# Tagged Questions

Theoretical issues related to the quantum treatment of information

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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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### 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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### 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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### What are the general classes of measured systems

Imagine there is a class of system such that a measurement can be performed on an exemplar of this class, each measurement producing 1 bit of information. There are no limitation on how many times the ...
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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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### 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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### 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 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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### 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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### 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 ...
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### 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 ...
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### How the errors of the measured quantities of an adiabatic Hamiltonian are inversely proportional to the square root of the number of measurements?

I am going through the paper, Solving the graph-isomorphism problem with a quantum annealer, by Hen et. al. In the last line of the second paragraph of the second column of page 2, it says, Since ...
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### Are two-qubit unitaries necessary for universal quantum computation?

I was going through Fast Universal Quantum Computation with Railroad-switch Local Hamiltonians by Daniel Nagaj. In the first sentence of the fifth paragraph on the fourth page, he said, Two-qubit ...