# Tag Info

Accepted

### What exactly is an oracle?

An oracle (at least in this context) is simply an operation that has some property that you don't know, and are trying to find out. The term "black box" is used equivalently, to convey the idea that ...
• 59.2k
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### How is the oracle in Grover's search algorithm implemented?

The function $f$ is simply an arbitrary boolean function of a bit string: $f\colon \{0,1\}^n \to \{0,1\}$. For applications to breaking cryptography, such as [1], [2], or [3], this is not actually a ‘...
• 1,058

### How would I implement the quantum oracle in Deutsch's algorithm?

There are two questions here. The first asks how you might actually implement this in code, and the second asks what's the point if you know which oracle you're passing in. Implementation Probably the ...
• 4,138

### How to prove that the query oracle is unitary?

Apply it twice: $$O_xO_x|i\rangle|b\rangle=O_x|i\rangle|b\oplus x_i\rangle=|i\rangle|b\oplus x_i\oplus x_i\rangle=|i\rangle|b\rangle$$ Hence, $O_x$ is its own inverse, and therefore reversible. To ...
• 59.2k
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### Nielsen and Chuang, Exercise 6.5: How to simulate oracle for n+1 qubits using one oracle gate for n qubits and one extra qubit?

The simplest solution is to use an ancilla in the $|+\rangle$ state. Swap that ancilla for the oracle's output qubit, conditioned on the control qubit being false, before and after applying the oracle....
• 38.5k
Accepted

### Preparing a quantum state from a classical probability distribution

Suppose we have two quantum circuits, the first one $S$ computes (or at least approximates) the classical squareroot function ($\sqrt{\cdot}$) via $$S|x\rangle|0\rangle=|x\rangle |\sqrt{x}\rangle,$$ ...
• 2,048
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### Implementing Grover's oracle with multiple solutions in Qiskit

There are different ways to achieve that, my favorite is probably this one: The oracle you describe above is just a classical function ("True if my bitstring is 101 or 110") converted to a ...
• 2,953
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### In Grover's Algorithm, does the exact solution need to be given to the oracle?

The first example you're looking at is closer to the process of building an oracle for practical applications than the second one. The oracle circuit has to encode the Boolean formula for a specific ...
• 9,135

### How is the oracle in Grover's search algorithm implemented?

Well, Grover's original paper, "Quantum mechanics helps in searching for a needle in a haystack" clearly states, it assumes that C(S) can be evaluated in a constant time. Grover's search is not ...
• 313

### How to implement an Oracle

In general, you want to understand the process by which you compute the matrix elements if you were doing it by hand. In the example you give, for instance, you're effectively computing $|i-j|==1$. ...
• 59.2k
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### How can Grover's algorithm be implemented when having a string or other data type as input?

A lot of explanations of Grover's search suffer from the common issue of claiming it's a database search or, worse yet, looking for a hardcoded element. (You have examples of both in your question, so ...
• 9,135

### In the adiabatic version of Grover's algorithm, how is the Hamiltonian constructed?

Grover's algorithm We are given a function $f(a)$ such that $f(a)=0$ for all of the $N$ possible values of $a$, except when $a=\omega$ in which case we have $f(\omega)=1$. Assuming that this $f(a)$ ...
Accepted

### What is "Fixed-Point" in the Fixed-Point quantum search?

"Fixed-point quantum search" refers to variants of the quantum amplitude amplification algorithm (i.e., the generalization of the Grover algorithm) where the more iterations one does, the ...
• 1,127

### How would I implement the quantum oracle in Deutsch's algorithm?

There is no way to build the oracle in a way which would not defeat the point of Deutsch's algorithm - that's why it is an oracle-based algorithm. The only way would be if you would come up with an ...
• 6,918