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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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26 views

Many Worlds Interpretation and Quantum Key Distribution / Quantum Computing

I'm trying to understand how to interpret Quantum Key Distribution and Quantum Computing in terms of the Many Worlds Interpretation of Quantum Mechanics. So according to the many worlds ...
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21k views

Why is Google's quantum supremacy experiment impressive?

In the Nature paper published by Google, they say, To demonstrate quantum supremacy, we compare our quantum processor against state-of-the-art classical computers in the task of sampling the output ...
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1answer
55 views

Is quantum entanglement contradictory with Schrödinger's cat?

As I understand, an electron spin is in a superposition state until the spin is observed. Due to the observation, it will either be spin up or spin down. Due to quantum entanglement, if one electron ...
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1answer
57 views

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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142 views

Properties of controlled $z$-rotations

Given $n$ qubit gate of the form c-z-z-z... (shorthand for c-z between qubit 1 and 2 followed by c-z between 1 and 3 and so on up to n qubits) it seems to be possible to find local unitaries which ...
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45 views

Is there a geometrical representation of classical bits, like that of the Bloch Sphere for quantum bits?

Consider only a single qubit. We know that it can be accurately described using the so called Bloch Sphere. Is there a similar geometric construction used to describe classical bits?
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52 views

What problems (other than crypto) can quantum computing solve?

So my (limited) understanding of quantum computing lends its self very well to breaking public-private crypto; by being able to factor products of large primes. However in some press releases (google ...
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247 views

In quantum Fourier transform, why can any controlled $R_{k}$ gate be formed by two controlled-Not gate?

Controlled $R_{k}$ gates are implemented in the quantum Fourier transform as shown here: Each of the $R_{k}$ on a qubit is in this matrix form: $$\begin{pmatrix}1 & 0 \\ 0 & e^{2\pi i/2^k}\...
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2answers
87 views

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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1answer
42 views

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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178 views

Quantum Computer Implementation

Hey I recently finished my bachelor in nanotechnology and am rather interested in quantum computation. I've already looked at the recommendation threads for this topic but they tend to be about ...
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96 views

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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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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34 views

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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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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11 views

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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119 views

Simulation probabilistic classical computation on quantum computers

Given an $N$-level quantum system with computational basis $\{|1> ,|2> , \cdots, |N> \}$, if we perform an unitary operation $U$ on a computational basis state $\{|j> \}$ and then measure ...
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1answer
33 views

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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1k views

How does Landauer's Principle apply in quantum (and generally reversible) computing

I understand that a reversible computer does not dissipate heat through the Landauer's principle whilst running - the memory state at all times is a bijective function of the state at any other time. ...
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1answer
25 views

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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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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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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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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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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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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Could quantum computers break any cipher? [closed]

I've been told that physicists and computer scientists are working on computers that could use quantum physics to increase significantly computation capabilities and break any cipher so cryptography ...
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The physical picture of uncle Hamiltonian?

Uncle Hamiltonian was built to show the complex relationship between MPS (Matrix Product State) states and Hamiltonians, which claims that for a block injective MPS state, we can build a local ...
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1answer
566 views

Hamiltonian reduction having constant of the motion

I have this $2^n*2^n$ matrix that represent the evolution of a system of $n$ spin. I know that I can have only one excited spin in my configuration a time. (eg: 0110 nor 0101 ar not permitted, but ...
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45 views

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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288 views

What is the decoherence time scale for the most promising quantum computing implementations

I'm searching for some data about decoherence time scales for qubits in modern quantum computing implementations. The only reference I have is a table in "Quantum computation and quantum information"...
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202 views

Quantum Approximate Optimization Algorithm

I try to understand the 'Quantum Approximate Optimization Algorithm' (QAOA) by Farhi et al. - arXiv:1411.4028. I understand that the solution is hidden in the unitaries, but I do not understand how ...
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Understanding amplitude amplification in quantum computing

In short, what is the essence of amplitude amplification type of techniques that appear in quantum computing? More precisely, my main questions are, relating them more to Grover's search which ...
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82 views

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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1answer
33 views

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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1answer
36 views

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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1answer
47 views

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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1answer
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What does “interference” mean when referring to quantum computation?

I keep coming across off-handed references to "interference" in the context of discussions of the unique features of quantum computers. I understand that these references may mean (or seem to mean) ...
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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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1answer
2k views

Quantum circuit for a $3$-qubit $|W \rangle$ state

Can someone specify a quantum circuit that will deterministically output the $3$-qubit $|W \rangle$ state, if the input to the circuit is $|0,0,0 \rangle$? Or, is there a quantum circuit with a ...
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44 views

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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1answer
39 views

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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35 views

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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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 ...