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An approach for Hamiltonian simulation:
Any Hermitian (Hamiltonian) matrix $H$ can be decomposed by sum of Pauli products with real coefficients (see this thread). An example for 3 qubit Hamiltonian:
$$H = 11 \sigma_z \otimes \sigma_z + 7 \sigma_z \otimes \sigma_x - 5\sigma_z \otimes \sigma_x \otimes \sigma_y$$
The final circuit for $e^{iHt}$ can be ...
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Designing a logical function for quantum computer is similar to same process for classical one. You can also use truth tables. But you have to design the function to be reversible. Assume you have truth table for logical function $f(x): \{0;1\}^n \rightarrow \{0,1\}$, then reversible equivalent can be build in this way:
$$
|x_n\rangle |y\rangle \rightarrow |...
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First it is instructive to ask oneself: "how does classical data get into my computer?" In a classical computer, your data is always stored in bits. Because calculations in base 2 are not very straightforward for most people there are abstractions like int types for integers and float types for rational numbers with the associated math operations readily ...
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You cannot deploy C# to Q# Azure platform; Q# Azure platform executes a Quantum Simulator. The C# host program calls Q# operations to be executed on the Quantum Simulator - the code you have here will execute on a traditional computing processor.
Please read this link - https://docs.microsoft.com/en-us/quantum/quickstart
And this link more about the ...
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I disagree. By no means is there a scarcity of quantum algorithms. Consider for example this review on Quantum Machine Learning. Therein the term qBLAS is contained for Quantum Linear Algebra Subroutines. This term describes all the quantum algorithms that exist for basic linear algebra tasks. Together with the (in)famous Grover Algorithm that gives a ...
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Controlled version of $e^{iHt}$:
Often in the algorithms (e.g. in HHL or PEA), we want to construct not the circuit for Hamiltonian simulation $e^{iHt}$, but the controlled version of it. For this, we will use the result obtained from the previous answer. First of all, note that if we have $ABC$ circuit, where $A$, $B$ and $C$ are operators, then the ...
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Here's an image from a previous answer of mine:
If you replace the $\sigma_1\otimes\sigma_2\otimes\ldots\otimes\sigma_n$ with the tensor product of operators that you want (a single tensor product; a sum of terms needs some extra techniques based on, at its most simplistic, a Trotter expansion), and set the phase of the phase gate, $t$ equal to $-2\theta$, ...
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He generally refers to QRAM. But there are other ways to load data in a quantum computer, generally referred as quantum embeddings or quantum feature maps. They are generally more near-term oriented than QRAM. Yet with a QRAM, you can design an algorithm with the goal of obtaining a possible expression of a speedup against a classical version.
This article, ...
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I tried to simulate on IBM Q. I realized that input states $|01\rangle$ and $|10\rangle$ have oposite phase in comparison with others. This is desired behavior of the algorithm because these states have to be marked. Phase of other two states is intact. Because two states are marked and two do not, average amplitude is zero. When you rotate amplitudes around ...
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I would recommend the following resources. Quantum annealing is about QUBO/Ising formulations. First thing would be to get familiar with the formulations, and see examples of how do you formulate a few problems:
A Tutorial on Formulating and Using QUBO Models
Ising formulations of many NP problems
Then, if you have a specific problem you would like to ...
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Regarding (c) -
Too see what can go wrong, we'll need to take a step back and look at Shor's Algorithm assumptions.
Basically, the algorithm says we need to pick a random $X$, find its order $r$, and finally calculate $X^\frac{r}{2} \pmod N$ to get information about $N$.
$N$ is of the form $2P$, thus by Chinese Remainder Theorm it will only have two roots ...
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