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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144 views

Why is the partial trace of this subsystem equal to this? [closed]

I am doing my bachelors dissertation based on an article by David Deutsch. He defines the action of a quantum gate as: $$ U = \sum_{x, y \in \mathcal{Z}_{2}} |x \dot{+}y\rangle|y\rangle\langle x|\...
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Hermitian quantum gate's Hamiltonian

Looking the formal solution of Schrödinger's equation: $$ \tag 1 \Psi (t) = \hat{\mathrm T} \exp\left[-i \int \limits_{0}^{t} \hat{H}(t^{\prime})~\mathrm dt^{\prime}\right]\Psi (0), \qquad t>0, $...
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39 views

What is a finite cellular automaton?

I found this paper: https://arxiv.org/abs/1606.08764 There, it is said "We realize constant-space quantum computation by measure-many two-way quantum finite automata" What are "finite automata"? ...
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750 views

Projection Operator in Quantum Mechanics

From a $9\times9$ Hamiltonian lying 9D space, I choose a certain subspace of 4D for designing a two qubit gate. Now the original unitary time evolution operator also lies in 9D space and it's a $9\...
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116 views

The hamiltonian of single trapped ion model: ion trap quantum computer

This question is related to the textbook, "Quantum Computation and Quantum Information written by M. A. Nielsen and I. L. Chuang. I tried to derive a relation when we deal with a model system where a ...
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2answers
401 views

Are photons being considered as qubits for a potential quantum computer?

I've been reading a few articles on photons that are capable of carry bits of information. I was wondering if anyone knew if there are any team of research scientist who have tried to use a photon as ...
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41 views

what is a topical qubit and how do they correct each other? [closed]

In an article I read " What sets company X apart are topical qubits that correct each other." Google did not return results for "topical qubit". Can someone explain the topical qubit - assuming ...
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1answer
188 views

quantum superdense coding -How many qubits are needed?

This is an extract from Wikipedia about superdense coding: "In quantum information theory, superdense coding is a quantum communication protocol to transmit two classical bits of information (i.e., ...
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Suggestion for books about mathematics of quantum entanglement and computation [duplicate]

I am reading book called Mathematics of Quantum Computation by Ranee K. Brylinski and Goong Chen, and it's really what I need since I am working on quantum entanglement and this kind of stuff, but the ...
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Grover's algorithm: a real life example?

I'm fairly confused about how Grover's algorithm could be used in practice and I'd like to ask help on clarification through an example. Let's assume an $N=8$ element database that contains colors ...
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Trying to prove the Hadamard gate leaves a state unchanged

It is known that the Hadamard gate is the equivalent of doing a 180 degree rotation about the x + z axis. I am therefore trying to prove that applying the gate on the state ...
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202 views

Quantum computer vs. classical probabilistic computer

Is it possible to make a quantum computer from a perfect random number generator. I'm wondering if anybody that's studied it could make one from that type of random number generator.
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Can adiabatic quantum computing be faster than Grover's algorithm?

It has been proven that adiabatic quantum computing is equivalent to "standard", or gate-model quantum computing. Adiabatic computing, however, shows promises for optimisation problems, where the ...
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46 views

Electronic states of a molecule for qubit in quantum computing

Can electronic states of a molecule be used for representing qubits? I recently studied quantum computing a little bit with "Quantum Computation and Quantum Information" written by M. A. Nielsen and ...
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214 views

Proof of the Universality of Toffoli and Hadamard Gates

I was trying to reproduce the result that the Toffoli gate and the Hadamard gate are universal for quantum computation as proved by Shi in "Both Toffoli and Controlled-NOT need little help to do ...
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How to physically implement quantum X and Y logic gates in cold atoms?

The Z quantum logic gate can be represented as $$\left( \begin{matrix}1 && 0 \\ 0 &&-1\end{matrix} \right)$$ and can be physically implemented with a rotation around the $Z$ axis by $...
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How Forces are Represented from Quantum Computation or Entanglement Perspective?

In the fields of Quantum Computation and Entanglement there is content on the structure of quantum systems and artificial quantum systems like qubits and quantum cellular automata. I have even seen ...
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How do you write the matrix form of $Z_1 Z_2$ as a quantum circuit?

I am reading about the quantum bit flip error correction on the wikipedia page: https://en.wikipedia.org/wiki/Quantum_error_correction In order to perform the projective measurement to identify the ...
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219 views

Does the physical distance between qubits influence the speed of quantum computers?

I've heard lots of talk over the past decade about the potential of quantum computing. Most of what I've read about the topic (mostly articles targeted at the layman) focuses on the exponential ...
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54 views

Example of Quantum Fourier Computation for three qubits [closed]

I am currently going through Nielsen's QC bible and having still some foundational / conceptual problems with the matter. I have tried to retrieve this $8 {\times} 8$ matrix describing the QFT of 3 ...
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57 views

Example for Digital Quantum Simulation of k-local Hamiltonian

I am currently going through Nielsen's Quantum Comp. and Quantum Information. I don't understand how this computes the time step for our three cubits. Why is there any action at all, the gate is just ...
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Is there any long-term drawback of circuit QED systems for Quantum Computation?

As many of you will well know, circuit QED has dominated the QIP scene with astonishing results in the last decade. Almost all industrial approaches use this environment aswell and I could not find ...
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115 views

Models for non-universal topological quantum computation

Anyon models do not lead in general to universal topological quantum computation (= existence of a universal set of quantum gates) when only the braiding is used for implementing gates. The Fibonacci ...
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Why quantum computing companies use superconducting qubits? [closed]

Why are superconducting qubits superior to other types of experimental realisation of qubits? I assume this because Dwave, IBM, rigetti among other companies in the quantum computing business use ...
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208 views

What happens to a qubit in superposition that goes through a Pauli-X gate?

Suppose, you have the following quantum circuit: We start with a qubit and put it through a Hadamard gate which will put the qubit into superposition. Now, we apply the Pauli-X gate to the qubit in ...
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Does “natural” superposition of particles exist?

While studying the basics of quantum computers, I came across Hadamard gates and learned, that these gates are used to put qubits into superposition meaning that these qubits are both, 0 and 1 at the ...
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Classical analogy for why driving a quantum harmonic oscillator creates a coherent state?

If we drive a quantum harmonic oscillator (e.g. starting from its ground state) at its resonance frequency then it will not just create an excitation in the first excited state but will create a ...
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759 views

How many maximum possible combinations can be stored in qubit?

I read the basic introductory information about qubits on Wikipedia: There are two possible outcomes for the measurement of a qubit—usually 0 and 1, like a bit. The difference is that whereas the ...
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1answer
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Is it possible to build a “DIY” quantum memory?

I am currently working on a home project which is a computer which will be capable of doing basic quantum computations (my first goal is a random-number generator) based on optical devices. Nowadays I ...
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1answer
95 views

The factorization of a qbit product state is not unique; how should the different factorizations be interpreted?

Consider two arbitrary qbits; their product state is as follows: $ \begin{bmatrix} a \\ b \end{bmatrix} ⊗ \begin{bmatrix} c \\ d \end{bmatrix} = \begin{bmatrix} ac \\ ad \\ bc \\ bd \end{bmatrix} $ ...
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If a state can be efficiently represented by a Projected Entangled Pair State (PEPS), can we prepare it physically?

If we can use PEPS (Projected Entangled Pair State) to represent a many body quantum state, can we generate it by a quantum computer? As far as I can understand, PEPS is dual to a quantum computer ...
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64 views

How is Deutsch-Jozsa algorithm for quantum computation useful?

In Deutsch–Jozsa algorithm, in order to encode the function into a unitary which can be used for the computation, we need to know the function beforehand. What is the use of finding whether a function ...
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Quantum teleportation reversible?

The following figure displays a circuit implementing quantum teleportation. It uses Haramard transform (H), controlled not (+), measurements (meas), a Not gate (N) and a phase shift gate (P) to ...
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Time for Quantum Computational Prime Factorisation

I ran into this graph where the red one is $$x^3$$ and represents the number of steps as a function of factorised bits for a quantum computer. The blue graph represents the classical computer and has ...
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Again: why do quantum computations need to be reversible?

In quantum computing, there is famous "law" which is to say that all the computation must be reversible. I understand that, for simplicity, it may be easier to consider reversible operation, and that ...
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Is a GPU accelerated Quantum computer simulator publishable research?

I have built a GPU accelerated quantum computer simulator that is quicker then libquantum and the IBM QISkit simumators. Is the work done on this (methods, archetecture) publishable?
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Intuition on quantum teleportation

I'm trying to understand quantum teleportation and I was wondering if anyone could provide an intuition about it. I have seen the derivation but it still bugs me. You start with an entangled pair of ...
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181 views

Extract single qubit state from combined state in QuTiP using a Hamiltonian

This questions is very similar to another question asked a couple of months ago. I would like to extract the state of single qubits from combined states, using QuTip (the Quantum Toolbox in Python) ...
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268 views

Simple proof of classical fidelity of teleportation

I understand that the optimal value, i.e 2/3, can be achieved if Alice and Bob are connected via a classical channel, and Alice makes a projective measurement. Note that this is just one of the ways ...
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412 views

Quantum computing: CNOT gate

A CNOT gate can be written as follow: $$\begin{pmatrix}1 & 0 & 0 & 0 \\\ 0 & 1 & 0 & 0 \\\ 0 & 0 & 0 & 1 \\\ 0 & 0 & 1 & 0 \end{pmatrix}$$ So using ...
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What is a “fiduciary” quantum state?

In Giovanetti et al.'s paper "Quantum Random Access Memory" (arXiv:0708.1879) they state: If the qutrit is initially in the $|wait\rangle$ state, the unitary swaps the state of the qubit in the two ...
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63 views

Can a quantum computer implement a classical one?

The normal question about this topic would be: Can a classical computer implement a quantum computer? But now I wonder the exact opposite: can a quantum computer implement a classical one? Can we say ...
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313 views

Why is the projection operator corresponding to $\tilde M$ given by $P_m\otimes I_B$?

Nielsen and Chuang, Chapter 2 (Box 2.6): Suppose $M$ is any observable on a system $A$, and we have some measuring device which is capable of realizing measurements of $M$. Let $\tilde M$ ...
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86 views

Are eigenvalues of the states $|0\rangle$ and $|1\rangle$ always same?

Nielsen and Chuang, Chapter 2 (Box 2.6): Suppose $M$ is any observable on a system $A$, and we have some measuring device which is capable of realizing measurements of $M$. Let $\tilde M$ ...
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How to write the probability of ending up in a state where qubit $A$ is in the state $|0\rangle_A$ when $A$ is measured, in the bra-ket notation?

I need some help with the bra-ket notation. Suppose we have a normalized wavefunction for a two-qubit system (where $A$ and $B$ denote the two qubits respectively), like: $$|\psi\rangle_{A B} = a(|0\...
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69 views

Which set of basis states can a quantum system of qubits actually collapse to?

I was watching a video on "How Does a Quantum Computer Work?". I'm confused about what they mean by: "Although the qubits can exist in any combination of states, when they are measured they must ...
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Can you use Quantum Annealing to calculate a Hash collision?

I saw in another stack exchange post that the same way quantum annealing can be used to factor primes, it can also be used to calculate a collision in SHA-1 and it references this paper https://arxiv....
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61 views

Is Trojan-Horse attack possible in BB84 QKD?

In some QKD phase-encoded schemes, a third party can perform a trojan-horse attack to observe the settings of Bob's phase modulator. Does this compromise the established secret key in the BB84 ...
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How do expected values of observables depend on the current state?

I'm currently looking into quantum computing following the book The Nature of Computation. On pages 835/836 they define observables and the expected value of an observable corresponding to a hermitian ...
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What are the quiescent states of the surface code?

Notation $$X \equiv \sigma_x \qquad Z \equiv \sigma_z$$ Introduction The surface code is a quantum error correction code. In the surface code, we have a two-dimensional grid of qubits each coupled ...