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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What is the link between regular quantum mechanics and quantum computing?

In the quantum mechanics we are taught first at uni, we learn about schrödinger equation, $i \hbar \partial_t |\Psi\rangle = \hat H |\Psi\rangle,$ eigenvectors $|\Psi \rangle$, and operators on the ...
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Qubits of higher dimension

In Quantum Computing, one usually looks at two-state-systems named qubits to perform a computation. One problem arises when the number of qubits is increased, because the whole system becomes in such ...
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Neutrinos, quasiparticles and Majorana fermions

In connection with topological quantum computing I encountered term Majorana fermions. According to Wikipedia these are: A Majorana fermion, also referred to as a Majorana particle, is a fermion ...
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Measuring overlap of two quantum states

I have a qubit state $|\psi\rangle = a|0\rangle + b|1\rangle$, and another qubit state $|\psi'\rangle = a'|0\rangle + b'| 1 \rangle$. I want, through quantum gates, to measure the overlap $|\langle \...
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Compute the Schmidt Decomposition of a two-qubit state

I'm trying to compute the schmidt composition of $$ |A\rangle = \frac{1}{2 \sqrt{2}}(|00\rangle + \sqrt{3}|01\rangle + \sqrt3 |10\rangle + |11\rangle) $$ I've calculated the eigenvalues to be $$ 1+\...
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Can we obtain the same result as Deutsch algorithm using a XOR gate?

If I understand correctly, Deutsch's algorithm is useful to know if a function $f(x)$ is constant ($f(0)=f(1)$) or balanced ($f(0) \neq f(1)$). And the advantage is that it only requires the ...
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Action of quantum fourier transform on two-fermion states

In section 2.2 of the paper https://arxiv.org/abs/1807.07112, there appears a Fourier transformation named $F_k^n$ that comes out of a matrix called $F_2$, $$ F_2 = \begin{pmatrix} 1 & 0 & 0 &...
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Quantum gate fSWAP acting on two-fermion states

When we have identical particles which are fermions, any exchange (swap) among 2 states introduces a minus sign. In the paper https://arxiv.org/abs/1807.07112, the Eq. (7) aims to represent that ...
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Is there an analog of the Solovay-Kitaev Theorem for approximating quantum states?

The Solovay-Kitaev theorem shows that we can approximate arbitrary unitary transformations with polynomially many quantum gates. Can we approximate the resulting state vectors in the same way by ...
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What is the precise mechanism for the speed of a quantum computer? [closed]

This site may not be the right place to ask this question because it is both a physics and a computing question. In quantum computing, I get that qubits have many more states than zeros and ones. But ...
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Can quantum computing solve the curse of dimensionality?

Edited version The curse of dimensionality is ubiquitous in machine learning (ML) modeling, stochastic control and reinforcement learning, arising in a probabilistic sense, with strong connections to ...
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What happens to the Universe if a quantum coin in a black box is secretly flipped for zillions times?

First, let us using an IBM quantum processor (QP) to run the following simple quantum circuit: The IBM $U_3 (\pi/3,0,0) $ gate transforms the initial state $q[0] = \vert0\rangle$ to a biased quantum ...
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Finding the lowest eigenvalue using VQE-like circuits

I want to find the lowest eigenvalue for the following hamiltonian using VQE_like circuits (in python), but I don't want to use quantum libraries. \begin{eqnarray} H &=& \frac{-3}{2} I \...
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Prove that there exists a $d \times d$ unitary matrix $U$ which cannot be decomposed as a product of fewer than $d-1$ two-level unitary matrices

This is exercise 4.38 from Nielsen and Chuang: Prove that there exists a $d \times d$ unitary matrix $U$ which cannot be decomposed as a product of fewer than $d-1$ two-level unitary matrices. If ...
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What is a Polariton and why are they useful in unconventional computing?

My lecturer has frequently mentioned the term polariton and a quick search on the Internet lead me to its Wikipedia page (which is not surprising but the page is not particularly helpful) as well as a ...
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What operator do we use to measure at the end of a quantum search algorithm?

Perhaps an obvious question, but I do not have the answer to it, so I though I would still ask. In the below quantum search algorithm, also known as Grover's algorithm, what operator are we ...
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Which technologies are currently known for building quantum gates? [closed]

Which approaches/technologies are currently known for building quantum gates? Apparently, there are different methods proposed in different methods in different papers for this purpose.
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Good resourse for Ising Problem Model

I am student of mathematics, and I will wrote theoretical article about Ising problem in Adiabatic Computation. Do you have a good resource where it is good explaining? In my context I have ...
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How is the Hamiltonian changed in Adiabatic Quantum computing?

In adiabatic quantum computing, we define a time-dependent Hamiltonian, which is then changed gradually to obtain a solution to an optimization problem. Is the Hamiltonian changed automatically, or we ...
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Wick-rotated quantum computers e.g. to be realized with Ising-like systems?

Quantum mechanics is equivalent with Feynman path ensemble, which after Wick rotation becomes Boltzmann path ensemble - and e.g. Ising model is a basic condensed matter model, which is assumed to use ...
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Can a quantum computing advantage exist in a deterministic universe?

Is a deterministic universe with nonlocal hidden variables incompatible with the quantum superpositioning of states that is required for quantum computing?
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How does QC work? [duplicate]

I watched this video https://m.youtube.com/watch?v=g_IaVepNDT4 That says QC has 2 to the N bits. And that is somehow useful. But they don’t say why lots of bits can be useful. Can anyone please ...
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How are topological qubits encoded in the Majorana-fermion-based platform for quantum computing?

Where is “the two level system” of a topological qubit encoded in the Majorana-fermion-based platform of quantum computing? If the Hamiltonian in a topological quantum field theory is absent (H=0), ...
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Understanding surface code diagrams

I'm trying to understand the diagrams used in the following paper. I'm new to the area so I don't have experience with the stabilizer formalism, but I'm trying to figure out what's going on in the ...
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Nuclear Fusion and Quantum Annealing

This is a pie in the sky idea, and a problem finding sort of question that can probably be dismantled easily, but in light of alternative energy needs with climate change, I think it would be ...
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Degree of Quantum Entanglement

I am a bit confused about the definition of "degree of quantum entanglement". 1- Could anyone give me a generic definition for that? Moreover, it is not intuitive for me the strategy by which we ...
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Can a Hadamard gate be realized with perfect precision?

This is my first question on the Physics Stack Exchange; I hope it is not be a duplicate… :-| I am not really a physicist (I am actually a professional mathematician), but I have already read quite a ...
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Does any practical system actually use the Kirchhoff-Law-Johnson-Noise (KLJN) secure key distribution mechanism?

http://www.scholarpedia.org/article/Secure_communications_using_the_KLJN_scheme describes the Kirchhoff-Law-Johnson-Noise (KLJN) secure key distribution scheme, which is based on two switches and an ...
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Is there a common mathematical foundation for quantum and classical computation?

Is there a (natural) formalism that neatly and insightfully includes classical and quantum computation? I have a mostly sound basis in quantum mechanics (as a physics grad), and a much less sound but ...
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Classical brain - quantum world [closed]

A noted author (physicist) recently stated that he perceived the human brain as a classical mechanism powered by quantum mechanics. He went on to say that we are reaching the point where we are ...
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Hamiltonian Simulation in Qiskit

I would like to simulate the time evolution of a quantum system Qiskit. Qiskit, however, only supports Hamiltonians that are a sum of hermitian matrices and that can be expanded into tensor products ...
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Non-Abelian Statistic of Majorana Fermions and Quantum Computing

I read in many sources that braiding operations of Majorana excitations in (topological) superconductors do not commute, and that this fact is useful in quantum computing. However, about this last ...
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Hamiltonian for 2-qubit system

What is the general form of a Hamiltonian for a 2 qubit system? The Hamiltonian for D-Wave system is: $H = K_1\sigma_x^1 + K_2\sigma_x^2 + H_1\sigma_z^1 + H_2\sigma_z^2 + J_{12}\sigma_z^1\sigma_z^2 ...
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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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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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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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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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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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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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