All Questions

Consider the 2 x 2 Hadamard matrix together with its three rotated forms—for fun, let's call them all the “Damhard” matrices: 1 H = [1 -2] : H2 - 6 1] 1] H3 = [1'1 H4 = Begin a quantum circuit C with ...

The most general formula of Kraus operator on density matrix is: $$\rho\to \sum_k A_k^\dagger\rho A_k.$$ If I want to write this equation for one qubit, the most general way will be: $\rho_f = (a*I+b*...

Find a 4 x 4 unitary matrix U such that U = eiA. (Possibly up to multiplying by a unit scalar, U is a matrix seen in the course.) Verify your calculation by showing how if U were given, one can obtain ...

Consider the 4-cycle graph G with edges (1, 2), (2,3), (3, 4), and (1,4). Construct the corresponding graph state (@G) without the second bank of Hadamard gates. Call the nodes Alice, Bob, Charlie, ...

I wonder what is the Hartree Fock state in openfermion. Is it 110000 or 000011, assume 6 qubits and 2 particles?

The error rates that I found on the calibration files are given in percentage, but I couldn't find whether it is calculated on full-scale (% FS) or on percentage of reading (% RD). If I do $20000$ ...

This question has a couple of parts: Do all IBM systems (except IBM Armonk) utilize frequency division multiplexing for qubit readout? If yes, is there a way of finding which qubits constitute a ...

I'm reading a paper Cost function dependent barren plateaus in shallow parametrized quantum circuits. There they introduce what is called Alternating Layered Ansatz (ALA). It is said that: The ...

I've seen the uncertainty of $A$ written as $$ (\Delta A)^2 = \langle (A - \langle A \rangle)^2 \rangle. $$ But what does this even mean since $ A $ is an operator and $ \langle A \rangle $ is a ...

Can somebody please explain me what is a Haar random state? I am not able to find any friendly resource to read about it.

I am currently learning surface code. In this framework, we can either do a quantum memory (for which we have good knowledge of how to do it), but we can also "in principle" perform an ...

Quantum circuits composed by Clifford gates can be simulated by classical computation in polynomial time. More precisely, this simulation should be a weak simulation, i.e. it is possible to sample the ...

I'm trying to recreate from this paper in the IBM Quantum Composer. However, this circuit isn't enough understandable for me to do so. I have tried to recreate the above circuit in the composer as ...

in Nielsen and Chuang's book in Box 6.1 (page 256 for 10th edition) there is a example of Grover's search algorithm for 3 qubits (2 as search space + 1 for oracle). I am currently trying to implement ...

I've been studying quantum computing for a little while now (I'm still very new to it), and I'm now studying algorithms (Deutsch's and Simon's). But I'm having some trouble understanding what exactly ...

I'm trying to put together a demo using the Quantum Teleportation example provided by qiskit. The quantum circuit runs as intended when it's initialized to the state $|0\rangle$, and the measured ...

I was looking into the partial trace and ran into the following equation shown below. Though I understand the general notion of the partial trace, I cannot derive how these two are equal in the ...

To detect noise through stabiliser measurement, in the circuit formalism, there is usually an ancilla which stores a parity check result. However, what happens if also the ancilla suffers from the ...

I am trying to play with NoiseModel of qiskit, and I noticed that error on id gate is not giving any error results, while error ...

I’m looking for resources or literature that compares photonic devices and other quantum computing hardware using some performance metric. In other words, I am looking for grounds that compare the ...

I have a Stim detector error model file derived from a surface code circuit. I'm trying to understand exactly what lines like error(0.00033) D0 D9 L0 ^ D7 ^ D8 from ...

I am reading Samuel L. Braunstein, Arun K. Pati, Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox. I am puzzling over the derivation ...

Apologies if this is the wrong place to ask this kind of question. I have a simple question about Openfermion. I have two normal ordered FermionOperators ...

I am trying to implement the quantum PCA algorithm to reduce the number of features (over 700 features) for a machine learning model. The original algorithm is proposed in this paper. I found a ...

How can I express Hadamard gate using only RZ and RX where RZ and ...

Suppose one has parameterized a swap test by using an ansatz $U(\theta) = \exp(-i\theta \text{ CSWAP})$, and one tries to find an angle $\theta$ such that one can distinguish given two quantum states ...

I am trying to find a circuit to represent a 3 Qubit unitary matrix such that $U|0\rangle = |b\rangle$ for $b = \left[0~c~c~c~c~c~c~0\right]$, where $c = 1/\sqrt{6}$. Although I am working in Qiskit, ...

I am trying to implement Grover's algorithm on an entangled state. The idea is that I will have a state $\sum_x\alpha_x|f(x),x\rangle$ and I want to measure the $x$, for which $f(x)=0$. Note that $f$ ...

I am starting to study quantum error correction and it's the first time that I see the operators (usually Pauli) as projective measurements which seem to just identify a syndrome but do not destroy ...

Consider the learning with errors(LWE) problem which is known to be hard for quantum computers. Let $q \geq 2$ be a prime integer. Consider us being given (polynomially many samples of) either: $$A, ...

I've been reading a paper about Entangled-quantum GAN (see this PDF) and wondering why descriptions below Eq.(3) in the paper are in fact true. To summarize the description, suppose we have two ...

I am reading Samuel L. Braunstein, Arun K. Pati, Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox. I am puzzling over the derivation ...

I am reading this paper, in particular the part where they explain it is possible to move qubits in the surface code. I don't understand the procedure that allows to move logical qubits on the array. ...

I'd like to study the important operator set Clifford+T from a quantum information theory perspective. The Clifford+T set is universal and it is important because allows for efficient error correction ...

I'm reading Ronald de Wolf's lecture notes, and in chapter 4.5 he writes that $$ \frac{1}{\sqrt N}\sum\limits_{j=0}^{N-1}\prod\limits_{l=1}^{n}e^{2\pi i j_l k / 2^l}|j_1...j_n\rangle = \bigotimes\...

I am reading this paper, in particular the part where X-cut and Z-cut are being defined. My question is highly connected (but different) to this one I previously asked. In this paper, they show the ...

I am trying to understand to properly read the graph below, provided in this post It is said that the black elements are the $Z$ stabilizers and the grey ones are the $X$ stabilizers. I am trying to ...

I've been reading through some papers about quantum autoencoders and often the topic of quantum communication comes up -- that autoencoders can be used for learning codes for qubit transmission. What ...

There is a very nice python library, to analyze surface codes https://github.com/yaleqc/qtcodes I tried to run this tutorial - https://github.com/yaleqc/qtcodes/blob/master/tutorials/xxzz/3-...

I wonder if there exists a way to map the square of a 2-body Ising Hamtiltonian (which will make it 4-body) back to a 2-body Hamiltonian that has the same ground state? Let me explain what I mean by ...

The question Say I have a completely-positive (CP) map $\mathcal{A}_{ij}$ defined in terms of two projectors $\Pi_i = |i\rangle \langle i |$ and $\Pi_j = |j\rangle \langle j |$ that acts on a density ...

Consider the following scenario: Alice and Bob are in two labs far apart, and they each have one qubit. Can joint measurement (for bipartite projective measurement, they are measurements that cannot ...

I am trying to represent a quantum circuit schematically with some operators in QISKIT. I know I can create some operator with Operator() in quantum_info from a ...

When the use of LaTeX or MathJax or other typesetting system is not an option, one can still type the braket notation $\left<\psi\right|$ and $\left|\psi\right>$. The simplest way is probably to ...

Writing a ket $\vert{\phi}\rangle$ in position basis. Defining $\langle x\vert\phi\rangle = \phi(x)$, we can write the ket in position basis as $$\int_{-\infty}^{\infty}dx \hspace{1mm}\phi(x)\hspace{...

I am trying to understand the quantum image processing. Please refer the link- https://qiskit.org/textbook/ch-applications/image-processing-frqi-neqr.html. I am not able to understand how to process ...

In papers, one of them being An Experimental Study of Shor's Factoring Algorithm on IBM Q is stated that replacing QFT with the semiclassical QFT (Kitaev's approach) reduces the needed number of ...

Can anyone provide a good link to understand how to implement qgan using pytorch in qiskit. Trying to understand this ( https://qiskit.org/documentation/machine-learning/tutorials/...

It was numerically shown in this paper that the ExactCover problem, given the unique satisfying assignment (USA) assumption, could be solved by an adiabatic quantum algorithm (AQC) in time polynomial ...

Let $A$ be an $n \times m$ matrix, and $x$ be an $m \times 1$ vector and $q$ be a number such that $q$ is polynomial in $n$. Let us be given both $A$, $q$, and $x$ as input and let us also have a 2D ...