# Tagged Questions

Quantum computation and computational issues related to quantum mechanics

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### Why is it impossible to work with polylog length encoding schemes for quantum circuits?

I am going through Quantum Computational Complexity by John Watrous. On page $12$, he said: The encoding disallows compression: it is not possible to work with encoding schemes that allow for ...
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### Non-commutative quantum counting with aggregate constant work per increment

Classically, it's very easy to create an incrementing function that can perform up to $n$ increments with $O(n)$ work: ...
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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 ...
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### Why there is no quantum walks on hypergraph?

As a beginner,I find that there is no quantum walks on hypergraph.why?
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### How to represent quantum multiplication

Say I have a 4 core processor and I wish to multiply 2 matrices of dimensions 2x2 A = 1 2 3 4 B = 1 2 3 4 Each member of the resultant computation can ...
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### When is a non-unitary quantum system only theoretical?

Suppose we construct a non-unitary quantum system α in hilbert space. It entails that this system would have no direct parallel in quantum circuitry as it is a requirement that all quantum gates ...
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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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### How to interpret these adiabatic evolutions?

I was trying to study the adiabatic Hamiltonian defined in the paper (arXiv:1207.1712) titled 'Solving the Graph Isomorphism Problem with a Quantum Annealer'. My case is the cycle graph $C_n$ when $n$...
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### States and Probability distributions that the 5-qubits IBM computer can produce

IBM has recently built a 5-qubits quantum computers based on superconducting qubits. It is even possible to make experiments over the cloud. The space of pure states for 5 qubits is the unit sphere ...
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### How do I figure out how to combine simpler quantum gates to create the gate I want?

I want to create other quantum gates from the basic building blocks of a universal quantum gate set. I've been playing with IBM's quantum computing interface for that. I wanted to create a Toffoli ...
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### Can a measurement commuting with the stabilizer of a state disturb the state?

In Nielsen and Chuang's "Quantum Computation and Quantum Information", Section 10.5.3, the authors claim the following: With a system in state $|\psi\rangle$ with stabilizer $g_1,...,g_n$, if a ...
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### theorems for universal set of quantum gates for SU(d)

It seems that there is a theorem that for prime dimension d, the set of Clifford gates and one non-Clifford gate together forms a universal set of quantum gates for SU(d). It also seems that for a ...
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### Is it possible to MAC a quantum state with a classical key under reasonable assumption?

Assume that classical one-way functions secure against quantum adversaries exist. Is it possible, given a quantum state $Q$ and classical secret key $k$, produce a quantum state $AuthQ$ such that: ...
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### Is it possible to encrypt quantum states under reasonable assumptions?

Is it possible to encrypt a quantum state, such that a $BQP$ attacker who does not know the secret key cannot obtain any information about the original state, but a $BQP$ decryptor with the key can ...
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### Is there a survey of the field of quantum automata?

I'm looking for a survey paper of the important concepts in the field of Quantum Automata. I've found Quantum Automata Theory -- A Review by Hirvensalo, but it sounds too succinct to grasp the topic. ...
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### In the algorithm of quantum phase estimation, how the deviation of unitary operation affect the result of obtained phase?

Given an unitary operation $U$ and one of its eigenvector state $|u\rangle$ such that $U|u\rangle=e^{2\pi i \phi}|u\rangle$, the algorithm of quantum phase estimation can be utilized to estimate the ...
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### Quantum complexity of maximum inner product search

Given two matrices $X \in \mathbb{R}^{m \times k}$, $Y \in \mathbb{R}^{n \times k}$, maximum inner product search (MIPS) asks for the largest $l$ entries of $X Y^T$. Typically $k \ll m, n$ (many ...
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### Quantum Data Compression Schemes

Quantum Computation has given speedups in algorithms, and even though we do not know the exact relationship of $BQP$ to $NP$ -we have many algorithms in quantum computation that give speedup in ...
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### Quantum algorithms for generalizations of determinants

There are a wide variety of determent-like constructions. Some like the permanent or immanents are variations on the ordinary determinant for matrices over fields or commutative rings. Some like ...
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### On FFT and trigonometric matrix eigenvalues

Let $N=2^n$ for a natural number $n$ and $B$ be the $N\times N$ square matrix of $0$'s and $1$'s  B=\begin{pmatrix} 0 & 1 & 0 & \ldots & 0 \\ 1 & 0 & 1 & \ldots ...
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### Quantum computer versus Random 3-SAT?

It seems to be commonly believed that quantum computer cannot efficiently solve NP-hard problems. What about the challenging problems in average-case, such as Planted Clique and Random 3-SAT?
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### Quantum GCD circuit: On reversibility and clearing ancillae

Originally posted on PHYS, however, obviously it has more to do with CS I am currently trying to implement a circuit for computing the greatest common divisor in the Quantum Computing Language. In my ...
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### Is unbounded quantum fanout operation experimentally feasible?

It is known that the "unbounded quantum fanout operation" is very powerful: (See, for example, Hoyer et al. : http://theoryofcomputing.org/articles/v001a005/v001a005.pdf). In particular, it is known ...
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### How the hardness of hidden subgroup problem in $S_n$ changes as the order of the subgroup grows?

In Normal Subgroup Reconstruction and Quantum Computation Using Group Representations by Hallgren et al. In this paper it is showed that no hidden subgroup algorithm can distinguish the trivial ...
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### Measurements in non-Abelian hidden subgroup algorithms

More than one measurement take place in a non-Abelian hidden subgroup algorithm. In this question, I would like to verify whether my understandings about them are right. I am using Andrew Childs' ...
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### Choice of basis for non-Abelian hidden subgroup problems

I am going through QUANTUM MECHANICAL ALGORITHMS FOR THE NONABELIAN HIDDEN SUBGROUP PROBLEM by Grigni et al. In section 1.1 it is said that, It is still possible that a clever choice of basis ...
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### Is there any hidden subgroup of a symmetric group which can be efficiently determined?

There have been a number of cases where efficient hidden subgroup algorithms have been found for specific non-Abelian groups with very specific structures. Why haven't we found any efficient quantum ...
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### Why hidden subgroup problem is easy for very large subgroup?

I am going through QUANTUM MECHANICAL ALGORITHMS FOR THE NONABELIAN HIDDEN SUBGROUP PROBLEM by Grigni et al. On page 2, it is said that solving the hidden subgroup problem becomes very easy when the ...
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### BQP algorithm for two graph bisection problems and its implications on NP $\subseteq$ BQP

I read the paper Ahmed Younes, "A Bounded-error Quantum Polynomial Time Algorithm for Two Graph Bisection Problems", 2015. doi:10.1007/s11128-015-1069-y which is published in Springer's journal ...
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### 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 ...
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### 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 ...
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### Fourier transformation of the automorphism group of a graph

Following is an example of permutation cycle graph $\Gamma$ for a given permutation $\pi = \left(1\text{ } 2\right) \left(3\text{ } 4\text{ } 5\text{ } 6\right)$. The adjacency matrix $A$ is given ...