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Hadamard Matrix [closed]

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 ...
0
votes
1answer
21 views

How to write the Kraus representation for many-qubit states?

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*...
-4
votes
1answer
29 views

Quantum Linear Algebra [closed]

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 ...
-3
votes
0answers
16 views

Quantum Mathematics with Linear Algebra [closed]

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, ...
0
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0answers
10 views

Hartree Fock state in Openfermion

I wonder what is the Hartree Fock state in openfermion. Is it 110000 or 000011, assume 6 qubits and 2 particles?
0
votes
0answers
7 views

Is the error rate of IBMQ devices full-scale (% FS) or on percentage of reading (% RD)?

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 $20000$ ...
0
votes
0answers
4 views

Can we find which qubits are multiplexed for readout in IBMQ systems?

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 ...
0
votes
0answers
16 views

Hardware efficient ansatz versus Alternating Layered Ansatz

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 ...
1
vote
2answers
50 views

Whad does $ A - \langle A \rangle $ mean?

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 ...
6
votes
1answer
220 views

What is a Haar random quantum state?

Can somebody please explain me what is a Haar random state? I am not able to find any friendly resource to read about it.
2
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3answers
70 views

State of the art logical gate implementations for surface code

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 ...
2
votes
1answer
70 views

Weak simulation of Clifford circuits

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 ...
3
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0answers
26 views

Implementing Shor's algorithm on IBM Quantum Composer

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 ...
1
vote
1answer
29 views

Grover search in Quantum Computation and Quantum Information (Nielsen and Chuang)

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 ...
0
votes
1answer
23 views

Is the blackbox already a reversible operator, or are we the ones that convert it into one?

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 ...
1
vote
1answer
31 views

Quantum Teleportation Algorithm Always Ends in State $|0\rangle$

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 ...
0
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0answers
20 views

Partial trace formulation

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 ...
0
votes
2answers
23 views

Noise on the ancilla for syndrome measurement

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 ...
0
votes
1answer
31 views

Error Model on id gate, is not giving any error

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 ...
1
vote
0answers
27 views

Looking for detailed comparisons between photonic vs other quantum hardware

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 ...
2
votes
1answer
29 views

Where do lines like "error(0.00033) D0 D9 L0 ^ D7 ^ D8" come from in a stim detector error model?

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 ...
0
votes
0answers
19 views

The derivation of the quantum information no-hiding theorem, question 2

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 ...
1
vote
1answer
29 views

Evaluating $\texttt{FermionOperator}$ equality in Openfermion

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 ...
0
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0answers
20 views

How to implement purification of the density matrix into a pure state of enlarged system in the quantum PCA algorithm?

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 ...
-1
votes
0answers
30 views

Expressing Hadamard Gate with only rotation around x- and z-axis? [duplicate]

How can I express Hadamard gate using only RZ and RX where RZ and ...
0
votes
1answer
36 views

Parameterized swap test and perfect swap test

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 ...
2
votes
3answers
71 views

Find a circuit implementing a 3-qubit unitary matrix preparing $|b\rangle\simeq(0,c,c,c,c,c,c,0)$ with $c=1/\sqrt6$

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, ...
0
votes
1answer
34 views

Using Grover on entangled states

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 $f$ ...
0
votes
1answer
42 views

The meaning of non-destructive measurements in QEC

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 ...
2
votes
0answers
32 views

What is the explicit best known quantum algorithm for LWE?

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, ...
3
votes
1answer
47 views

Helstrom Measurement when two quantum states are close

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 ...
2
votes
0answers
65 views

The derivation of the quantum information no-hiding theorem, question 1

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 ...
1
vote
0answers
27 views

Moving qubits in surface code: I don't get why it works

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. ...
1
vote
0answers
52 views

How to understand Clifford+T from a quantum information theory perspective [closed]

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 ...
1
vote
3answers
88 views

How to show that the QFT satisfies $\frac1{\sqrt N}\sum_j\prod_le^{2\pi i j_l k/2^l}|j_1...j_n⟩=\bigotimes_l \frac1{\sqrt2}(|0⟩+e^{2\pi i k/2^l}|1⟩)$?

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\...
3
votes
1answer
30 views

How to know whether or not we have an X-cut or Z-cut without information on the boundaries

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 ...
2
votes
1answer
26 views

How to read a graph representing the stabilizers and data qubits in surface code

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 ...
1
vote
0answers
28 views

Quantum Autoencoders for Communication with Entanglement Assistance

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 ...
-4
votes
0answers
33 views

Benchmarking tutorial is not finding any error actually [closed]

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-...
4
votes
2answers
247 views

Map a 4-body Ising Hamiltonian to a 2-body Ising Hamiltonian

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 ...
2
votes
0answers
43 views

How to write the joint action of a CP map that acts on a single qubit of a bipartite state?

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 ...
3
votes
1answer
170 views

Can joint measurement be achieved in two labs far apart?

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 ...
2
votes
1answer
49 views

Representing Qubit Operator in Circuit

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 ...
1
vote
1answer
47 views

Which unicode character should be used for the angle brackets in braket notation?

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 ...
-2
votes
0answers
51 views

How to write this in expression in python [closed]

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{...
0
votes
1answer
39 views

Retrieve image from Histogram data of Qiskit

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 ...
4
votes
1answer
61 views

Difference between semiclassical QFT and QFT

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 ...
0
votes
0answers
36 views

Quantum GAN implementation

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/...
3
votes
0answers
25 views

Quantum Adiabatic algorithm and Hardness of ExactCover

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 ...
2
votes
1answer
39 views

Multiplication using nearest neighbour quantum gates

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 ...

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