

The circuit below implements the following two-level unitary transformation: $\tilde{U}$ is a unitary matrix: $\tilde{U} = \left[\begin{matrix} a & c \\ b & d \end{matrix}\right]$ where $a, ...
1
vote
1answer
15 views

Applying Group Leaders Optimization to Quantum Belief Systems

Context: I am particularly interested in quantum cognition & would like to use a tool like pyZX to perform the following types of optimizations. In Preparing a (quantum) belief system they "...
5
votes
0answers
27 views

Discrepancy regarding Husimi Probability distribution

I am trying to simulate a system of j qubits and for visualization of the dynamics considering the Husimi distribution of the state. To carry out the projection ...
0
votes
2answers
17 views

How does the stated Pauli decomposition for $\operatorname{CP\cdot A\cdot CP}$ arise?

I'm having a bit of trouble understand @DaftWullie's answer here. I understood that the $4\times 4$ matrix $A$ $$ \frac{1}{4} \left[\begin{matrix} 15 & 9 & 5 & -3 \\ 9 & 15 & 3 &...
3
votes
3answers
84 views

What is the matrix for the operator that implements a function to tell the parity of its argument?

$\newcommand{\qr}[1]{|#1\rangle}$ I gave myself the task of building an operator that implements the following function: $f(0) = 0$, $f(1) = 1$, $f(2) = 1$, $f(3) = 0$. I restricted myself to $x$ up ...
4
votes
3answers
53 views

What's an example of building a circuit $U_f$ that implements a simple function $f$?

I'd like to be able to program simple functions into simulators such as QCL. I read that any function $f$ can be implemented, but I don't know how to get say a unitary matrix that implements $f$. $\...
2
votes
0answers
66 views

Physics World - Questioning quantum speed [on hold]

My question is definitely regarding quantum-speedup but the quantum-speedup tag is confined to algorithms... and my question is definitely not on algorithms. So, this is just my best shot at tagging. ...
1
vote
1answer
54 views

Resources to keep a track on open Ph.D. positions in specific sub-fields/topics of quantum computing

I was wondering where to look for open Ph.D. positions for specific sub-fields/topics of quantum computing like error correction, optimization, quantum chemistry, etc. It is preferable if the offers/...
2
votes
0answers
20 views

Why does Fourier sampling allow to efficiently recover hidden subgroups?

The hidden subgroup problem is often cited as a generalisation of many problems for which efficient quantum algorithms are known, such as factoring/period finding, the discrete logarithm problem, and ...
1
vote
2answers
40 views

Why does a rotation of $\pi/2$ on $|1\rangle$ yield $i|1\rangle$?

$\newcommand{\q}[2]{\langle #1 | #2 \rangle} \newcommand{\qr}[1]{|#1\rangle} \newcommand{\ql}[1]{\langle #1|}$ It seems $V(\pi/2, \qr{1}) = i \qr{1}.$ I didn't expect that. To me $\qr{1}$ points ...
0
votes
0answers
13 views

How to compute the tensor product in QCL?

When I look at QCL (the documentation of the language begins in chapter 3) I don't see a way to compute the tensor product between two q-bits. Is the programming operator ...
3
votes
1answer
52 views

Quantum teleportation: second classical bit for removing entanglement?

I have read about how Alice can send Bob a qubit $\alpha |0\rangle + \beta|1\rangle$ if they share an EPR pair. This gives an initial state: $(\alpha |0\rangle + \beta|1\rangle) \otimes (\frac{1}{\...
4
votes
1answer
62 views

Understanding the Group Leaders Optimization Algorithm

Context: I have been trying to understand the genetic algorithm discussed in the paper Decomposition of unitary matrices for finding quantum circuits: Application to molecular Hamiltonians (Daskin &...
4
votes
2answers
68 views

Do the probability amplitudes of the superposition state produced by the QFT transform convey useful information?

I have been studying on Quantum Fourier Transform (QFT) by myself, and I am little bit confused about how could QFT be used. For example, if the QFT of three quantum bits is $a_1|000\rangle + ...
4
votes
3answers
134 views

Quantum Computing Project

I am currently working on a quantum computing subject for my coding school, and I had some questions for you. My objective would be to introduce students to Quantum Computing with an algorithmic ...
5
votes
1answer
44 views

Efficiently performing controlled rotations in HHL

This question builds off of this question. In the HHL algorithm, how do you efficiently do the $\tilde{\lambda}_k$-controlled rotations on the ancilla qubit? It seems to me that since you don't know ...
2
votes
3answers
76 views

Calculating measurement result of quantum swap circuit

Consider the following circuit, where $F_n$ swaps two n-qubit states. If the inital state is $|0\rangle \otimes |\psi\rangle \otimes |\phi\rangle = |0\rangle|\psi\rangle|\phi\rangle$, the state ...
2
votes
0answers
21 views

Weak Fourier Sampling vs Strong Fourier Sampling?

I'm having trouble understanding the difference between weak fourier sampling and strong fourier sampling. From this paper: ...two important variants of the Fourier sampling paradigm have been ...
2
votes
2answers
36 views

How to run algorithms on IBMQ via Qiskit-Aqua?

I am trying to run an optimization problem on IBMQ. Running the same code on QASM simulator works fine. However, changing only the backend name to IBMQX takes long time. I am aware of the queues ...
5
votes
2answers
56 views

Simulation vs Construction of Fredkin gate with Toffoli gates

I'm working my way through the book "Quantum computation and quantum information" by Nielsen and Chuang. (EDIT: the 10th anniversary edition). On chapter 3 (talking about reversibility of the ...
0
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0answers
20 views

Qiskit SDK problem

So I am getting this error when I fire the command on Ipython or Jupyter Notebook ...
1
vote
1answer
40 views

Can quantum computers be clustered together?

I have been interested in the idea of computer clusting which is about making multiple pysical computer system to act as one whole logical computer system computing the same task at the same time, but ...
3
votes
1answer
48 views

Why does Grover's search invert about the mean?

Let $\vert s\rangle = \frac{1}{\sqrt{N}}\sum_{i=1}^N\vert x_i\rangle$ be an equal superposition over states from which we need to find one solution state $\vert w\rangle$. The phase flip operator in ...
8
votes
3answers
94 views

How is computation done in a 2D surface code array?

In a 2D surface code lattice, there are some data qubits and some measurement qubits. Suppose we want to do a 2-qubit computation, for example, let say, an X-gate on qubit-1 followed by a CNOT gate ...
6
votes
3answers
64 views

$R_z$ gate representations

Why is the $R_z$ gate sometimes written as: $$ R_{z}\left(\theta\right)=\begin{pmatrix}1 & 0\\ 0 & e^{i\theta} \end{pmatrix}, $$ while other times it is written as: $$ R_{z}\left(\theta\...
2
votes
2answers
129 views

Many-Worlds Interpretation and GHZ States

I'm working through a problem set, and I've come across the following problem: In this problem, you'll explore something that we said in class about the Many-Worlds Interpretation of quantum ...
2
votes
0answers
45 views

Simulating Read only QRAM (constructing an oracle)

In many algorithms an array that stores a classical data or quantum data is crucial. The QRAM (quantum random access memory) that stores classical data in the circuit has been done. My question ...
4
votes
1answer
40 views

Suggest, partly based upon limited numerical results, possible “elegant” exact formulas for Bures two-qubit separability probability

Lovas and Andai (https://arxiv.org/abs/1610.01410) have recently established that the separability probability (ratio of separable volume to total volume) for the nine-dimensional convex set of two-...
3
votes
2answers
79 views

Are the squared absolute values of the eigenvalues of a unitary matrix always 1?

I'm going through the phase estimation algorithm, and wanted to sanity-check my calculations by making sure the state I'd calculated was still normalized. It is, assuming the square of the absolute ...
5
votes
1answer
61 views

Relating min-entropy with conditional entropy

Suppose we have a classical quantum state $\sum_x |x\rangle \langle x|\otimes \rho_x$, one can define the smooth-min entropy $H_\min(A|B)_\rho$ as the best probability of guessing outcome $x$ given $\...
7
votes
2answers
110 views

Do any educational quantum computing toys or devices exist?

Question inspired by this article from IEEE Spectrum on blocks containing different polarization filters for use in classrooms, and my previous question on representing the three-polarizing-filter ...
6
votes
1answer
61 views

Relation between $\mathrm{QMA}$ and $\mathrm{P^{QMA}}$

What is the relation between $\mathrm{QMA}$ and $\mathrm{P^{QMA}}$ and how do we prove it? Are these classes equal?
6
votes
0answers
47 views

How significant are the variants of Grover's Algorithm?

I found a paper by Grover titled "How significant are the known collision and element distinctness quantum algorithms?", in which he expressed criticism to several famous algorithms, including ...
2
votes
1answer
48 views

How to make “random U3” in QASM?

I want to make an operator: $\mathrm{U3}(\arccos(\sqrt p),0,0)$, when $p$ is a random value between $0$ and $1$ How do I write code in QASM language of this "random $\mathrm{U3}$" operator?
6
votes
1answer
32 views

Lattice based cryptography vs BB84

Am I correct in thinking that post-quantum cryptography such as lattice-based solutions run on classical computers are resistant to quantum attacks (as opposed to RMS), whereas quantum key ...
6
votes
1answer
92 views

Depolarizing channel implementation on IBM Q

Given a single qubit in the computational basis, $|\psi\rangle =\alpha |0\rangle + \beta|1\rangle$, the density matrix is $\rho=|\psi\rangle\langle\psi|=\begin{pmatrix} \alpha^2 & \alpha \beta^*\\ ...
9
votes
1answer
101 views

Does the D-Wave 2000Q satisfy DiVincenzo's criteria?

DiVincenzo's criteria for quantum computation are the following: A scalable physical system with well characterized qubits. The ability to initialize the state of the qubits to a simple fiducial ...
4
votes
1answer
78 views

Introductory resources for learning about quantum Hamiltonians

I am seeking introductory resources which will enable me to answer these questions (textbooks, lecture series, etc.): Given a simple quantum system, how do I derive its Hamiltonian? Given a ...
6
votes
1answer
192 views

What's a Qubit on D-Wave 2000Q?

From D-Wave flyer: The D-Wave 2000Q system has up to 2048 qubits and 5600 couplers. To reach this scale, it uses 128,000 Josephson junctions, which makes the D-Wave 2000Q QPU by far the most ...
5
votes
2answers
107 views

Is there a general method to implement a 'greater than' quantum circuit?

I am interesting in finding a circuit to implement the operation $f(x) > y$ for an arbitrary value of $y$. Below is the circuit I would like to build: I use the first three qubits to encode $|x⟩$, ...

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