For questions about how a quantum state (wavefunction, density matrix, Wigner distribution, etc.) changes with respect to time. Also for questions about how to calculate quantum dynamics.
Questions tagged [dynamics]
18 questions
12
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2 answers
How are elementary quantum gates realised?
When expressing computations in terms of a quantum circuit, one makes use of gates, that is, (typically) unitary evolutions.
In some sense, these are rather mysterious objects, in that they perform "magic" discrete operations on the states.
They are…
glS
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What are the preferred numerical methods to simulate the evolution of a state through a time-dependent Hamiltonian?
Under the influence of a time-independent Hamiltonian $H$, a state $|\psi\rangle$ will evolve after a time $t$ to the final state $|\psi(t)\rangle=e^{-iH t}|\psi\rangle$, while in the most general case of a time-dependent Hamiltonian $H(t)$, the…
glS
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8
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3 answers
If a Hamiltonian is quadratic in the ladder operator, why is its time evolution linear in the ladder operator?
How can one show that $\hat{U}^\dagger\hat{a}\hat{U}$ (with $\hat{U} =e^{-i\hat{H}t}$) involves only linear orders of the ladder operator, when $H$ is the general quadratic Hamiltonian $(\hat{H} = \alpha (\hat{a}^\dagger)^2+ \beta…
heromano
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7
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How to prove that a naive quantum random walk is non-unitary
A 2000 paper by Nayak and Vishwanath provides an analysis of the dynamics of quantum random walks. In this paper, they mention a "naive" approach to defining a walk. I include the quote as follows:
In direct analogy, one may naively try to define…
Shadow43375
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Discrepancy regarding Husimi Probability distribution
I am trying to simulate a system of j qubits and for visualization of the dynamics considering the Husimi distribution of the state.
To carry out the projection onto coherent states I have proceeded in the following manner
…
Sudheesh
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5
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2 answers
Only assuming the universe evolves according to a positive trace-preserving map, is there a proof that all subsystem evolution must be CPTP?
If we only assume that the wavefunction of the universe evolves according to $e^{-iHt}$, is there any proof that all subsystems of the universe (partial traces over parts of the universe) must evolve according to a completely positive,…
user1271772 No more free time
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5
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Computing the expectation values of a Hamiltonian constructed from a cost functions in combinatorial optimization
One of the main steps in Hybrid Quantum algorithms for solving Combinatorial Optimization problems is the calculation of the expected value of a hermitian operator $H = \sum{H_i}$ (where $H_i$ are products of Pauli Matrices on a subset of the…
César Leonardo Clemente López
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4
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3 answers
Why does joint ground state not change under action of beam splitting unitary operator?
How can one show that $\hat{U}|00\rangle=|00\rangle$ where $\hat{U}=e^{-igt(\hat{a}^\dagger_2\hat{a}_1+\hat{a}^\dagger_1\hat{a}_2)}$ and $|00\rangle$ is the unique joint zero eigenstate of the annihilation operators $\hat{a}_1$ and $\hat{a}_2$, i.e.…
heromano
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What are the quantum simulation problems where AI doesn't eat quantum computing's lunch?
The provocatively titled Why AI could eat quantum computing’s lunch provides an overview about what kinds of quantum systems that AI can tackle. The most interesting part of this article is that, apparently, AI can come up with "good enough"…
Victory Omole
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3
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How to construct solution based on the Schrödinger equation and split it into gates?
To the best of my knowledge, the gate notation forms the quantum programming. For instance, I use qiskit, pennylane, etc. products to see how the algorithms do their job. At the same time the "quantum" world relates to the Schrödinger equation. But…
Марина Лисниченко
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1 answer
Quantify the probability in guessing the Hamiltonian?
Background
Let's say I know my experimentalist friend has been measuring the eigenvalues of a physical system. I can see the $M$ measurements are noted in a sheet of paper and I assume the dimensionality of the Hamiltonian to be $K$. I also note…
More Anonymous
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Is there a way to obtain statevector results from pulse circuits in qiskit?
As shown in Ref, the amplitude of a pulse determines the rotation on the x-axis, while the angle determines the rotation on the z-axix. According to the paper, the author proved such results with pulse experiments and plot the results on the Bloch…
Tyler Zhu
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1 answer
Quantum gates for more than two basis states
Lets say I have a time dependent hamiltonian of the form $$H(t) = H_0 + f(t) H_{drive}$$ (where $H_0$ may represent the hamiltonian for a superconducting qubit) and I want to find the optimal pulse $f(t)$, such that the infidelity between some…
SphericalApproximator
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2
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How to comparing a quantum channel with a unitary?
I have a target unitary that I want to implement and I have a known dynamics that results in a quantum channel. I already have some fidelity measures to characterize the overlap between them. (like: https://arxiv.org/abs/0909.0077) But I want a more…
Will Yang
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Is every quantum channel covariant with respect to some non-trivial Hamiltonian?
When asking whether every channel is covariant with respect to some non-trivial unitary channel I mean the following:
Does there for every CPTP map $\Phi:\mathbb C^{n\times n}\to\mathbb C^{n\times n}$ exist a unitary $U\in\mathbb C^{n\times n}$…
Frederik vom Ende
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