Questions tagged [dynamics]

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.

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4
votes
3answers
99 views

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 ...
7
votes
3answers
308 views

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} = \...
6
votes
1answer
159 views

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 ...
5
votes
0answers
58 views

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 ...
1
vote
1answer
68 views

What is the physical meaning of the Hamiltonian $H = \alpha ( |01 \rangle \langle10| + | 10 \rangle \langle 01| )$?

In natural basis $| 0 \rangle = \begin{pmatrix} 1 \\0 \end{pmatrix}$, $| 1 \rangle = \begin{pmatrix} 0 \\ 1 \end{pmatrix}$, what physical situation/model does the following Hamiltonian represent: $H = ...
2
votes
1answer
206 views

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 ...
6
votes
0answers
70 views

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 ...
6
votes
1answer
276 views

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 ...
5
votes
2answers
266 views

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 ...
12
votes
1answer
489 views

How are quantum gates realised, in terms of the dynamic?

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 "...