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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 model in your question, which is very special to be exactly solvable. General Method The method to obtain the tightest bound to date (for a generic short-range ...


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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, you can think of this as renormalizing time). Here comes the catch with bosonic systems: For bosons, the norm of interactions is unbounded (e.g. $a^\dagger a$ ...


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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 quantum optics can be thought of as "combining different qunits" as well: a photon in a superposition of many spatial modes (high-dimensional qudit), together with ...


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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 Rubik’s Cube. This is already implicitly answered in the question: you need 27 bits, 14 trits.... However, this is labouring under the assumption that you can ...


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Excellent question! You are asking if we can, given a property we want in a quantum system (for example superconductivity in a chemical compound), efficiently find one example of such a compound. First of all, it is perhaps not yet a completely settled question if we can calculate such properties in the forward direction efficiently: Given a compound, does ...


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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 BQP and QMA is similar to the relationship between P and NP: it would be very surprising if there were efficient quantum algorithms for QMA-complete problems.) ...


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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 system we can control in the actual experiment and the theoretical one, in terms of system size (degrees of freedom that we care about) and in terms of ...


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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 concurrently. Remember 10k bits is only 1.25kB which is not even enough to store a typical operating system. If you want to consider each qubit as a "client" in ...


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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.


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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 it is will all likelihood hard even for a quantum computer.


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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


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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 each cell of the cube, because then twists/turns of the faces almost immediately present themselves as (controlled) $\mathsf{SWAP}$'s of the respective cells. For ...


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