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 does the energy level structure of a hyperfine qubit look like, and how does it compare to the energy level structure of a Zeeman qubit?
I'm looking for a visual representation of the energy level structure for:
hyperfine qubits
Zeeman qubits
If you are able, please describe the differences between the two structures.
Thanks in ...
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Does increasing numbers of qubit come with increasing decoherence?
Does increasing numbers of qubit come with increasing decoherence? I assume it does for superconducting, but what about photonic or ion trap?
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Quantum Computing is not Analog Computing. Really?
Let's review first these two computation processes to see if in their core fundamental nature are actually different:
1) Quantum Computing
One of the properties of quantum mechanics that is exploited ...
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How can one compute the quantum motion of an ion in a trapped ion quantum computer?
I am trying to get a conceptual idea of a trapped ion quantum computer.
For simplicity, I am looking at a single ion in a Paul ion trap.
It is easy enough to define the potential of the ion trap and ...
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What exactly is meant by the quality of a qubit?
When looking at a quantum annealer, we can see that D-Wave solutions have produced an annealer with over 5000 qubits whilst other companies that take a quantum gate approach have only managed 127 (IBM)...
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What does the "quantum mutual information" quantify?
I'm having some difficulty understanding the physical meaning of the mutual information that two subsystems share with each other. For example, if $\rho_{AB}$ defines the matrix of a bipartite state, ...
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Can a quantum field theory be completely simulated by a quantum computer? [closed]
I heard a talk on quantum computing and black hole. In this talk Leonard susskind raised a question: can QFT be completely simulated by using a quantum computer? But he said he was not going to answer ...
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How much classical information is transmitted in continuous variable teleportation?
In order to do quantum teleportation of $n$ qubits, you need to send $2n$ bits of classical information, in order to ensure that you get the original state and not a relative phase change of the ...
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What is the difference between "cluster states" and "graph states"?
I wonder about the difference between the cluster state and the graph state.
I guess the only difference is the graph of the cluster state is limited to a two-dimensional square lattice
The concept of ...
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Unitary transform using displacement operator to get time-independent Hamiltonian?
I am considering a driven cavity field with Hamiltonian
$$H = \hbar\omega a^{\dagger}a + f(t)(a + a^{\dagger})$$
where $f(t) = \epsilon e^{-i\omega_{d}t} + \epsilon^* e^{i\omega_{d}t}$ is a classical ...
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Quantum and classical physics are reversible, yet quantum gates have to be reversible, whereas classical gates need not. Why?
I've read in many books and articles that because Schrödinger's equation is reversible, quantum gates have to be reversible. OK. But, classical physics is reversible, yet classical gates in classical ...
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Are qubits just analog, continuous classical bits?
Topologically, classical bits (cbits) are essentially special cases of qubits restricted to the poles of the Bloch sphere. However, this restriction doesn't seem to be classical per se, but is simply ...
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Is the Hilbert-space description of quantum many-body physics misleading and unphysical?
It is well known that any quantum time-evolution of local, time-dependent Hamiltonians can be described using a poly-depth (in number of qubits) quantum circuit (DOI:10.1103/PhysRevLett.106.170501; ...
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Can Quantum Computers test modified quantum mechanics?
I wonder if with the raise of the quantum computing era, we could test somehow non-linear quantum mechanics failures up to certain scales. That is, how could quantum computers test key assumptions of ...
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Why is it easier to construct 2-qubit gates than 3-qubit gates?
In Quantum Computer Science, by Mermin, it is stated that $1$- and $2$-qubit gates are more feasible to construct than $3$-qubit gates or more. Given a fixed collection of qubits, are there any ...
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Deutsch-Jozsa algorithm
Quantum queries
We just apply the boolean function to the computational basis labels.
X is an n-bit string representing an n-qubit state, then we can try $|x\rangle$ to $f(x)$. but if $f(x)$ is ...
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Scalability of quantum optimal control
I'm curious to know how scalable in general the quantum optimal control method is to qubit systems. I've looked through many resources and it seems like it only has been applied to small system sizes (...
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Could we have a quantum algorithm that have the quantum speed-up, but don’t need universal gates?
When it comes to building a quantum computer, it's like we need to consider how to perform universal gates fault-tolerantly, which is an unsolvable problem so far. While Clifford gates may be easier ...
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What errors can be detected in QEC (Quantum Error Correction)?
In the introduction of Eastin and Knill's paper on the no-go Theorem for universal and transversal quantum gate sets, they assert that an error E can only be detected if PEP∝P, where P is the ...
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What is the idea behind quantum speed limits?
Could someone please explain to me how the very basic idea behind existence of a quantum speed limit arises?
I think I understand (if it's correct) how it arises naturally between two pure states ...
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How does non-commutativity of observables lead to quantum speedup in solving algorithms in quantum computing?
The question might be misleading, but I'd like to understand a thing. By reading this really interesting question, one realises that the relevant thing in quantum mechanics and not reproducible in ...
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Filling factors and implementation for non-Abelian models
Currently reading through Pachos' Introduction to Topological Quantum Computation, and perusing other related articles and papers online. Have seen in many places that the 5/2 filling factor for ...
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Wavelength-dependence of optical elements in integrated photonic circuits
I am interested in integrated photonic circuits or silicon photonic circuits. In the long run, I would like to analyze these circuits using a rigorous and analytical mathematical approach, taking the ...
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Quantum Computer - Rotation Bloch Sphere [closed]
please can anyone help?
What gate combination allows moving from the state between |0> and |1> states. In terms of bloch-sphere from the north pole to the south pole as an example. And how can ...
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Implementing the CZ operator using Ising Hamiltonian
$$ U = e^{-it H_{CZ}} $$" />
I am struggling to understand how for the $ \ket{11}$ in the last line, the minus signs in the exponents have been removed, to give the overall minus in front. If they ...
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How to calculate the exact evolution of a one-body fermionic operator?
To simulate fermionic systems on a quantum computer, one has to do transformation from fermionic to bosonic operators. This transformation can be done for example with the Jordan-Wigner transformation....
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Quantum computing and string theory: which path should I pursue first? [closed]
I'm an undergraduate physics student waiting for responses from graduate programs I applied to. I apologize if this question is slightly off-topic for physics SE, but I really want to hear some advice ...
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Is the eigenvalue of an eigenstate the same as its (global) phase?
I'm trying to understand Shor's Algorithm by reading this Qiskit textbook. At some part the following equation comes up:
\begin{equation}
U |u_0\rangle = \frac{1}{\sqrt{12}} \begin{pmatrix} |3\rangle +...
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Is vortex physics key to understand the universe simulation hypothesis? [duplicate]
Seth Lloyd, US computer scientist and Professor of Mechanical Engineering and Physics at the renowned Massachusetts Institute of Technology (MIT) says that the universe itself is a giant quantum ...
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Meaning of Continuous Charge in the Inductively Shunted Cooper Pair Box
I asked this question on QC.stackexchange before, but received no answers and only the advise to post ist here. Thus:
In the Cooper Pair box, the conjugate momentum $\hat{n}$ of the reduced ...
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Truncated Completely Positive Trace Preserving (CPTP) maps
Let us consider the the Liouville equation of a level $N$-system with density matrix $\rho$ together with its standard properties (positive semi-definite, unit trace, etc). The evolution of the system ...
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Reconstructing state from density matrix (and implications for Grover search)
If I am given a density matrix $\rho$ that I know corresponds to a pure state (i.e., $\rho = |\psi\rangle\langle\psi|$ for some $|\psi\rangle$), then is it possible for me to infer the state $|\psi\...
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Infinite qudit to solve halting problem
My understanding of qudits and quantum computing isn't exactly the best, but as far as I know, a qudit is defined as a superposition of D states. Reading this, as best I could tell, a qudit such that ...
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Normalizer of $SU(2)\times SU(2)$ in $SU(4)$
What is the normalizer of $SU(2)\times SU(2)$ in $SU(4)$ or how would I find it?
Reason for the question: with 2 qubits, if I was interested in conjugation of 2-qubit gates with generic $SU(2)$ ...
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Why is Measurement Device Independent (MDI) Quantum Key Distribution (QKD) truly MDI?
I am having a hard time understanding why MDI-QKD is truly measurement device independent.
My current vision is that Charlie (the one who performs the Bell state measurements) is simply sampling the ...
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Why are rotation operators and Pauli rotations defined so that $R_x(\pi)\neq X$?
When applying a Hadamard Gate Wikipedia defines it as $XR_y(\frac{\pi}{2}) = H$. The effect of a Pauli Gate $X$ is defined as a Rotation of $\pi$ radians about the x-Axis on the Bloch sphere. The ...
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Is Shor's algorithm for factoring still efficient in the presence of small phase noise
Quantum Fourier transform of $|a\rangle\in H_N$
$$|a\rangle\longrightarrow\sum_{l=0}^{N-1}e^{\frac{i2\pi a l}{N}}|l\rangle$$
where $N=2^n$ and $H_N$ is $N$-dimensional Hilbert space.
The ...
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Applying CNOT in series to ancilla qubit
$\renewcommand{ket}[1]{\left| #1 \right\rangle}$
$\renewcommand{bra}[1]{\left\langle #1 \right|}$Suppose we have to qubits both in the state $\ket{+ }= \frac{1}{\sqrt{2}}(\ket{0}+\ket{1})$, and we ...
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Matrix multiplication in Feynman's paper on quantum mechanical computers
In a paper by Feynman, on how to embed a Turning machine in the ground state of a many-body quantum system, a product of two matrices is defined (equation 1). This product does not appear to have the ...
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How practical is the Landauer limit to actual computing (including distant future)?
Landauer's Principle is often presented as a fundamental limit of efficiency for classical computing. It states that in order to erase one bit of information, at least the following amount of heat has ...
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How to generate a Hadamard Gate in Spin 1 NMR?
I am studying about the gate controllability of Spin 1 systems and I would like make a Hadamard gate using only X,Y rotations and the offset. I want to do this without invoking techniques for making ...
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How Do Quantum Computers Work, Like Really [closed]
I understand in plain terms superposition and entanglement, but I'm very unclear how either of these could work as a means to increase computation power.
A helpful metaphor is that of the maze. A ...
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CNOT quantum gate output when the control qubit is already in a superposition of states
The CNOT gate output states are clearly defined when the control qubit is in either of the the "pure" state of 0 or 1, as in the following diagram:
However, when the control bit is already ...
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Hadamard Gate: randomness and hidden variables in quantum systems
The nicest exposition I have found about the Hadamard gate in quantum computing is as follows:
So, the Hadamard gate essentially takes a known input (black ball or white ball in this case) and ...
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If two Hamiltonians produce the same evolution up to a phase, are they equivalent?
Consider two Hamiltonian operators $H_1, H_2$ and the evolution of some fixed single-qubit state $|\psi\rangle$ and yielding:
$$
\exp(i H_1t)|\psi\rangle = |\phi\rangle \\
\exp(i H_2t)|\psi \rangle = ...
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How does CNOT gate work?
In Quantum Computation there is (among others) a so called CNOT gate. Its control input |x> is "driven through", while the other input |y> is converted to some other state, depending ...
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What optical elements can you use to implement an S gate in practice?
How do you implement an S gate using an optical element or combination of optical elements in the following 2 scenarios?
The S gate acts on a polarization qubit (polarization of a photon)
The S gate ...
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Two qubits entanglement in different basis - quantum circuit
I am trying to build a circuit that can detect which of the 4 entangled states i am in. The states are
\begin{align}
|0+\rangle &+ |1-\rangle\\
|0+\rangle &- |1-\rangle\\
|1+\rangle &+ |0-\...
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Has anyone come across the relationship between Higher order confinement wave-functions and corresponding Zeeman Interaction?
I'm studying a hole quantum dot in Germanium. The problem is described in the Luttinger Spin-3/2 basis and takes Fock-Darwin states as solutions in the Quantum Dot plane(xy plane). Furthermore, I ...
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Why/how does Microwave pulse cause electron spin to rotate in the Bloch sphere?
I recently started studying pulse techniques for electrons in the context of quantum computing/sensing/optics/etc.
For spins in solid state (like color centers in diamond or SiC, or metal centers in ...
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