# Questions tagged [deutsch-jozsa-algorithm]

The Deutsch–Jozsa algorithm is a quantum algorithm, proposed by David Deutsch and Richard Jozsa in 1992. Although of little practical use, it is one of the first examples of a quantum algorithm that is exponentially faster than any possible deterministic classical algorithm. It is also a deterministic algorithm, meaning that it always produces an answer, and that answer is always correct. (Wikipedia)

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### How can a half-wave plate affect the position qubit and not the polarization qubit of a photon?

I recently was watching these 2 videos on Coursera which show how to build a simple quantum computer that can implement the simplest case of the Deutsch-Jozsa algorithm (which uses only 2 qubits). ...
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### Question about DIY Quantum Computer Prototype

I recently came across these 2 videos on Coursera which show how to build a simple quantum computer that can implement the simplest case of the Deutsch-Jozsa algorithm (which uses only 2 qubits). ...
42 views

### Hamming Weight algorithm

Is there any quantum algorithm that can improve a calculation time for determining the Hamming weight of an arbitrary bit string? The Deutsch-Jozsa algorithm seems like it would be useful for this ...
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### Example of a quantum algorithm better than its classical counterpart which involves only $1$ qubit?

I was reading over the proof of the Deutsch-Jozsa algorithm, which in its simplest case, involves at least 2 qubits. Is there an example of a quantum algorithm that is better than it's classical ...
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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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### Deutsch's algorithm in Qiskit

I am trying to understand and implement the Deutsch algorithm. I follow the logic from Nielsen book and I started to implement it in Qiskit. For implementing the oracle, I use a CNOT gate and now I ...
145 views

### Any other quantum algorithms than Jozsa-Deutsch decision algorithm, Grover search algorithm, Shor factorization algorithm?

I have been working on implementing Jozsa-Deutsch decision algorithm, Grover search algorithm, Shor factorization algorithm on my home-made 2 qubits device. I am wondering if there are any other ...
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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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### Understanding Steps in Deutsch's Algorithm

I am currently working my way through the book Quantum Computation and Quantum Information by Chuang and Nielsen. So far it has been a joy to read, however I am hung up on a couple aspects of quantum ...
73 views

### Why do multi-bit hadamards expands to what they do?

I'm a Computer Scientist undergrad student studying for an exam in Quantum computing. In all of the algorithms I have been studying (Deutsch–Jozsa, Simons, Shors, Grovers) I constantly see multi-qubit ...
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### How to factor the output of a CNOT acting on the input $|-,+\rangle$

I am trying to implement the Deutsch oracle in classical computer, using direction from this talk. There is this slide where they show how the CNOT gate modify 2 Hadamard transformed Qubits: While ...
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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-Josza 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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### 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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### What does a zero state combined state vector for 2 qubits mean?

I was fiddling with the quantum circuit used for Deutsch's algorithm and I was led to a zero state as a result which is bizarre. I don't know how to explain this result. ***I'm using Nielsen and ...
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### How can a CNOT gate change the control qbit (e.g. in the Deutsch Oracle problem)?

It is very confusing how the CNOT gate can change the properties of the controlled qubit (possibly because I am still stuck in the classical programming mindset): Many books have explained the ...
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### Implementing Deutsch's problem on IBM Q composer

I tried to implement the Deutsch's problem on IBM Q but didn't get the results as expected. So here is the circuit for the Deutsch algorithm and this is my implementation on the composer: so let me ...
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### How to understand Deutsch-Jozsa algorithm from an adiabatic perspective?

I'm trying to understand the Deutsch-Josza algorithm from an adiabatic perspective as presented in Adiabatic quantum computing A: Review of modern physics, vol 90, (2018) pp 015002-1 (arXiv version). ...
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### Understanding the oracle in Deutsch's algorithm

I am reading John Watrous' notes from his course CPSC 519 on quantum computing. In a pre-discussion before presenting Deutsch's algorithm to determine whether a function is constant or not, the author ...
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### What happens in Deutsch algorithm if I use equal input bits?

I am currently working on the algorithm of Deutsch. The algorithm defines two starting states, which are for $|x\rangle = |0\rangle$ and for $|y\rangle = |1\rangle$. So far, that's clear to me. But ...
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### Deutsch-Jozsa algorithm as a generalization of Bernstein-Vazirani

It is known that both algorithms use the same gates: $H^{\oplus n}U_fH^{\oplus n}$. After the circuit, the qubits are in the state $\sum_y \left( \sum_x (-1)^{f(x)+xy} \right) |y\rangle$. In DJ's ...
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### Correct way of expressing a measurement in a different computational basis

Sometimes we find that the result we want from a quantum algorithm is expressed in terms of a basis that is different from the usual computational basis, which I will call  B_C = \left\{ \lvert 0 \...
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### Deutsch–Jozsa algorithm: why is $f$ constant?

I'm trying to understand how the Deutsch–Jozsa algorithm works with the following circuit: Circuit in Quirk Since we have the top 2 wires measuring $|0\rangle$ with 100% probability, it means $U_f$ ...
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### What can be a mini research project based on Grover's algorithm or the Deutsch Jozsa algorithm?

I need to work out a research project on quantum computing as a part of my curriculum. I was wondering how to implement something theoretically with the basic knowledge I have. I have learned about ...
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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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### Balanced vs unbalanced superposition distinguisher

I've been looking at basic quantum algorithms such as the Deutsch-Jozsa algorithm that are able to characterize functions very well and I was wondering if similar approaches exist to characterize ...
There is something I really misunderstand about the Deutsch-Jozsa algorithm. To check if $f$ is balanced or constant, we use the following algorithm : Where $U_f$ gives \$(x,y) \rightarrow (x, y \...