# Questions tagged [quantum-computing]

Quantum computation and computational issues related to quantum mechanics

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### Differences between Quantum Computing and Parallelism [closed]

What are the differences between Quantum Computing and Parallelism? thanks in advance
1answer
255 views

### Finding all solutions by Grover search(not superposition)

When there are multiple marked elements, grover search provides only superposition of them. If I want to find all the marked elements, not superposition, I could try this: 1) Do Grover search, get ...
1answer
85 views

### Question about discarding the second register in the standard approach of hidden subgroup algorithm

My questions: What does discarding the second register mean for the standard approach of hidden subgroup algorithm? Why does discarding let the first register end up in a mixed state? My ...
1answer
63 views

### Grover's algorithm, M out of N, when M is large

The more general version of Grover's algorithm searches for one of $M$ entries that match a criterion, out of $N$ total entries. I have seen it written that this takes $O(\sqrt{N/M})$ iterations, to ...
1answer
90 views

### Confusion with the proof of constraints for a particular adiabatic quantum evolution

[This might be related to one of my previous unanswered questions.] This proof belongs to the paper, How to Make the Quantum Adiabatic Algorithm Fail by Edward Farhi, Jeffrey Goldstone, Sam Gutmann ...
1answer
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### How are new probabilities computed when simulating measurement on a set of qubits?

Suppose I have a set of 3 qubits and I have the probabilities for their distribution. This could be arbitrarily entangled or pure: |000> -> a |001> -> b |010> -> c |011> -> d |100> -> e |101> -> f |...
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259 views

### Quantum Fourier Transform question regarding measurement

When we use the quantum fourier transform, for a function, the output is entangled, so if a measurement is made on the output, the result may not be that of the function that one wanted in the first ...
1answer
131 views

### How does one extend local checkability to quantum complexity classes?

How does one extend local checkability to quantum complexity classes like BQP? Or are quantum algortihms inherently holistic?
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### Questions about the definition of the Quantum Turing Machine

I am trying to have a better understanding of the definition of the Quantum Turing Machine. My questions: If the output of a quantum program is the eigenvalue of the ground state of a Hamiltonian ...
0answers
94 views

### What is the relationship between quantum tomography and quantum error correction?

To realize correct quantum computing it seems that both quantum error correction and quantum tomography would be necessary. Is this true? What is the relationship between these two fields?
0answers
29 views

### Hardness of finding similar (quantum) states

Consider a quantum state $\lvert \psi \rangle$, we know from the no cloning theorem, that it cannot be perfectly cloned. Also, loosely speaking, that it can be imperfectly cloned s.t. one can produce ...
0answers
124 views

### Determining if a function is constant or not using period finding

Consider an arbitrary boolean function $$f: {\lbrace 0,1 \rbrace}^n \rightarrow \lbrace 0,1 \rbrace$$ which we write as: $$f(x_1, x_2 ... x_n)$$ where each $x_i$ is a boolean variable We note ...
0answers
123 views

### Computing the period of a function using a quantum computer

Consider a blackbox function $$f(x): Z \rightarrow \lbrace 0,1 \rbrace$$ Which inputs an integer and outputs 0 or 1 with bit complexity n. If the period P of this function satisfies P \in O(2^{...
0answers
383 views

### Is it possible to add quantum physics theory to traditional machine learning algorithms to get more accurate results

Lets suppose your data set includes locations in several dimensions and the kind of entity which is the class of the data set, is there other kind of information you need to add (such as times, ...
1answer
183 views

### What would be a complete QC circuit?

In classical computing NAND is a complete set (functionally complete) of binary operations, namely any Boolean circuit can be expressed using NAND gates. Is there an equivalent for quantum computing ...
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50 views

### QMA definition of difference between probabilities intuition

I'm reading about the complexity classes related to quantum computation, currently I'm studying QMA class. A language is in QMA(c,s) if there exists a polynomial time verifier and polynomial $p(n)$ ...
2answers
280 views

### Will we be able to use the current software in quantum computers? [closed]

I'm not sure if this should go here, so my apologies. The fact is that lately I have heard a lot about quantum computers and that they are not that far away. As it is a totally new technology, which ...
2answers
249 views

### How can I get $\sum_n e^{i a_n} |n\rangle$ from $\sum_n a_n |n\rangle$?

Suppose that I have a normalized quantum state $\sum_n a_n |n\rangle$, is there a quantum operation/circuit so that I can get $\frac{1}{N} \sum_n e^{i a_n} |n\rangle$ at output? How?
1answer
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### Addition on a quantum computer

From reading https://arxiv.org/pdf/quant-ph/0008033v1.pdf 3n qubits are required to add two n bit numbers. For a simple arithmetic operation such as a+b+c+d where ...
0answers
66 views

### Is BQP upper bounded by the class of problems computable by an exponential number of GPUs?

Consider the class $EXPGPU$ that informally contains all problems that can be stocastically solved in polynomial time by an exponential number of processors. Question: Is $BQP \subset EXPGPU$? My ...
1answer
140 views

### Complexity class on quantum computation and classic ones

Does the complexity speedup in superpolynomial by quantum computation mean it is possible to find new algorithm on classic Turing Machine which can speedup in classic Turing Machine in ...
1answer
136 views

### Dimension of the Fourier transform for $S_5$ [closed]

My question: What is the dimension of the Fourier transform for $S_5$? My effort: The dimensions of the seven irreps of $S_5$ are $1,1,4,4,5,5,6$. According to the notes of Andrew Childs, the ...
2answers
392 views

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1answer
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### The factoring problem reduces to order finding or is it the other way around? [closed]

initially i was not at all equipped in theoretical computer science and knew only basics of number of theory. I started working from scratch on the age old problem of primality testing which led me to ...
1answer
163 views

### Lower bounds on $Q_{\epsilon}(IP)$

I want to show that $Q_{\epsilon}(IP) \geq (1-O(\epsilon))n$, where $IP:\{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}$ is the usual mod 2 inner product. I have Nayak's lower bound, but I am not sure ...
1answer
126 views

### Can a computer generated organism be self aware? [closed]

Imagine that a computer generating a small universe similar to our own. Same table of elements, same physics, ect. Starting from the very beginning, with the creation of all the atoms in the ...
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205 views

### Is the sub-bit model of quantum computation equivalent to other models? [closed]

In a comment to this question Peter Shor asked me for a reference about the third described in the question point of view, namely, that quantum computers can be described as computers that can ...
1answer
341 views

### Quantum complexity class vs classical complexity class [closed]

What is the relation between BQP complexity class and P and NP?
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3k views

### Travelling sales man with Quantum Computers [closed]

I know that it takes billions of years to solve the travelling sales man when n = 25 (Number of cities). I am wondering how fast can a quantum computer solve the travelling sales man problem (for ...
1answer
428 views

### Duality computers

There is a lot on the internet about quantum computers and how they could factor integers. However, there is a type of computer which also uses the principles of quantum mechanics, which can be used ...