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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101 views

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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80 views

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 ...
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How do I apply no signaling condition for the given Quantum Adder problem

The Unitary transformation for the Imperfect Quantum Adder problem is such: Both the states belong to two Hilbert Spaces and we are trying to add both states to one system using Ancillary qubit. I ...
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How to measure a Bell inequality violation in IBM Q? (Or analytically)

I made some circuit to prepare a 2 qubit state, but I am having trouble understanding how to measure Bell's inequality. I know the inequality is of the form $$|E(a,b)-E(a,b')+E(a',b)+E(a',b')| \leq 2$...
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Doing addition and subtraction with tensor diagrams?

Tensor diagrams are a beautiful and useful tool for making calculations with tensors, up until you need to contract with the sum or difference of two tensors, at which point it seems to become awful. ...
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Which system for a quantum computer?

We are aware that we use binary system for our present day digital computers as they comprise of two states (0&1). But what system would fit the states of a quantum computer?
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Literature Anyons [duplicate]

In a few months I have to give a talk about Identical Particles in Quantum Physics, which should answer the following questions or explain following concepts: Why are there only Fermions and Bosons ...
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Encoding infinite information in a qubit vs. classical system

In this Quantum Computing article by Michael Nielsen he argues about some of the limitations imposed by quantum measurement. In particular how the amplitude $\alpha$ of a single qubit $\alpha |0> +...
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Intuition behind quantum CNOT gate applied to a pair of electrons [duplicate]

I'm looking for some intuition behind how a cNOT gate works. I think I understand the mathematics; but, I'm having trouble imagining how two electrons would interact to produce the predicted result. ...
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Rydberg Blockade's experimental mechanism

This idea for an experiment is for a high school competition (bl4s). Utilizing a positron beam,can we knock out gas which has been energized to its Rydberg state.I plan to do this to verify when the ...
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Do quantum error correction codes depend on the type of quantum computation (circuit QED/topological/etc)?

So I know that there are different types of quantum computation that can be realized (cQED, topological quantum computation among others), and different error correction codes that exist. Naively I ...
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Can we recover a state on a composite system from a state on the subsystem?

$\renewcommand{\ket}[1]{\left \lvert #1 \right \rangle}$ $\renewcommand{\bra}[1]{\left \langle #1 \right \rvert}$ I'm wondering if we can recover the state of a composite system from the information ...
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Say you run qubit $A = (|0⟩ + |1⟩) / √2$ and qubit $B = |0⟩$ through a CNOT gate. What is the state of qubit $B$ afterwards?

I am new to the weeds of quantum computing and this question is probably pretty elementary. Say you run qubit A = (|0⟩ + |1⟩) / √2 and qubit B = |0⟩ through a CNOT gate. What is the state of qubit B ...
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About superposition of states

In quantum computing, we can always create an arbitrary superposition of states by rotation of $|0\rangle$ state for one qubit. This raises a question: for arbitrary superposition of states, is there ...
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What's wrong with this method of solving NP problems using a quantum computer?

As far as we know, Quantum Computers can not solve arbitrary NP problems in polynomial time. I have what appears to be a solution, but it is obviously to simple to be correct, since otherwise the ...
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Does adiabatic quantum computation require the initial and final ground states to be non-orthogonal?

Background At a recent talk, I was told by the speaker that it is not possible to adiabatically transfer from one ground state $|\psi_0 \rangle$ to another $|\psi_1 \rangle$ if these states are ...
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Do qubits need to be in superposition to be entangled? [closed]

Do qubits need to be in superposition to be entangled? Put another way, can qubits be entangled but not in superposition?
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Is a mixture of Bell states entangled?

Setup: I have a two qubit system $\mathbb{C}^2 \otimes \mathbb{C}^2$ an we consider the Bell states $\newcommand{\ket}[1]{\left|#1\right>}$ $\newcommand{\bra}[1]{\left<#1\right|}$ $\...
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Quantum computing explanation for the quantum Zeno effect

I'm playing around with the IBM Q to demonstrate the qunatum Zeno effect. If we prepare a qubit in the $|0\rangle$ state and apply 5 consecutive $R_y(\pi/5)$ gates, we should end up in state $|1\...
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Faster than light speed transfer of certain event

I am CS/Math person I am not quite sure what it means in physics information cannot be transferred faster than light (FTL). I tried to understand the proof of no transfer theorem but I lacked the ...
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Is the eavesdropper detected by chance in QKD?

So I was starting to familiarise myself with QKD when I came across this video on YouTube breaking down the process (I believe this is the E91 protocol but I could be mistaken) using an animation that ...
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Rank of a density matix

I was just trying to understand the meaning of rank of a density matrix. I came across the following post, which says that the rank of density matrix is the number of non-zero eigenvalues. And for a ...
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Is there a physical limit to memory reading and writing speed?

Is there a limit to the speed at which a memory, quantum or classical, can be read or written into? I've seen this interesting question : Is there a physical limit to data transfer rate?. Here I'm ...
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Pauli projector for multiple qubits

When operating on a single-qubit, any two-outcome measurement can be viewed as measurement of the Pauli observable $$v \cdot \sigma \equiv v_1 \sigma_1 + v_2 \sigma_2 + v_3 \sigma_3$$ The projectors ...
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Is quantum computation just an advanced data compression algorithm?

When we are talking about the quantum computation and classical computation, we are saying that quantum computation is exponential faster than the classical one. And that's because the Kronecker ...
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Has hydrogen ever been used in Quantum Computing?

What I'm talking about is hydrogen atom quantum dots, where a hydrogen atom is embedded in a semiconductor. The reason for asking is because the Hydrogen atom is a Quantum mechanical system with a ...
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1answer
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How are quantum computers different from non-deterministic Turing machines?

I was reading about non deterministic Turing machines and I thought that they were the same as quantum computers. However I was told they were not, therefore I am curious to know the difference.
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Quantum Simulation of Hamiltonian $H=Z_1 \otimes Z_2 \otimes Z_3$ (Nielsen 4.7.3)

In section 4.7.3 of the Nielsen & Chuang they are talking about a quantum simulation of the Hamiltonian \begin{equation} H=Z_1 \otimes Z_2 \otimes Z_3 \end{equation} on 3 qbits. They propose ...
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Understanding projective measurements as a special case of POVM measurements (“third postulate” in Nielsen and Chuang)

I am working through Nielsen and Chuang's book and am confused about a detail from sections 2.2.3 and 2.2.5. On page 88 of my copy (section 2.2.5), they write Projective measurements can be ...
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About 2D graph state and branching MERA

In my former post I asked if a 2D graph state on a 2D lattice can be represented by branching MERA. I got an answer that it seems this is true. Then I have to following deductions (1) 2D graph state ...
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Can 2D graph state be represented by branching MERA?

A 2D graph state is a highly entangled state to support general measurement based quantum computation. But its state complexity is relative low. Branching MERA represents also a set of low complexity ...
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Relation between quantum entanglement and quantum state complexity

Both quantum entanglement and quantum state complexity are important in quantum information processing. They are usually highly correlated, i.e., roughly a state with a higher entanglement corresponds ...
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Why do quantum memories have to be so cold?

I understand that currently, atomic qubits, or just atomic ensembles are kept near absolute zero, in order to try to create an ideal gas structure. For higher temperatures the individual ions will ...
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Are there any physical realizations of a rebit (a qubit with real coefficients for probability amplitudes of a two-state system)?

While being introduced to the world of quantum computation and qubits, I’ve come across the term rebit, which I understand to mean a two-state quantum system that may be expressed as a real linear ...
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Could a quantum computer calculate the values of the riemann zeta that are currently out of reach with classical computers?

Could a quantum computer calculate the values of the Riemann zeta function that are currently out of reach with classical computers? Any counterexamples to the RH would be somewhere in the range ...
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von Neumann measurement model of a qubit with continuous detector

I have a two state qubit system with initial state $|\psi_s\rangle_i = a|0\rangle+b|1\rangle$ and a detector with initial state $$|\psi_d\rangle_i = \int_{-\infty}^{\infty}\left(N \exp[-\frac{q^2}{2\...
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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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How can blackholes be fast information scramblers?

I noticed that there was already a post discussing the fast scrambling property of black holes. But it seems no satisfactory answer was given. As mentioned by L. Susskind et. al, the fast scrambling ...
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How does this beam splitter work? [closed]

Did I draw this beam splitter diagram correctly? Two entangled light beams start at the lower corners of the square and travel along the line, colliding at the junction. What exactly happens at the ...
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Concise way to express commutators of two-qubit quantum gates

I would like to calculate the commutator of quantum operations $C^{(ij)}$ (by that I mean CNOT with $i$ being the control qubit and $j$ being the target qubit; please correct me if there's a better ...
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Entanglement fidelity for a single qubit?

So I have been working out problems from the book "Quantum Computing Explained" by David McMahon. On page 166 he defines "Entanglement Fidelity" and says the following: Consider a density operator for ...
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Transmons and cooper pair box qubits: two islands or a single island and a reservoir

In scientific literature, one typically describes Cooper pair boxes as a small superconducting island coupled to a superconducting reservoir (say, a large ground plane of superconducting metal, or a ...