Questions tagged [quantum-computer]
The quantum computing tag is relevant for computing that uses quantum states such as superposition and/or entanglement to locate low energy states as solutions to complex problems (rather than laboriously enumerating and checking solutions as would be done with non-quantum traditional computing).
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Exercises with solutions on entanglement and quantum computing - a resource recommendation
I'm reading the book "Entangled Systems: New Directions in Quantum Physics" by Jurgen Audretsch to learn more about entanglement and quantum computing. I have looked on Library Genesis and plenty of ...
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Prove that the Quantum Fourier Transform satisfies $F_N(\sum_x |xr \rangle) \simeq \sum_y |y N/r \rangle $ when $r$ divides $N$
Before I start, this is a homework question, but I have spent the last 7 hours on it and gotten nowhere. I will mention what I've tried and noticed, but it's not much. At this point, I'm wondering if ...
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What does it mean to simulate a quantum system?
What does it mean by simulating quantum system? Can I simulate Young's double slit experiment with a quantum computer? If yes, won't it violate no-cloning theorem?
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Hamiltonian capable of quantum computation
Suppose we have a 1D spin chain evolving in time according to some Hamiltonian $H_t(p_0, p_1, p_2 \ldots)$, where $p_i$ are classical parameters ``set by the lab equipment". Divide time into discrete ...
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Why a quantum computer simulation is not a quantum computer?
Is it because the inability to generate true random numbers (I dont think so) in the host machine or something else?
My understanding is that the ability to emulate a quantum computer in a ...
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Why do quantum computation models based on open quantum systems receive so little attention?
In almost all research on (universal) quantum computation the common models assumed from the outset are either the quantum circuit model with unitary gates, the measurement-based one-way model or the ...
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Is there a theoretical limit on the smallest angle that can be used in a quantum rotation gate?
Assuming ideal conditions and no error, what is the smallest $\theta>0$ that can be used in $R_x(\theta)$ or $R_y(\theta)$.
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Why doesn't using quantum error-correction increase the production of entropy and decohrence?
Error-correction in quantum computing is designed to get around the decoherence "washing out" the answer to a computation. But wouldn't the introduction of error-correction procedures or apparatus ...
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Spintronics: How can we inject a spin current into/onto a sample without physically touching it, ie: modulation with a field?
So background, I'm imagining a black box scenario where we have some spintronic system.
It might be a topological quantum computer that uses spin currents running across it's memory to connect ...
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Do rotating phases limit the possibility to perform quantum computing?
Let me try to make several statements which I believe to be true - I'm basically hoping that somebody will point out where I make an error (or errors).
1) per wikipedia, any two-level quantum ...
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Can a Controlled-Swap gate control itself in a Quantum Computer?
Let there be a system of three qubits, $a,b,c,d$ where $d$ is an ancilla qubit. We can add more ancilla if required. The operation I want to implement is as follows:
"If $a$ and $b$ are both in the '$...
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How does quantum computing work if the wavefunction has no reality?
This is probably a dumb layman question but as I understand it quantum computing makes use of the superposition principle in which a qbit can be in more states at once until it’s observed. A ...
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Can someone help in applying covariance condition to this unitary transformation?
I am trying to apply covariance property on this Quantum adder transformation in which a two particle input state is mapped onto a two particle output state. I am trying to represent these states into ...
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Wave function collapse of photon state transformed by beamsplitter
$\newcommand{\ket}[1]{\left|#1\right>}$I am trying to make sense of the math behind transforming the state of a photon with a beam splitter.
Suppose I have a beamsplitter crystal which split by ...
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General structure of parity preserving two qubit gate
I am trying to decompose a set of two qubit gates repecting parity, though I am not sure whether parity is the right word for this. The gate has the following structure:
$$\begin{bmatrix}
u_{11}&...
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Exchange Non-abelian Anyons results in rotation in Vacuum degenerate space?
A basic notion when studying non-abelian anyons is that the system's groundstate is degenerate. Not only that, but exchanging two anyons' position rotates the state in this degenerate subspace. I'm ...
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Does $U^T U$ have real eigenvectors if $U$ is unitary?
I was reading a paper by Kraus and Cirac on general two qubit gates. A crucial step is to decompose an arbitrary unitary operator acting on two qubit space into a special form:
$$ U_{AB} = U_A\otimes ...
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Question about implementation of a “reflection” w.r.t a state in quantum computing
I'm going through a paper that uses quantum amplitude estimation, and one of the ingredients to the algorithms is an operator that flips the sign of a state based on the state of a control qubit. ...
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Can quantum disentanglement be triggered by time dilation?
The question is really one question that leads to the final one:
Is it possible to realize a qubit that naturally flips between two quantum states on a definite and fixed period without any ongoing ...
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Why do we need Jordan-Wigner transformation when simulating fermionic systems on quantum circuits?
Why do we need to do a Jordan-Wigner transformation when we want to simulate the fermionic systems with a quantum circuit model? I understand that the spin operator $\sigma_x, \sigma_y, \sigma_z$ on ...
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What distinguish a non-interacting two fermions gate from an interacting one?
We start with a Hilbert space consists of two fermions(a and b), which is 4-dimensional. The basis would be $|vec>$,$b^\dagger|vac>$,$a^\dagger|vac>$,$a^\dagger b^\dagger |vac>$.
Denote ...
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Can quDit gates be non-unitary
I have derived a quantum quDit gate that is implemented by photon Fock state inteference. It turns out to be non-unitary. I thought I must have made a mistake, so I have checked several times. I know ...
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how to construct a triple-controlled unitary gate?
I try to construct multiply-controlled qubit gates and I did. But I'm not sure how to construct a triple-controlled unitary gate for four
qubits, starting from a version that controlled by only one ...
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Inverse covariance matrix for a Gaussian state
I was reading an article about Gaussian Boson Sampling (https://arxiv.org/pdf/1801.07488.pdf) and following some calculation appear an inverse covariance matrix when he defines the following matrix A.
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Quantum Gates: What is the mathematical difference between the the phase shift gate and the Pauli Z rotated by pi/2?
I come from computer science, and I am trying to get into quantum computing research. I am going through Microsoft's quantum katas and I'm struggling to grasp some of the mathematical nuances ...
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Understanding Skein relations
I'm just studying some concepts in the topology, but I cannot figure out totally how Skein relations work.
in the following I've one example:
which tries to relate Reidmeister II to the Skein ...
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Is it possible to know whether an arbitrary system is performing a quantum computation?
Without knowing in advance that a physical system has been configured to do so, is it possible to determine whether that system is preforming, or has just performed a quantum computation?
That is, if ...
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Can all CFT state be prepared through scale invariant MERA
It is known that in numeric computation, scale invariant MERA is useful for representing a CFT vacuum state. Is the converse true? i.e. all CFT vacuum state (the quantum state with translation and ...
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What is the simplest circuit on a quantum computer that “proves” superposition/entanglement
I am a Physics Teacher at pre university level.
Tunneling, wavefunctions and uncertainty are on the syllabus on a very vague way. Quantum superposition and entanglement are not but tie in well and I ...
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5 qubit quantum error correction property [closed]
Having
$$\eqalign{
|v_0⟩&=|00000⟩+|11000⟩+|01100⟩+|00110⟩+ {}\cr
&\quad |00011⟩+|10001⟩−|10010⟩-|10100⟩− {}\cr
&\quad |01001⟩−|01010⟩−|00101⟩−|11110⟩− {}\cr
&\quad |...
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Random quantum walk related to quantum computing
I am an undergraduate doing research on QC/QI. My current topic to learn is continuous-time quantum walks, but first I must learn the random quantum walk. That being said, I was wondering if someone ...
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For Grover's search: How can a quantum computer store the data, and how can it overall be faster than a classical computer
I think Grover's algorithm can be used to find which entry in a list of names contains a given name, say "Fred" in entry number 12345.
Each name can be seen as a binary number, so we might expect to ...
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In quantum search algorithm, how to interpret the effect of $U(t)$ as a rotation on the Bloch sphere?
In Nielsen's QCQI, in page 259, it reads,
$$U \left ( \Delta t \right ) = \left ( \cos^2 \left ( \frac {\Delta t} 2 \right ) - \sin ^2 \left ( \frac {\Delta t} 2 \right ) \vec \psi \cdot \hat z \...
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How to perform quantum logic gates on plasmons?
in the link provided researches utilize strong two-plasmon absorption in graphene nanoribbons to create a “square-root-of-swap”, could such a device be utilized to perform other quantum logic gates?
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Topological superconductors
I have been reading a lot about quantum computation by using topological materials and I could see that the standard approach is to engineer a p-wave superconductor by using a 1-D semiconductor wire ...
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Universe simulation
Is it theoretically possible to simulate the universe? I know that some philosophical theories say that our universe is a computer simulation, but is this feasible? Would it ever be possible for a ...
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What happens to physical qubits when they decohere during quantum error correction?
Say you have a scaled up system with 98% fidelity so 2% decoheres. These are physical qubits doing error correction on information encoded on logical qubits. 98% of these entangled qubits will be ...
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Understanding Anyonic Exchange
In the book of "Introduction To Topological Quantum Computation" by Jiannis K. Pachos, in chapter 5, it tries to explain anyonic exchange.
In the following, the $m$ and $e$ quasi-particles are ...
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Why can a nitrogen-vacancy center be viewed as a basic unit of a quantum computer?
I was on the Wikipedia page for Nitrogen-Vacancy Center and in the first paragraph the following statement is made:
An individual N-V center can be viewed as a basic unit of a quantum computer, and ...
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What does $e^{i\alpha}$ stand for in the general expression for a qubit gate $e^{i\alpha}R_n(\theta)$?
All qubit gates can be written in the form of:
$$U = \exp(i\alpha)R_n(\theta).$$
I know $R_n(\theta)$ is a rotation of $\theta$ about an arbitrary axis n in Bloch sphere, but what does $\exp(i\alpha)...
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“Quantum information and quantum computation”: quantum period finding algorithm
The procedure for a quantum period-finding algorithm is described on page 236 of "Quantum Computation and Quantum Information" by Isaac Chuang and Michael Nielsen.
In step 3 of the procedure, authors ...
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Fluxes on a finite group $G$
So I've been studying about topological quantum computation and I have a few questions I haven't been able to solve. The first one is why fluxes take values on a finite group $G$? Does it have to do ...
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What quantum volume is needed to represent a single fault-tolerant logical qubit?
The quantum volume metric $V_Q$ is a proposed metric for quantifying and comparing the performance of quantum computers[1]. The quantum volume is defined as
$$V_Q = \max_{n<N} \left(\min\left[n, d(...
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Can any 1D critical state be represented by a MERA tensor network?
My understanding of the Multiscale Entanglement Renormalisation Ansatz (MERA) is that it is designed to represent highly entangled, but low complexity states.
Is MERA capable of representing high ...
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Why is EIT needed to story memory using rydberg atoms?
I was going through a paper explaining how the write-in and read-out efficiencies can be increased using cold atoms where they used Rydberg atoms, and mentioned that they were probed using EIT(...
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Isn't the Church-Turing-Deutsche (CTD) Principle an empirical question?
The Church-Turing-Deutsche (CTD) Principle is the idea that all physical processes are computable by a quantum computer (i.e. quantum Turing machine).
Before I knew this idea had a name, I always ...
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Superoperator cannot increase relative entropy
So I have to show that a superoperator $\$$ cannot increase relative entropy using the monotonicity of relative entropy:
$$S(\rho_A || \sigma_A) \leq S(\rho_{AB} || \sigma_{AB}).$$
What I have to ...
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How to identify whether a quantum state is entangled or separable if you can measure it only in one basis?
Suppose you have two qubits and don't know whether they're in an entangled state $ \frac{1}{\sqrt{2}}\left(|0,0\rangle + |1,1\rangle\right)$ or in an equal mixture of states $ |0,0\rangle $ and $ |1,1\...
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Can someone explain how does Gisin apply the No Signaling criterion here?
So given the density operator for the state. He uses the no signaling condition which says that "If we have an entangled state between Alice and Bob and Alice measures the state in any basis pair the ...
