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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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“Quantum Coding” Can we recover a state on a composite system from a state on the subsystem?

I'm wondering if we can recover the state on the composite system from the information of its subsystem. For instance, say, the state on the composite system is $|\psi>=\alpha |00>+\beta |11>\...
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How does quantum memory work using atoms? [on hold]

My understanding is that two photons are prepared together which are said to be entangled, one of the photons interacts with an atom and the state of the atom changes according to the what state the ...
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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 superposition entangled Qubits need to be collapsed at the same time to reveal the same state? [closed]

Or can one set of entangled Qubits be collapsed first, with the second set collapsed later and achieve the same values?
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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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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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Are strings capable of information processing? If so would string computers be more powerful than quantum computers?

A deterministic computer is weaker than quantum computer at least quadratically for (almost) all kinds of tasks. This is proved and the difference arises from Grover's search algorithm, which allows ...
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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 ...
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Characterisation of the generalised Bloch sphere in spherical coordinates

I'm so confused by the following definition in the "Quantum Error Correction" by Lidar and Brun that not even sure how to formulate the question properly. Let $\mathbf n$ denote a unit vector, i.e.,...
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Derive unitary matrix for Tofolli gate

I know that for two qubits, the CNOT matrix is given by $CNOT=P_0 \otimes I + P_1 \otimes X.$ But I cannot figure out how to get the matrix if I have two control qubits, acting on a third, like in ...
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Resonant frequency shift for cavity superconducting circuits

For superconducting circuits coupled to a resonator, we get a shift in the transmission spectrum (vacuum Rabi splitting) because of the interaction of the qubit and the resonator. Then one goes to ...
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Negative of Quantum Gates and Entangled States

I'm well aware that using this quantum circuit: $\hskip2in$ $\hskip2in$Quantum circuit used in the generation of EPR pairs. It is possible to create entangled state of two qubits (EPR pairs), in ...
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Is there a theoretical limit to efficiency of a quantum computer?

As an example, say you ran a computation on a quantum computer. It results in a wavefunction: $\alpha |1\rangle + \beta |2\rangle$ Now assume that the question is true if $\alpha^2<0.5-10^{-100}$ ...
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What is the basis of the use of Hermitian matrices as quantum gates?

Because all quantum gates must be unitary matrices, it is possible to prove the no cloning theorem by showing that no quantum gate can output two identical copies of an arbitrary inputted qubit. This ...
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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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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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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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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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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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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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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 ...