Questions tagged [oracles]

An oracle O is a "black box" operation that is used as input to another algorithm.

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Convert a quantum Phase Oracle into a Probability Oracle

Suppose we have an oracle $O_f$ that given an initial state $|x\rangle$ maps it into the following state: $$ O_f : |x\rangle \mapsto e^{if(x)} |x\rangle $$ Now, assuming that $f(x) \in [0,1]$, is it ...
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1answer
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How does $U_f$ in Deutsch's Algorithm affect the state $|x\rangle$?

I am trying to read Nielsen's and Chuang's book on quantum computing and I am having problem understanding Deutsch's algorithm. According to my understanding of the algorithm, the state $|x\rangle$ ...
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1answer
57 views

Controlled NOT gate using multiple control qubits in Q#

I am trying to implement the Grover's search algorithm using Q# and I am not able to implement the oracle (black box) part for the search of state $|1010\rangle$. How to implement the controlled NOT ...
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3answers
425 views

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?

In Chapter 6 of "Quantum Computation and Quantum Information" textbook by Nielsen and Chuang, Exercise 6.5 p.255: We have an oracle gate $O$ for $n$ qubit ($2^n=N$ searching items), and we would ...
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2answers
130 views

In Grover's Algorithm, does the exact solution need to be given to the oracle?

From my understanding, the oracle function in Grover's algorithm is used as a way to check for the desired outcome. I have looked at this example which implements the Exactly-1 3-SAT problem and the ...
4
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0answers
30 views

Oracle for welded tree walk

There is a famous paper by Childs, et al, in which it is shown that a quantum algorithm can find the name of the exit node for a certain graph in a way that is exponentially faster than any classical ...
3
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1answer
182 views

Deutsch-Jozsa on non-balanced oracles

I'm interested in deciding if an oracle is constant or not, but cannot guarantee that the non-constant oracles are balanced. The Deutsch-Jozsa seems like the obvious starting place, but handling the ...
7
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0answers
120 views

What are examples of non-oracular versions of famous oracular problems?

Most quantum algorithms proposed, including Deutsch-Jozsa, Simon's, Bernstein-Vazirani etc, involve querying an oracle. If I understand correctly, the speedups depend on the oracle being efficiently ...
2
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1answer
48 views

Hamming with prefix oracle

I'm doing the Q# quantum katas and I'm stuck on an oracle in the Deutsch-Josza algorithm katas. Let $|x\rangle=|x_0x_1\dots x_{n-1}\rangle$ be a qubit array and $r$ be bit string of $k\leq n$. The $...
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1answer
166 views

Separating NP from BQP relative to an oracle

I was looking at this lecture note where the author gives an oracle separation between $\mathsf{BQP}$ and $\mathsf{NP}$. He hints at how "standard diagonalisation techniques can be used to make this ...
4
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1answer
75 views

Implementing the one-bit Deutsch Oracle algorithm using phase

The standard method of implementing the one-bit Deutsch Oracle algorithm is to use two qbits, one as input & one as output (which allows you to write the non-reversible constant functions in a ...
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1answer
157 views

Coding an oracle for Simon's algorithm

I am trying to implement Simon's algorithm which calls for a 2-to-1 mapping function that satisfies $f(x) = f(x⊕s)$. I am looking for a simple way to code the oracle (using $H$, $Cx$, and $R$ gates), ...
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1answer
75 views

Why is the second register needed to define bit flip quantum oracles in a way that distinguishes between complementary oracles?

If our input $x \in \{0, 1\}^{n}$ is given as a black box, we usually query an oracle as follows. $$O_{x}|i, b \rangle = (-1)^{b x_{i}} |i, b \rangle$$ $i = \{1, 2, \cdots, n \}$ is the index of the ...
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3answers
342 views

Why is the application of an oracle function not a measurement?

Why is the application of an oracle function not a measurement, causing the collapse of the system? How can you know the state of the system (the input of the oracle function) without measurement?
5
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1answer
614 views

How does an oracle function in Grover's algorithm actually work?

I have lately been studying quantum algorithms. I have gone through the Deutsch algorithm and Grover's algorithm. There's always a function in the oracle which somehow 'recognizes' the solution ...
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2answers
156 views

Show that these two expressions for the oracle transformation are equivalent

Suppose $x \in \{0,1\}^n$. The standard way to make a query is with an oracle $O_x$ that given an input $|i,b \rangle $ returns $|i,b \oplus x_i \rangle$. Via the phase kick-back trick, this can be ...
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1answer
4k views

What exactly is an oracle?

What exactly is an "oracle"? Wikipedia says that an oracle is a "blackbox", but I'm not sure what that means. For example, in the Deutsch–Jozsa algorithm,$\hspace{85px}$,is the oracle just the box ...
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5answers
2k views

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

I am trying to simulate Deutsch's algorithm (elementary case of Deutsch-Josza algorithm), and I am not entirely sure how I would go about implementing the quantum oracle necessary for the algorithm to ...
9
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1answer
399 views

Grover's algorithm: what to input to Oracle?

I am confused about what to input to Oracle in Grover's algorithm. Don't we need to input what we are looking for and where to find what we are looking for to Oracle, in addition to the ...