7
votes
Accepted
Explicit Lieb-Robinson Velocity Bounds
Let me first answer the general question how to get a reasonably tight Lieb-Robinson (LR) speed when you are facing a generic locally interacting lattice model, and then I'll come back to the 1D XY ...
- 176
7
votes
Accepted
Can we always simultaneously diagonalize $H_A \otimes \mathbb{1}$ and $\mathbb{1} \otimes H_B$?
TL;DR: You can always achieve simultaneous diagonalization of $H_A\otimes\mathbb{1}$ and $\mathbb{1}\otimes H_B$ even if $[H_A, H_B]\ne 0$. And yes, this does follow from the fact that $[H_A\otimes\...
- 20.7k
5
votes
Accepted
Jordan-Wigner Transform and Trotterization: which goes first?
Short answer:
When you do the Jordan-Wigner transformation, you essentially insert a linear combination of tensor products of Pauli matrices for each fermionic creation and annihilation operator. As ...
- 413
4
votes
Accepted
Combining Different Qunits
Quantum walks are a simple case of quantum dynamics that involves a qubit (named coin in this context) interacting with a high-dimensional qudit (named walker in this context).
Almost anything in ...
glS♦
- 23.3k
4
votes
Accepted
Hilbert space to accurately represent 3x3 Rubik's Cube
This question does not need to be phrased as a quantum question. One can equally ask what classical register can be used to store a string that uniquely identifies each different configuration of the ...
- 55.7k
4
votes
Can we synthesize quantum many body systems with quantum computers quickly in the general case?
It seems that most ways of formalizing your question would lead to a problem that's QMA-hard, and therefore we shouldn't hope for an efficient quantum algorithm to solve it. (The relationship between ...
- 369
4
votes
Accepted
Lieb-Robinson Bound in 2nd quantized description?
In the Lieb-Robinson bound, the velocity depends on the strength (operator norm) of the interaction. This is intuitive: Twice as strong couplings will propagate information twice as fast (effectively, ...
- 5,647
4
votes
Accepted
Do we know anything about the computational complexity of the exchange-correlation functional?
Computing the exchange-correlation functional to sufficiently high accuracy is QMA-hard, where QMA is the quantum version of NP. In particular, this means that in all likelihood, it will be hard even ...
- 5,647
4
votes
Can we always simultaneously diagonalize $H_A \otimes \mathbb{1}$ and $\mathbb{1} \otimes H_B$?
I'm assuming these Hamiltonians act on separate subsystems, since that's the only way to guarantee that $[H_A \otimes \mathbb{1}, \mathbb{1} \otimes H_B] = 0$. Since the two Hamiltonians act on ...
- 1,018
3
votes
Accepted
What is the "physical" Hilbert space for non-local Hamiltonians?
Your assertion that interactions such as the Coulomb interaction are non-local (in the quantum information sense of "k-local") is incorrect. The Coulomb interaction couples two particles, ...
- 5,647
3
votes
Can we synthesize quantum many body systems with quantum computers quickly in the general case?
Short answer for the superconducting -> formula example: no, we will not be able to do that.
Longer answer (and more optimistic)
We need a one-to-one correspondence between the Hamiltonian of the ...
- 3,777
3
votes
How could a quantum network be constructed to handle 10,000 clients concurrently?
Enabling network sockets to handle 10k clients at the same time with over 1 gigabit per second Ethernet (the C10k problem), is different from making a quantum computer that can handle 10k qubits ...
- 13.5k
3
votes
Combining Different Qunits
Yes. Just to give one example, the PPT criterion is necessary and sufficient to decide whether a state is separable for qubit-qubit and qubit-qutrit systems, but not beyond.
- 5,647
2
votes
Is it known whether the Fermi-Hubbard ground state can be prepared efficiently or not?
In this paper, Schuch and Verstraete determined the computational complexity of finding the ground state of the Fermi-Hubbard model, showing that it is among the hardest problems in the complexity ...
- 932
2
votes
Hilbert space to accurately represent 3x3 Rubik's Cube
Following up on @DaftWullie's answer, for certain combinatorial puzzles such as the 3x3 Rubik's cube, it might also be convenient to consider a fixed register of qubits (or qubits and qutrits) for ...
- 10.7k
2
votes
Accepted
Primer for learning about quantum circuits simulating systems
Here's a fairly thorough overview: https://arxiv.org/abs/1308.6253
For completeness I'll include the paper from the comment: https://arxiv.org/abs/quant-ph/0108146
- 579
1
vote
Survey of which 'physically interesting' many-body states can be efficiently prepared on a quantum computer?
This is only a partial answer, as it is not a survey paper/etc. and does not claim to be exhaustive, but the PhD thesis "Hamiltonian Complexity in Many-Body Quantum Physics" by James David ...
- 93
1
vote
Accepted
Survey of which 'physically interesting' many-body states can be efficiently prepared on a quantum computer?
I think it is really tough to provide a complete and comprehensive list of conditions describing which states can be efficiently prepared, at least because we don't know how to split BQP from QMA yet, ...
- 10.7k
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