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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"Jump" operators from Lindblad equation where the external system is measurements
How do we derive the "jump operators" for the Lindblad equation if the external system is measurements? For example in this article for the Bose Hubbard system the Lindblad operators ...
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Learning contextual data using a variational quantum circuit
This question is about contextuality in quantum mechanics, about non-quantum data also showing contextuality.
Definition for the specifics of the question as well as an example of contextuality in ...
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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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Phase accumulation in Rabi driving
When a single-qubit gate is operated by Rabi driving for a time $t$, the resulting operator is equivalent to
$ \hat{O} = R_z(\omega t) R_x(\Omega t)$
where $\omega$ is the frequency of the driving ...
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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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What guarantees a photonic quantum gate to be unitary?
So in my course of quantum computation i came across this question that "What guarantees a quantum gate to be unitary?" i was specially curious about photonic quantum gate.
At first i ...
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Can a hidden variable theory be seen as a map from unitaries to stochastics with the same dimensions?
In Quantum Computing in Hidden Variables, Scott Aaronson defines a hidden variable theory as something that transforms a unitary matrix mapping $\begin{bmatrix}\alpha_1 & \ldots & \alpha_n\end{...
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Exponential expression of controlled unitary gate
The controlled unitary gate $CU$, for some general unitary gate $U$, is (1):
$$CU=|0⟩⟨0|⊗I+|1⟩⟨1|⊗U$$
From the Wikipedia article on the CNOT gate (https://en.wikipedia.org/wiki/Controlled_NOT_gate) a ...
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Notation of 2-qubit quantum gates as "Matrix exponentiated by Matrix"
I am currently studying this paper about Cartan's KAK Decomposition. In the end of the section "Canonical Class Vector" some there is a calculation on how to find the canonical class vector ...
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Substituting qubit for classical memory
I recently came across a paper that argues that we can substitute a qubit for arbitrarily large number of bits in a physical system (https://arxiv.org/abs/quant-ph/0110166).
The notion of bit ...
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Understanding the Relationship Between Stochastic Reconfiguration and Natural Gradient in Variational Monte Carlo
I've been delving into variational Monte Carlo methods, particularly in the context of ground state energy minimization for quantum wave function ansatzes. In my studies, I've come across multiple ...
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Is it possible that when measured more than one Cooper pair will have tunneled across the junction?
If I've understood the idea correctly a charge qubit is formed by a superconducting island coupled by a Joseph junction to a superconducting reservoir. The state of the qubit is determined by the ...
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Where exactly lies the quantum supremacy?
What makes quantum computers faster in certain problems than normal computers? Does quantum computing means that many solutions are explored simultaneously instead of one at a time due to quantum ...
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Time complexity for quantum computing
Is there any systematic way to obtain a quantum algorithm's time complexity knowing the classical time complexity of the same algorithm type running for bits instead of qubits?
For example, we know ...
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For any unitary $U = e^{iA}$, question about the matrix element $A_{pq}$ of matrix $A$ and its functional derivative [closed]
Any unitary operation $U \in U(N)$ can be represented as $U = e^{iA}$, where $A$ is an arbitrary $N \times N$ Hermitian matrix. In the case of a time-independent Hamiltonian $H$, we have $A = -itH$ (...
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About the form of the cost functional for quantum optimal control theory
In quantum optimal control theory, the cost functional is often defined as (e.g, see Eq.(9) in here, as well as many other solid references such as this):
$$J = \langle \psi(T) \rvert O \lvert \psi(T) ...
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Is photonic computing subject to the Landauer limit?
In what way are they both related in terms of computation? Are photons subject to thermodynamic limits?
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Exercises on the subject Theory of Quantum Information
I have recently started to study quantum information theory on Nielsen and Chuang book, but in order to understand the theory better I need to solve more problems, there are in this book. Can you ...
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How to obtain quantum-state purity and concurrence by measurement on quantum computer?
My whole question is aimed at the implementation on quantum computers utilizing quantum circuits, i.e. we can assume, that I can prepare several "copies" of the same state, without really ...
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Intuition for Relative Phase of Energy-State Qubits
Consider a general qubit $|\Psi \rangle = \alpha |0 \rangle + \beta |1\rangle$.
My understanding is as follows:
If such a qubit is implemented using electron spin, for example, the computational basis ...
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When applying the adiabatic theorem, why doesn't the gap become doubly exponentially small generically?
Suppose we have a parameterised family of Hamiltonians $H(s)$, $s\in [0,1]$, acting on $n$ spins/qubits. When applying the adiabatic theorem, it is well known that if we wish to remain in the ground ...
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How do we measure the probability of outcomes in a quantum computer if qubits collapse when measured?
I understand the idea behind Quantum Computing being that we superpose all possible states of a system of qubits and amplify the probabilities of whatever it is that we want depending on the circuit ...
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When is Quantum State Teleportation useful?
I've been working through the Brilliant Course on Quantum Computing, and I've reached the lesson on Quantum Teleportation. After completing the lesson and reading several questions and answers here:
...
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Number of operations on Cbits and Qbits [closed]
What is the maximum number of operations that can be defined on Cbits (like mechanical switches) and Qbits (like quantum states)? If they are different how will the ratio change if we limit ourselves ...
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Is there an efficient way to execute a quantum channel using its Choi state?
Consider you are given a Choi state
$$
\sigma = (\mathcal{E} \otimes I) | \omega \rangle \langle \omega| \qquad {\rm with } \quad |\omega \rangle = \frac{1}{\sqrt{d}}\sum_{i} |ii \rangle \quad \textrm{...
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Looking at the Wigner function plot of a given state, how do we know if it's a good option for use as a qubit?
I am looking at GKP and cat states. Wigner plots are newish to me, and I'm trying to get an intuitive feel for the imformation they impart.
Just by looking at a Wigner plot, can one discern whether ...
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Why is a large magnetic field problematic (for topological physics)?
In papers studying or searching for topological order (intrinsic or symmetry-protected) in various condensed matter systems (e.g. Field-tuned and zero-field fractional Chern insulators in magic angle ...
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How to check that an element belongs to a stabilizer group?
My direct Question:
For a given stabilizer $S=\langle g_1,...,g_n\rangle$ (only represented by the generator) and an operator $g$, how can we check that $g\in S$? A wrong answer is to check that "...
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Implementing a POVM as a Quantum Circuit: Is There a General Method? [duplicate]
I am studying quantum information theory, and I have found an exercise about implementing a POVM as a quantum circuit. Specifically, the POVM is given by $\Pi_1= \lambda |0 \rangle \langle 0 |$ and $\...
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Is it enough to recovery density matrix for error correction in quantum computing?
When we discuss error correction, we always talk about the recovery of the density matrix of a single qubit. But somehow I feel that this is not enough. Consider a circuit that contains more than 1 ...
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How can a dephasing channel be formally represented by a unitary operation?
The dephasing channel is often represented as
$$\mathcal{E}\left(\rho\right)=p_0\rho+(1-p_0)\sigma_z\rho\sigma_z$$ that acts on a single qubit.
Another way of writing it down is by using Kraus-...
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Current Record for the Maximum Number of Ions Trapped in a Paul (Radiofrequency) Trap
What is the current known record for the maximum number of ions that have been successfully trapped in a Paul trap? Could you also share a reference to the scientific article or any form of published ...
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Distinguishing between two sets of quantum states
This problem has arisen in my research and reduces to the following.
Alice tells Bob she has secretly picked A or B. Depending on which she has picked she will send him states from a set. Bob can ...
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What is meant by " a basis is diagonal"?
I am trying to understand Schmidt decomposition. I am stuck in one sentence here. See the example picture.
Here, I can understand everything except the line "For both
HA and HB the Schmidt basis ...
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Derivation of QFT product formula
If the quantum fourier transform is defined as follows:
$$
U_{FT} |x\rangle = \frac{1}{2^{n/2}} \sum^{2^n-1}_{y=0} e^{2\pi i x y / 2^n} | y \rangle.
$$
We can rewrite the exponential term as:
$$
e^{2\...
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How is the measurement of the $Z_0Z_2$ error syndrome realised by these two circuits?
I am told that the following quantum circuit diagram implements the $Z_0Z_2$ error syndrome, but I don't follow.
I understand error syndromes when expressed in matrix form and how performing $Z_0Z_2|...
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Tensor product question in quantum computing context
I understand the basics of how to evaluate tensor products. For example:
$$\sigma_z \otimes I =
\begin{pmatrix}
1 & 0 & 0 & 0\\
0 & 1 & 0 & 0\\
0 & 0 & -1 & 0\\
0 &...
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Questions about the SQUID (Superconducting Quantum Interference Device)
If the bias current is approximately 2 Ic (double the critical current), wouldn’t the whole loop become normal? Or do only the Josephson junctions become normal? And when the junctions become ...
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Why is a CPMG sequence more resilient to errors in the pulse amplitudes than a CP sequence?
In the context of NMR (or in general qubits nowadays), a CP sequence is a refocussing sequence that looks like X/2 - X^n - X/2. A CPMG sequence instead is X/2 - Y^n - X/2. This change of axes is in ...
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Confusion regarding Bloch Sphere [closed]
$|Ψ> = 1/√2|0> + i/√2|1>$ (in $+i$ axis)
$α = 1/√2$ , $α^2 = 0.5$
$β = i/√2$ , $β^2 = -0.5$
$α^2 + β^2 = 1$
Ηere,
$α^2 + β^2 = 0$
How is this possible?
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Do Majorana qubits have a future?
There are still major efforts to observe Majorana Fermions in condensed matter systems (most recently this paper), with the ultimate goal of using topologically protected Majorana qubits for quantum ...
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State Spaces in Classical vs Quantum systems, in the context of classical & quantum computers
I am currently reading "Quantum Computing: A Gentle Introduction" by Rieffel & Polak. In describing the difference between classical and quantum state spaces, they say:
In classical ...
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Analog implementation of the Lipkin-Meskov-Glick using molmer soresen gates
I am making an analog implementation of the following Hamiltonian in Molmer Soresen gates and I would like to know if it would be possible to introduce the term dependent on S_z by varying the ...
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Is it possible to know/compute measurment impact to infer state before collapse? [duplicate]
Let say we have the state $ |\varphi⟩ = \alpha|0⟩ + \beta|1⟩ $
Measuring this state provoke a change, $\epsilon$ to the system, $S$, making the state of $|\varphi⟩$ collapse to either $|0⟩$ or $|1⟩$.
...
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Can reversible computers really perform truly reversible computations in practice? [closed]
Someone once told me that with reversible computers there is no energy cost for the computation itself, there is only a cost for running the hardware. But is this true in practice, or is it only an ...
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What is counterportation for the layman?
The word counterportation has been appearing in my sphere of the internet somewhat frequently and I don’t think I understand what it is.
See here:
https://phys.org/news/2023-03-counterportation-...
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Best books/notes for learning quantum computing for a mathematician with no quantum mechanics background [duplicate]
I have a PhD in numerical analysis for PDE, and for this reason I have a very strong background in functional analysis, Hilbert spaces / linear and nonlinear operators, algebra, but also probability.
...
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Error happened in quantum error correction
I have a question about the correction step in the quantum error correction.
Consider the three-qubit encoding in the quantum error correction, The following operations are performed to $|\phi\rangle=...
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Probability inequality for Quantum Approximate Optimization Algorithm (QAOA)
In arXiv:2207.14734 the authors claim that it is "straightforward to show that" their equation 8 holds:
$$\mathrm{Pr}_{x\sim q}[x:f(x)\geq \mu] \geq \frac{1}{M}$$
where we have an objective ...
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Symmetries of a 1 qubit universe [closed]
I am studying an isolated 1 qubit system trying to find its symmetries. By that I mean see what I can change without changing the physics. But I am having problems understanding what is the physics of ...
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