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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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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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 ...
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Macroscopic number of qubits (Sсhrödinger cat)

I noticed, that current designs if quantum computer like IBM Q, include supercooled chamber to allow matter to be in quantum state. I thought, if this really required? To obtain Sсhrödinger cat one ...
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Can this state be expressed as a product of three one-qubit states?

For the following three qubit state: This state can't be represented as a product of three single qubit's. The answer is that there are correlations between the three qubits, which I do not ...
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What does passing one qubit that is entangled with another through a CNOT gate do?

I am watching this video in which a programming language for quantum computing is introduced. There is code like this: ...
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Physical system for exchanging entanglement between types of particles

What is an example of physical system in which entanglement is transferred from one pair of particles to a different pair of a completely different type of particle? For instance, if I have two ...
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Efficient quantum circuit to prepare a set off entangled state

If I try to prepare an entangled state on $N$ pairs of qubits ($2N$ qubits) as $$|\psi\rangle=\sum_{i=1}^{2^N}w_i|ii\rangle , $$ with $w_i$ real factors, is there an efficient quantum circuit to ...
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Complexity of Ab Initio quantum computation of bulk properties [closed]

Background I'm an undergrad studying Computer Engineering, however I switched from ChemE. I just completed Physics 2, however I've a cursory understanding of higher level Physics concepts (Hamilton ...
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Testing Quantum Mechanics with Quantum Computing: beyond? [closed]

Quantum computing ONLY allows for unitary operations. At least in theory, as far as I know. Could we use Quantum Computing to test the limits of Quantum Mechanics or explore the emergence of quantum ...
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eigendecomposition of continuous formalism Hadamard gate for arbitrary amount of qubits

I have a problem in my simulation. I need to simulate a Hadamard gate by integrating Schrödinger equation (time evolution). This requires me to construct a Hamiltonian operator related to Hadamard ...
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Quantum measurements

I am reading the paper "Unconditionaly verifiable blind computation". It says at p.9: a measurement in the $\lbrace \vert +_{\phi_i^{\prime}}\rangle, \vert -_{\phi_i^{\prime}} \rangle\rbrace $ ...
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Reasonable to expect Moore's law for quantum computing?

Currently, the number of physical or logical qubits in different quantum computing prototype devices cannot be meaningfully compared because no one has demonstrated scalable fault tolerance, e.g., [...
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Improving classical processors with simulation or optimization on a quantum computer?

Two classes of applications for quantum computers are (1) solving constrained optimization problems [example] and (2) ab initio simulation of quantum systems [review]. Have there been any concrete ...
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Adiabatic QC: are there known difficult problems with spectral gap not exponentially decreasing?

Adiabatic quantum computers require slow evolution to maintain global minimum: $O(1/g^2)$ time, where $g$ is spectral gap: distance between two lowest energies. The danger is that this spectral gap ...
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203 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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Effect of Infinite Qubit Values in a Quantum Computer

Classical bits can be in one of two states 0 or 1, but a qubit can be in a superposition of those. Thus the number of states increase exponentially so does the computational power. I understand that ...
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What is a stoquastic Hamiltonian?

Recently, I've often read about the term 'stoquastic Hamiltonian'. But I couldn't find a precise definition anywhere. I found that the Ising-Hamiltonian is a stoquastic Hamiltonian, but that does not ...
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Relationship between the 'relevant states' and the states that can be generated by a quantum computer?

In the huge quantum state space, for example n-qubit space has a state number as $2^{2^n}$, usually we are interested in two different kinds of 'physical' states. Set 1: The relevant state which is ...
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Power consumption of a qubit?

I keep hearing “A quantum computer will consume so much power that it'll need a dedicated power plant.” I'm trying to find literature to back this up. I would love to get an estimate for the ...
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Extract single qubit state from combined state in QuTiP

I would like to extract the state of single qubits from combined states, using QuTip (the Quantum Toolbox in Python. Is there some QuTiP function that will extract a single qubit state from a ...
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Does having multiple quantum computers in parallel speed up Shor's Algorithm?

Essentially, how useful is it to have multiple quantum computers in parallel if the goal is to, for example, recover a 2048 bit RSA key?
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How hard is it to have loops in quantum architectures?

I recently discovered IBM's website where you can write a quantum circuit that acts on a few qubits, simulate it, and have it executed on an actual quantum architecture. (You submit your computation ...
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How much information can a qubit remember?

You can only extract one bit of information from a single qubit, but in some applications the ability to store a large amount of information and only later decide which portion is needed would still ...
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Is every fusion category with unitary $S$ a UMTC?

A tensor category whose solutions to the pentagon/hexagon equations are unitary and whose braiding is nondegenerate is called a unitary modular tensor category (UMTC). When trying to find UMTCs, ...
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How qubit would allow parallel operations?

Read Why Quantum Computers Will Be Exponentially Faster Than Digital Computers " Qubits can be both 1 and 0 simultaneously — meaning they can perform two calculations at once " How 2 ...
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Analyzing a quantum circuit

This is an exercise from Nielson Chuang that I am totally stuck at. First I can't understand why the measurement outcomes are related to the operation on the target bit at all. Second, why is the ...
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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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Is the choice of the automorphism of complex numbers relevant for Quantum Computing?

In Yale's paper, automorphisms on complex numbers $\mathcal{C}$ are shown to be wild, allegedly with cardinality $2^{\mathfrak{C}^{\mathfrak{C}}}$. There are two well-known ("trivial") automorphisms: ...
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Why does this Bernstein-Vazirani solution use $ (-1)^{f(x)} $

I am reading a solution to the Bernstein-Vazirani problem. For those unaware, the issue is to find a randomly selected $ 0 \leq a \lt 2^n $ given only a function $ f(x) = a_0x_0 \oplus a_1x_1 \oplus .....
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Constructing an arbitrary 2-Qbit state

I am reading a book on quantum computing. The author is constructing an arbitrary 2-Qbit state from unitary transformations. I need help understanding on step in his logic. He starts by noting that ...
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Why Do Multiple Hadamard Gates Return to Base State?

Reading through IBM's intro to quantum computing and gates and I'm confused about the Hadamard gate. When you use an H gate it appears to rotate the qubit along the X axis pi/4 putting it in a ...
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How to calculate the number of operations required to factor a number $n$ with Shor's Algorithm?

Essentially, how to find the number of clock cycles required to factor a number $n$ on a quantum computer with Shor's Algorithm? An example on any architecture would be helpful.
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why are qubits such a game changer in quantum computing? [duplicate]

Qubits are in a superposition which means that they can currently be both digits of 1 and 0 at the same time BUT this is my question: If Qubits have to be filtered to be used then what makes them ...
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Status of the discovery of non-abelian anyons and topological quantum computation?

This week Microsoft announced that it will make available the programming language for quantum computer available by the end of this (2017) year. https://news.microsoft.com/features/new-microsoft-...
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Topological Quantum Computation Resources Prerequisite

I am about to start my BSc Theoretical Physics project on Topological Quantum Computation. I have studied the basics of quantum mechanics, condensed matter phys, statistical mechanics. Are there any ...
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Will quantum computing provide any advantage for storing large amounts of data?

Essentially, does superposition or entanglement provide any advantage for data storage as opposed to classical memory.
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Distinguishable quantum states (“counterexample”)

In the book Quantum Computation and Quantum Information (Nielsen & Chuang) the section 2.2.4 discusses quantum distinguishability and arrives at the conclusion that if someone were to show me a ...
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QuantumControlled U gate

I'm reading about quantum circuits. I've just read about CNOT gate and after that, I read about the controlled U gate. Can someone please clarify what is the difference between the two circuits ...
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How to apply a general 2x2 quantum gate?

Say I have a standard qubit in it's basis state $\left|0\right>$, $\left|1\right>$ or in a superposition such as $\frac{\left|0\right>+\left|1\right>}{\sqrt{2}}$ or even a bell state $\...
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How would a quantum computer deal with small accumulated errors during a long computation?

As I understand it, a Quantum Computer has qubits, where the system is in a state such as: $$c_0 |S_0\rangle +\ c_1 | S_1\rangle \ + ... +\ c_n|S_n\rangle $$ where $c_0, c_1, ..., c_n$ are complex ...
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Recover information from unknown pair of qubits

If I have one of the following pair of qubits: $$ \frac{1}{\sqrt{2}}(|0\rangle+i|1\rangle)\text{ , }\frac{1}{\sqrt{2}}(i|0\rangle+|1\rangle) $$ And I measure it, I'll not be able to distinguish one ...
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Qubits from fermions?

I'm confused about qubits and fermions/bosons. I would like to look at a specific example: Take an electron (which is a fermion) with its spins as a qubit system. A spin up state is the $\lvert 0 \...
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What does “given one application of a black box” mean, in a quantum-computing context?

From Kaye, Laflamme and Mosca's An Introduction to Quantum Computing: Exercise 7.1.1 (Bernstein-Vazirani problem) Show how to find $\mathbf a \in Z_2^n$ given one application of a black box that ...
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In Grover's algorithm how do we flip all Fourier transformed states *except* the 0th?

According to this source, Grover's algorithm works as follows: Begin with uniform superposed state (i.e. Hadamard gate applied to |00000>) Apply the Oracle (flip amplitude of state that matches ...
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Difference Between Adiabatic and Superconducting Quantum Computing

Wikipedia (not the most stringent source, I know) has separate pages for adiabatic and superconducting quantum computing. It's my understanding that all superconducting quantum computers are adiabatic ...
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About complexity of quantum states

From quantum computation point of view, the complexity of a quantum state $|\psi\rangle$ can be defined as the the complexity of the quantum circuit that can generate the state $|\psi\rangle$ from an ...
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What was the first quantum error-correcting code?

Is the Steane code the first quantum error-correcting code?