All Questions

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 ...

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 ...

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 ...

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?

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 ...

I have this program derived from Microsoft Quantum Katas for counting (see here): ...

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 (...

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 ...

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 ...

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 ...

I wrote an implementation of Grover's algorithm that looks like this: ...

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. ...

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 ...

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 ...

I am trying to understand what physics is found behind labeling quantum states on the Ising Model.

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 ...

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,...

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 $...

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 ...

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....

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{...

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{...

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 \...

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 ...

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\...

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 ...

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....

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}...

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\}...

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 ...

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....

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 ...

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 ...

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 ...

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

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

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

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^...

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-...

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 ...

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

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 ...

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 ...

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?

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 ...

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 ...

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 ...

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), ...

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 ...

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 ...