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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 ...
Lagrenge's user avatar
  • 185
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\...
Adam Zalcman's user avatar
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5 votes
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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 ...
Norbert Schuch's user avatar
5 votes
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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 ...
cheetah's user avatar
  • 433
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 ...
Cody Wang's user avatar
  • 1,253
4 votes
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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, ...
Norbert Schuch's user avatar
4 votes
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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, ...
Norbert Schuch's user avatar
4 votes
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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's user avatar
  • 25.9k
4 votes
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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 ...
DaftWullie's user avatar
  • 59.9k
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 ...
Jalex Stark's user avatar
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 ...
agaitaarino's user avatar
  • 3,837
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 ...
user1271772 No more free time's user avatar
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.
Norbert Schuch's user avatar
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 ...
Mark Spinelli's user avatar
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
bRost03's user avatar
  • 579
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 ...
bm442's user avatar
  • 1,182
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 ...
lm1909's user avatar
  • 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, ...
Mark Spinelli's user avatar
1 vote

What is the "physical" Hilbert space for non-local Hamiltonians?

I don't think there's likely to be any efficient way to explore all corners of the Hilbert space on $n$ qubits to prepare any quantum state, regardless of the amount of locality or non-locality. For ...
Mark Spinelli's user avatar

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