All Questions

2
votes
1answer
25 views

How should we interpret these quantum logic gates as physical observables?

In quantum mechanics each operator corresponds to some physical observable , but say we have the operators $X,Y,Z,H, CNOT$. I understand how these Gates act on qubits, but what do they actually ...
0
votes
0answers
17 views

What is the difference in computational power between qubit and bit(transistor)? [duplicate]

If I use for example 5-qubit IBM-Q quantum computer and we accept the law of Quantum parallelism(n qubit = 2^n ordinary bits), so does it mean that computational power of this computer is equal to ...
1
vote
1answer
29 views

Why do we need reversibility

Suppose we have qubit $|a\rangle$. and we want to implement quantum addition say adding $|a\rangle$ and $|a\rangle$. When drawing the circuit for this operation one of the outputs that we get is ...
1
vote
1answer
33 views

What's the difference between Kraus operators and measurement operators?

It is said in a lecture note by John Preskill that, It seems that Kraus operators and measurement operators are the same thing. Is that right?
0
votes
1answer
56 views

Quantum representation of cube

Let say i have a square matrix of size $2^n\times 2^n$ with entries being 8 bit integers, where $2^n\times 2^n=b\times b\times b=2^l\times 2^l\times 2^l$, then if i want to represent that matrix in ...
3
votes
0answers
29 views

Counting in Q#: number of solutions

I have this program derived from Microsoft Quantum Katas for counting (see here): ...
3
votes
0answers
32 views

Does HHL implementation requires a priori eigendecomposition?

I am interested in HHL algorithm and despite all the problems related to current technologies, I am trying to understand how it has to be implemented. I have seen from these two available circuits (...
2
votes
2answers
48 views

What is the tensorial representation of the quantum swap gate?

I need to write the tensorial representation of the Controlled Swap Gate, what i have written is $\operatorname{CSWAP}=|0\rangle\langle0|\otimes I\otimes I+|1\rangle\langle1|\otimes U$, where U is ...
4
votes
0answers
43 views

Encoding bosonic degrees of freedom

A well-known way of encoding $N$ levels of a harmonic (bosonic) oscillator is as follows: \begin{equation} |n\rangle = |1\rangle^{\otimes n} \otimes |0\rangle^{\otimes N-n+1} \quad,\qquad ...
3
votes
1answer
41 views

Drawing tangent vectors to the Bloch sphere with qutip

I need to plot drawings of qubit dynamics on the Bloch sphere. I know QuTip allows to do such drawings but I specifically need to represent evolution velocities on the Bloch sphere so I need to draw ...
2
votes
0answers
51 views

Grover's Algorithm returns skewed probability distribution

I wrote an implementation of Grover's algorithm that looks like this: ...
8
votes
2answers
265 views

How is it possible to implement unitary operator when its size is exponential in inputs?

A quantum circuit can use any unitary operator. Its matrix is exponential in the number of input bits. In practice how can this ever be possible (aside from operators which are tensor products), i.e. ...
3
votes
1answer
49 views

Is the Bernstein-Vazirani algorithm dependent on the specific behavior of the oracle?

My understanding of the Bernstein-Vazirani algorithm is as follows: We have a black box oracle with secret string $s$. The black box does $$f(x) =s\cdot{x}(\sum_1^n s_i\cdot{x_i})$$ We run each qubit ...
3
votes
0answers
15 views

Finding separable decompositions of bipartite X-states using the methodology of Li and Qiao

Two recent papers of Jun-Li Li and Cong-Feng Qiao (arXiv:1607.03364 and arXiv:1708.05336) present "practical schemes for the decomposition of a bipartite mixed state into a sum of direct products of ...
-1
votes
0answers
17 views

What is the physics behind a quantum classifier for labeling quantum states? [on hold]

I am trying to understand what physics is found behind labeling quantum states on the Ising Model.
3
votes
2answers
369 views

How to show a density matrix is in a pure/mixed state?

Say we have a single qubit with some density matrix, for example lets say we have the density matrix $\rho=\begin{pmatrix}3/4&1/2\\1/2&1/2\end{pmatrix}$. I would like to know what is the ...
2
votes
0answers
29 views

What does it mean to have 2000 qubits and 6016 couplers?

From official D-Wave docs: The D-Wave 2000Q QPU has up to 2048 qubits and 6016 couplers. For example, I have the optimization problem defined as the QUBO problem. If I want to solve it on D-Wave,...
1
vote
1answer
72 views

Associating quantum states with decimal numbers

Let's say I have a vector $\vec{v}=(1,0)$ and a state $|10\rangle$, and a decimal number $3$. I know that I can associate the decimal $3$ with the vector $\vec{v}$, but can I also associate the state $...
2
votes
1answer
39 views

Eigenstate of unitary operator used for Order-Finding

In the "Quantum Computation and Quantum Information 10th Anniversary textbook by Nielsen and Chuang", chapter 5.3.1 introduces the concept of solving the Order-Finding Problem. (Eqn 5.36) states ...
3
votes
0answers
92 views

How to build a quantum circuit representing the Ising Model?

Can someone explain to me how to build a quantum circuit representing the Ising Model? I just want to understand how to represent the Ising Model for the purposes of quantum state label classification....
2
votes
1answer
39 views

What are the ranges of the four $q$ parameters in the magic simplex of Bell states formula?

Equation (7) in the 2012 paper, "Complementarity Reveals Bound Entanglement of Two Twisted Photons" of B. C. Hiesmayr and W. Löffler for a state $\rho_d$ in the "magic simplex" of Bell states \begin{...
2
votes
2answers
85 views

How does the probability of measurement turn out to be negative?

c) Compute $$\text{Prob}(\uparrow_\hat{n}\uparrow_\hat{m}) \equiv \text{tr}(\boldsymbol{E}_A(\hat{n})\boldsymbol{E}_B(\hat{n})\boldsymbol{p}(\lambda)), \tag{4.164}$$ where $\boldsymbol{E}_A(\hat{...
1
vote
1answer
43 views

Correct way of expressing a measurement in a different computational basis

Sometimes we find that the result we want from a quantum algorithm is expressed in terms of a basis that is different from the usual computational basis, which I will call $$ B_C = \left\{ \lvert 0 \...
5
votes
1answer
76 views

Quantum teleportation with “noisy” entangled state

This is actually an exercise from Preskill (chapter 4, new version 4.4). So they are asking about the fidelity of teleporting a random pure quantum state from Bob to Alice, who both have one qubit of ...
4
votes
2answers
509 views

How to superpose two composite qubit states?

Assuming we have two sets of $n$ qubits. The first set of $n$ qubits is in state $|a\rangle$ and second set in $|b\rangle$. Is there a fixed procedure that generates a superposed state of the two $|a\...
3
votes
1answer
46 views

Reversible crypto systems for use in the Grover's algorithm

I'm working on some papers (here and here) that use the Grover algorithm to crack krypto systems like AES and SHA. I had already asked a first question here. Now, however, a new question has arisen ...
4
votes
1answer
67 views

Controlled unitary from the HHL algorithm – practical implementation using Qiskit

I have a question about the implementation of the controlled unitary $e^{iAt}$, from the paper Demonstration of a Quantum Circuit Design Methodology for Multiple Regression, using the Qiskit framework....
1
vote
1answer
37 views

Burnside Decomposition in Kuperberg's Hidden Shift

In "Another subexponential-time quantum algorithm for the dihedral hidden subgroup problem", Kuperberg writes that $\mathbb{C}[G]$ has a "Burnside decomposition" of $$\mathbb{C}[G]\cong \bigoplus_{V}...
2
votes
1answer
116 views

Quantum addition and modulo operation using gates

I have a matrix equation $X_{\text{new}}=AX_{\text{old}}$, where $A=\begin{bmatrix}1 & 1 & 1\\ 2 & 3 &2\\ 3&4&4 \end{bmatrix}\bmod 64$, and $X_{\text{old, new}}\in \{1,2,...64\}...
3
votes
0answers
70 views

What can be some bachelor thesis ideas in quantum random walks?

Note: Cross-posted on Theoretical Computer Science Stack Exchange. I am an undergraduate, reading about quantum information and quantum technology. For about some time, I have been interested in the ...
1
vote
1answer
474 views

Preparing odd integers using quantum computation

This is just a basic question. I need to output odd integers till $15$, i.e $1,3,5,7,9,11,13,15$. Since $15$ requires $4$ bits, I prepare initial state by using Hadamard gate on initial $|0\rangle$, i....
4
votes
1answer
238 views

Understanding this description of teleportation

In the context of quantum teleportation, my lecturer writes the following (note that I assume the reader is familiar with the circuit): If the measurement of the first qubit is 0 and the measurement ...
3
votes
1answer
80 views

Notation for two qubit composite product state

In my lecture notes on quantum information processing my lecturer gives an example of composite systems as $|\phi\rangle=|0\rangle |0\rangle=|00\rangle$. I understand that if we have two qubits then ...
3
votes
1answer
124 views

Grover's algorithm – DES circuit as oracle?

In the literature before me, the quantum oracle of the Grover algorithm is shown as a function, in which a sign change is made possible $|x\rangle\rightarrow(-1)^{f(x)}|x\rangle$. I have read that it ...
4
votes
1answer
89 views

Prove that the operator $H U_{0^\perp}H$ can be expressed as $2|\psi\rangle\langle\psi|-I$

I'm trying to solve the following problem related to the mathematical explanation of Grover's algorithm. Let $$ \lvert\psi\rangle = \dfrac{1}{\sqrt{N}} \sum_{x=0}^{N-1}{\lvert x \rangle} \,\text{,} $$...
2
votes
1answer
74 views

Experiment runtime on IBMQ

I have been trying to get the runtime of my experiment on IBM's quantum computer. I am using the classic stuff, i.e ...
1
vote
1answer
37 views

How do you start a simulation with a random initial state in Cirq?

How do you create a random initial state by modifying the $2^{n}$ vector amplitudes instead of starting every simulation at $|0000...000\rangle$?
3
votes
1answer
132 views

Quantum Toffoli gate equation

I was reading a research article on quantum computing and didn't understand the tensor notations for the unitary operations. The article defined two controlled gates. Let $U_{2^m}$ be a $2^m \times 2^...
2
votes
0answers
28 views

What proportions of certain sets of PPT-two-retrit states are bound entangled or separable?

For two particular (twelve-and thirteen-dimensional) sets of two-retrit states (corresponding to 9 x 9 density matrices with real off-diagonal entries), I have been able to calculate the Hilbert-...
3
votes
0answers
43 views

Graphing the decoherence of qubits being used to perform an algorithm

How would I be able to graph the decoherence of qubits being used to perform an algorithm? I'm working with the IBMQ Qiskit framework and I'm trying to write a program that allows me to find the ...
3
votes
1answer
98 views

How to prove universality for a set of gates?

Which of the following sets of gates are universal for quantum computation? {H, T, CPHASE} {H, T, SWAP} And how do we prove it?
2
votes
1answer
43 views

Calculating entries of unitary transformation

Let $U$ be a unitary $n$-qubit transformation that applies a Hadamard on the $k$-th qubit and the identity on all the others. How would I go about calculating $U_{ij}=\langle i | U | j \rangle$ in ...
1
vote
0answers
45 views

Exception encountered while running quantum-enhanced support vector machines

I am trying to run the code of the notebook example aqua/artificial_intelligence/qsvm_kernel_classification.ipynb. I save it in a python file and I have an exception at runtime the display of ...
3
votes
1answer
71 views

Are there any other published quantum factoring algorithms that are simpler or more efficient than Shor’s?

How many qubits and what is the minimum number of gate operations needed to factor an n-bit integer? Are there any other published algorithms that are simpler or more efficient?
2
votes
1answer
37 views

How do I do printf debugging in Q# in a convenient way?

When initially writing an operator in Q#, I often want to see intermediate values of registers during the computation. This allows me to check that I haven't made ...
1
vote
1answer
42 views

Quantum transformation equivalent to Discrete Wavelet transform

Suppose we have a matrix $A=\begin{bmatrix} 2 &4 \\ 1 & 4\\ \end{bmatrix}$, when applying the discrete wavelet transform to this matrix we get 4 parts i.e smooth part ($1\times 1$) matrix, 3 ...
1
vote
1answer
57 views

(name of gate) is not in the list of basis operations

I'm trying to define a custom gate for my computations. I decided to copy the structure in one of the files in qiskit.extensions.standard package. Here is the code ...
2
votes
1answer
43 views

Qiskit DAG circuit - print information about individual gate/node by number

I created a DAG circuit in Qiskit and don't really understand how to see which gate is which. I want to call a function like dag_circuit.gate_info(gate_number), ...
1
vote
1answer
40 views

Using latest (GitHub) version of Qiskit as Python library

I just started working in Qiskit and want to use some of the new functions available to Qiskit on Github. Unfortunately, I don't know how to implement the latest GitHub version into my Anaconda ...
3
votes
2answers
70 views

What are the individual probabilities after √SWAP gate?

Say, qubit $\left|a\right\rangle = \alpha_1|0\rangle + \beta_1|1\rangle$ and $|b\rangle = \alpha_2|0\rangle + \beta_2|1\rangle$. After $\sqrt{\text{SWAP}}$(a,b) what are new probability amplitudes of ...

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