All Questions
Tagged with quantum-computing or quantum-computer
904 questions
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Replace $\vert1\rangle$ with identity operator
I am learning quantum computing recently and found an exercise on the Internet. I have been thinking about how to solve it but still confused. The following is the question
Consider a single qubit ...
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35
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How to find stabilizer generators of a subsystem from a known set of generators?
$\newcommand{\ket}[1]{\left|#1\right>}$
I am working on a problem and would appreciate some help. I'm working with a multi-qubit state defined by a set of stabilizer generators, ie $\ket{\psi} \in ...
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16
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Google, IBM, Rigetti, and IQM all manufacture superconducting quantum computers, what are the main differences of their chips? [migrated]
Google, IBM, Rigetti, and IQM all manufacture superconducting quantum computers. What are the main reasons for the differences in the accuracy of their chips?
IBM has recently released its latest ...
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Go a step further and get the both results of $f(x)$ in Deutsch algorithm
The Deutsch-Josza algorithm gives the result in one operation of the type of a $(0,1) \mapsto (0,1)$ function $f(x)$, i.e. if $f(x)$, is constant or balanced. With the parallel computing power of a ...
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Can a quantum computer simulate a classical field theory efficiently?
I know there’s a large speed-up in simulating quantum field theories, but was wondering if quantum computers are able to simulate a classical field theory as efficiently as they can simulate a quantum ...
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48
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Should one learn the math of quantum computing from a "pure" perspective, or is quantum computing texts "good enough"? [closed]
Math for quantum computing includes advanced linear algebra, functional analysis, group and representation theory, probability theory, and more.
There are plenty of pure math books out there for those,...
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65
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Can a universe-sized computer predict the universe? [duplicate]
I'm not asking about a simulation and so I don't see this as a duplicate, and I'm not a physicist or anything like that, I have some physics-related questions though.
Current models suggest local ...
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Relationship between coupling Strength in Cross-Resonance Gates and Coefficients in Hamiltonian Tomography
In the effective Hamiltonian for the cross-resonance (CR) gate, the interaction term is written as:
$$
\tilde{H}_{\rm eff}^{\rm CR} = - \frac{\Delta_{12}}{2}\sigma_1^z
+ \frac{\Omega(t)}{2} \left(\...
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67
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How to transform collapse operators in rotating frame?
I want to simulate the evolution of a transmon qubit driven by a classical voltage using qutip. The problem is that the qubit (and the drive) have a frequency of around 5GHz and I typically run ...
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60
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Are there quantum computing algorithms specialized for machine learning applications?
I've heard that some companies are attempting to utilize quantum computing algorithms for machine learning tasks (ex:protein folding and drug discovery). As far as I know, quantum computing has been ...
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Is useful Shor factorization really practically feasible?
INTRO TO THE ISSUE. After studying this beautiful math concept many years ago, I recently revisited Shor's algorithm for factoring integers and its implications for RSA encryption. This time, I needed ...
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How does Quantum Gate Teleportation Actually Work?
I am trying to understand how quantum GATE teleportation works. Abstractly, I understand it as the ability to do a 2-qubit operation between two qubits that are not located in proximity.
From ...
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42
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Why the parameters of quantum convolutional neural network (QCNN) is $O(\log N)$ for a $N$-qubits input?
I am currently reading the paper arXiv:1810.03787. The authors claim that QCNN uses only $O(\log N)$ variational parameters, where $N$ is the number of qubits. However, I am having difficulty ...
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A variant of Campbell (1897) identity (related to BCH formula)
Campbell's identity (see in https://en.wikipedia.org/wiki/Baker%E2%80%93Campbell%E2%80%93Hausdorff_formula) takes the form:
$$ e^XYe^{-X}\equiv ad_{e^X}Y=e^{ad_X}Y\equiv \sum_{n=0}^\infty\frac{[(X)^n,...
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48
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How to Construct Arbitrary Rotations from Discrete Rational Rotations?
One of the most commonly used universal quantum gates sets is the Clifford + T set, containing {CNOT, H, S, T}. However, as S is a $\pi / 2$ rotation about the Z axis of the bloch sphere and as T is a ...
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Scrambling Time in Black Holes
Peter Shor argues that the scrambling time for a black hole—defined as the time it takes for information to be thoroughly mixed across the event horizon—scales as $\mathcal{O}(M^2)$, where M is the ...
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146
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Using classical $g^{(1)}$ to calculate quantum $g^{(1)}$
Imagine a free space optical switch with several inputs and outputs. My question is: can we use the first order cross correlation between the complex amplitudes of two classical beams of light at the ...
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100
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Conjugacy of $x$ and $p$ for simulation of Schrodinger's equation
In Nielsen-Chuang, page 207, there is this box:
I have some strong doubts about the last passage. The logic they follow is that since $H_0$ is diagonal in momentum basis but not in position basis, ...
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95
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Edge Modes and SPT Order
I am trying to understand the notion of edge modes in the context of symmetry protected topological order (SPTO) and its relation (if there is any) with the virtual quantum register that sits at the ...
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312
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Why isn't spin-statistics applied in quantum computing?
Why isn't spin-statistics taken into account in quantum computing?
By spin statistics I mean the fact that fermion and boson states must by respectively totally anti-symmetric and symmetric. I say it'...
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85
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Questions on Matrix Product States (Tensor Networks)
I just have a few questions on Matrix Product States. I have learnt them from the point of view of performing cuts via Schmidt Decompositions, as seen in Chubb and Bridgeman 2017.
Is the bond ...
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How can a quantum gate be constructed to evaluate a blackbox function (as in the Deutsch's algorithm)?
The standard Deutsch's algorithm uses a control-U gate, which takes the control qubit state $x$ as input to get the output from a black-box function $f(x)$. And the output modifies the quantum state ...
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Photonic classical and quantum computing
How different is the hardware used for classical and quantum photonic computers? Are there any proposals on hybrid platforms? I'm curious why I never heard of both within the same context, except for ...
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Why the unit of quantum information for anyons systems should be the qubit?
I'm starting to learn more about anyons systems. I took a read on this article which is an introduction to topological quantum computing, and also took a look in other places like forums and some ...
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Is this an alternative realization of Deutsch's algorithm? [closed]
The standard Deutsch's algorithm uses two qubits and a control-$U_f$ gate, which transforms the two qubits,
$|x\rangle |-\rangle \rightarrow (-1)^{f(x)}\, |x\rangle |-\rangle $. To realize the ...
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Is two degree quantum entanglement possible? And by two degree of entanglement I mean one in space and other in time? [closed]
Whenever we try to entangle two particles, the entanglement lasts for a very short period. If we observe our present universe we can see that all the matters present in our universe are finely ...
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62
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Appling a Hadamard gate to a qubit in density matrix form
If a Hadamard gate is applied to a qubit that is in the state $|0\rangle$, then it becomes the state $$|+\rangle = \frac{1}{\sqrt{2}}\left(|0\rangle+|1\rangle\right)$$ In density matrix form, this ...
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105
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Why does the SWAP operator equal a particular integral over the unitary group?
Let $\mathcal{U}(d)$ be the group of $d$-dimensional unitary matrices and $P_{21}$ be the swap operator ($P_{21}$ operators on a tensor product of Hilbert spaces $\mathcal{H}_A$ and $\mathcal{H}_B$ ...
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Parallel State Machines as an Analog To Quantum Computing
I recently got into Michael Sipser's Introduction to the Theory of Computation. I've only done software a couple years professionally, but in that time have spent a lot of time thinking about state ...
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182
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What is the oracle in every quantum algorithm? [closed]
I hope this question won't be closed.
There is a machine called oracle which appears in a lot of algorithms of quantum computing, such as Deutsch's algorithm and QFT period-finding.
This oracle ...
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16
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Bit structure in Adiabatic Quantum Computing [closed]
https://arxiv.org/pdf/quant-ph/0007071.pdf
In Chapter 6 in the paper "A Numerical Study of the Performance of a Quantum Adiabatic Evolution Algorithm for Satisfiability”, by Edward Farhi, Jeffrey ...
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132
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Displacement operator and phase space
I read a paper on open quantum system, it's about non-Markovian process with memory effects.
They describe a generic model of two qubits interacting with correlated multimode field.
They describe the ...
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88
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Generator of two-qubit quantum gate
I would like to know how to derive the explicit form of the GENERATOR of a general two-qubit gate (also here), e.g., controlled-rotation Y.
From the definition: $$\exp(-i\theta G) \ ,$$
I see it is: $$...
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61
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Quantum oracle for boolean function
As a math student, I am doing some quantum computing. In the course notes of Ronald de Wolf, he says that any Boolean function $$f:\{0,1\}^n\to\{0,1\}^m$$ can be made into a unitary operation that ...
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Why does the Lamb-Dicke parameter decrease with the number of ions in an ion chain
I would like to understand (ideally with a nice pedagogic reference), why the fidelity of quantum gates in long ion chain decreases with the number of ions in the chain.
In this reference, it is ...
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86
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What is the difference between local operations and global operations for quantum systems?
When I hear people talk about qubit operations, they usually make a distinction between local and multi-qubit (global) operations. I understand what they mean intuitively (the local operations act on ...
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3
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Why does this not break the security of quantum teleportation
I am taking an course on quantum mechanics, and we have just encountered the quantum teleportation protocol that allows for the transfer of one qubit from Alice to Bob. I think I have a way for Eve to ...
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Defining the Problem Hamiltonian for Quantum Annealing in Solving the Shortest Path Problem [closed]
I’m currently studying quantum annealing and its application to solving the shortest path problem. However, I’m facing challenges in defining the problem Hamiltonian, whose ground state should encode ...
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How can we have two independent parameters (physically) during Rabi Oscillations happening in Rydberg Atoms?
Rabi Oscillations are explained as electric interaction between atom and EM field, here. This can be true for any two-level system with specific interactions that can lead to the Hamiltonian given in ...
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217
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How to actually implement a global phase gate?
I've been trying to model some single qubit gates via Rabi oscillations for a project. In this we have some Hamiltonian (in this case it's due to an oscillating electromagnetic field) that when ...
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How can the Rabi frequency be complex?
I've been doing some reading and came across a simple implementation of the Hadamard gate using Rabi oscillations of an atom in a laser field. However, the author mentions that it required the Rabi ...
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How to construct the jump operator in the Lindblad Equation for a 2-qubit system?
I am working on a project for my degree to model a CNOT gate and I'm trying to do this with the Lindblad equation.
$$
\dot{\rho} = -\dfrac{i}{\hbar} [H, \rho] + \sum\limits_i \gamma _i (L_i \rho L _i ^...
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How to construct a quantum circuit for quantum Fourier transform in a prime dimensional Hilbert space?
Consider a Hilbert space of dimension $p$ where $p$ is a prime number. Quantum Fourier transform (QFT) in this space is defined as
$$
|j\rangle \rightarrow \frac{1}{\sqrt{p}} \sum_{k=0}^{p-1}e^{\frac{...
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3
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Noise in quantum computing
Consider a quantum computer, and one specific qubit $q$ in it. With the computer, we perform a series of operations which manipulate the qubits including $q$. I am interested in the time interval ...
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16
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Fastest rate of entangling atomic qubits
Many quantum computing systems, most notably trapped ions, propose to use optical heralded entanglement schemes to entangle small 'modules' of qubits that are further apart. Typically one puts two ...
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179
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Black holes as Quantum Computers
I have been hearing lately that Black holes could be Quantum Computers or that some processes in a black hole simulate the operation of Quantum Computers. This is not my field of study, but I am ...
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71
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Equivalence of two entangling operators with respect to local operators
Suppose that $U_1$ and $U_2$ are two (entangling) operators that act on a quantum system consisting of several qubits. Is there any criterion to tell if these two are equivalent up to applying ...
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57
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How do you solve the eigenproblem for the adiabatic Grover algorithm?
The adiabatic version of Grover's algorithm relies on a straightforward solution of the Schrodinger equation when the Hamiltonian is allowed to linearly vary from its initial state to its final state. ...
2
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Josephson supercurrent measurement in a lab
This may be a very trivial question but I am a theoretician and can't find the answer to this question for the life of me. Is it possible to actually measure the Josephson supercurrent flowing through ...
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How are quantum gates encoded in voltage/current waves for superconducting qubits?
From what I understand, the voltage and current waves propagate down the input transmission line, hit the nonlinear oscillator, and then bounce back toward the generator. How are gates such as the X ...
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