Questions tagged [oracles]
An oracle is a "black box" operation (function) that is used as an input to an another algorithm (for example Deutch-Jozsa, Grover etc.). A parameter or feature of the Oracle is infered by the algorithm.
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Simon's Algorithm - Equivalent Oracles Giving Different Results
In Simon's algorithm is it possible to have two different oracles that return the same results on their own but cause Simon's algorithm to return different results from one another? What sort of ...
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Quantum Katas - Tutorials - Oracles - Task 3.3 (OR oracle of all bits except for a single bit)
Let $x$ be an arbitrary state composed of $N$ qubits and $k$ be an integer such that $0\leq k \leq N.$
The task is to ignore the $k$-th bit and to flip the sign of $x$ if any of the remaining bits are ...
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Implementing 3-Qubit Grover Algorithm in Qiskit
The Qiskit tutorial on Grover's Algorithm shows an example of finding two marked solutions out of 8 items, produced by 3 qubits. Using the general diffuser code it provides, however, I realize that ...
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In the adiabatic version of Grover's algorithm, how is the Hamiltonian constructed?
X-posted on physics.stackexchange
In quantum computation, there is a famous algorithm to search a marked item in an unstructured database called Grover's algorithm. It achieves a quadratic speedup ...
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In Grover's oracle, how is the matrix $U_f$ derived for a generic $n$?
Grover's algorithm works by iteration of the operator $$\tag{1}G:=U_S^\perp U_f=H^{\otimes n}U_0^\perp H^{\otimes n}.$$
I know how to write down the matrix for $U_S^\perp$ (the inversion about the ...
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Implementing Grover's oracle with multiple solutions in Qiskit
I want to turn a state
$$
|\Psi_1⟩ = \frac{1}{\sqrt{8}}(|000⟩+|001⟩+|010⟩+|011⟩+|100⟩+|101⟩+|110⟩+|111⟩)
$$
into
$$
|\Psi_2⟩ = \frac{1}{\sqrt{8}}(|000⟩+|001⟩+|010⟩+|011⟩+|100⟩-|101⟩-|110⟩+|111⟩)
$$
...
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In Simon's algorithm, is there a general method to define an oracle given a certain periodicity?
I have to implement Simon's algorithm in Cirq. I have problems determining the oracle $f(x)$ defined such that $f(x)=f(x\oplus a)$ from a certain value of $a$.
Given a random $a$, is there a general ...
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1answer
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Weird Grover's Algorithm Behavior
I am attempting to use Grover's to find elements in an array that satisfy a comparative query (=, <, >, etc). I am using Qiskit, and am using a qRAM to encode my array.
I have experimented with ...
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Grover's algorithm for finding 6/8 states
I'm trying to apply the diffusion operator to this state (normalization factors excluded):
$|000\rangle + |001\rangle - |010\rangle - |011\rangle - |100\rangle - |101\rangle - |110\rangle -|111\...
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1answer
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Is it possible to construct Grover search from Clifford gates only?
In the article Is Quantum Search Pratical the authors emphasized that a complexity of an oracle is often neglected when advantages of Grover search are discussed. In the end, a total complexity of the ...
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Is Grovers Algorithm Oracle creation a hardware level aspect?
There are numerous questions that asks about practical application demonstration of the Grover algorithm for arrays and databases.
However examples are not seen anywhere.
While searching for its ...
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1answer
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Is Grover's algorithm only applicable to a pure state?
I've been trying to perform Grover's algorithm on entangled states, e.g. $|00\rangle + |11\rangle$. However, the algorithm apparently doesn't seem to amplify the amplitude of the state $|11\rangle$ ...
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What is the relationship between quantum circuit and quantum query complexities?
I am trying to ascertain a precise understanding of the relationship between the quantum query model of complexity and the quantum circuit model of complexity. Specifically, is there an established ...
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Proof using hybrid method that inverting a permutation requires exponential queries for BQP machines
Let's say I am given a permutation $\sigma$ that maps $n$ bit strings to $n$ bit strings. I want to output $1$ if $\sigma^{-1}(000\cdots1)$ is even and $0$ if $\sigma^{-1}(000\cdots1)$ is odd. It can ...
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Deutsch-Jozsa algorithm: an oracle implementation
I would like to implement the Deutsch-Jozsa algorithm myself using cirq.
However, I faced the problem of the implementation of the oracle.
I endeavored to apply the Deutsch-Jozsa algorithm for $n+1$-...
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Deutsch-Jozsa: why is only one evaluation of $f$ needed? [duplicate]
I might be asking something quite obvious but why is it stated that only one evaluation of $f$ is needed in the Deutsch-Jozsa algorithm?
If we have a quantum oracle for $f:\{0,1\}^n\rightarrow\{0,1\}$ ...
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Is there a way to construct a quantum circuit/oracle to check if 2 qubits in an unknown pure state are entangled?
I have 2 qubits which are in an unknown pure state i.e. their density matrix $\rho$ can be expressed as $|\psi\rangle\langle\psi|$.
Let the initial state be $|\psi\rangle = c_{00}|00\rangle + c_{01}|...
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How to implement an Oracle
Often when reading about QC algorithms the Authors assume the existence of an Oracle. I understand this is so that they can focus on the overall structure of the algorithm, and an Oracle can be seen ...
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Recording Quantum Queries
Question is about techniques from this paper. Essentially the paper provides a way to record what queries were asked to a quantum-accessible oracle. We have the oracles: \begin{aligned}
&\text { ...
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Why is the function $f_s(x)=\sum_i x_i s_i \pmod 2$ balanced?
A parity function $f_s:\{0,1\}^{n}\rightarrow\{0,1\}$, for some $s\in \{0,1\}^n$, is a function of the form $f_s(x) = x \cdot s$, where the inner product is taken modulo 2.
Show that $f_s$ is a ...
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Equality comparator for two qubits each
I'm trying to implement Grover's algorithm. For the oracle I have three nodes which are represented by two qubits for each node. How can I check if the states of two nodes are not equal?
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Preparing a quantum state from a classical probability distribution
Suppose I have a black-box unitary $U_p$ which is described as follows: given a finite probability distribution $p:\{1,\ldots,n\}\rightarrow \mathbb{R}_{\geq0}$, where $\sum_{x=1}^n p(x)=1$, the ...
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How to write decent code for oracle in Qiskit without custom circuit or long truth table?
I am now practising using Qiskit. The example of Grover's algorithm in tutorials suggests using logical expression, truth table or circuit to construct the oracle. In most textbooks on quantum ...
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How does the Grover's Algorithm work with a real example? [duplicate]
I am new to this field and I have been baffled by the idea of Oracle for a long time.
I am aware of the procedure, but I am very confused about how we choose the oracle.
Let say we have 4 poker ...
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Graphs are represented using oracle, where oracle is the adjacency matrix. Is there any simple example of this? [closed]
I have been reading papers on graph theory in quantum computing. Mostly, papers explain that they use adjacency matrix to represent the graph. But I could't find the practical simple example to ...
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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
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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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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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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 ...
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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 ...
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1answer
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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 ...
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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 ...
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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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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 ...
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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
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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
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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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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?
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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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How to prove that the query oracle is unitary?
The query oracle: $O_{x}|i\rangle|b\rangle = |i\rangle|b \oplus x_{i}\rangle$ used in algorithms like Deutsch Jozsa is unitary. How do I prove it is unitary?
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Implementing an oracle
Suppose $x$ is an $N=2^n$ elements database. Let's define a $2N$-bit database with $y \in \{0,1\}^{2N}$ indexed by $(n+1)$-bit strings $j=j_1\ldots j_n j_{n+1}$, where
\begin{align}
y_j=\begin{cases}...
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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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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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How would I implement the quantum oracle in Deutsch's algorithm?
I am trying to simulate Deutsch's algorithm (elementary case of Deutsch-Jozsa algorithm), and I am not entirely sure how I would go about implementing the quantum oracle necessary for the algorithm to ...
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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 ...
