For questions related to microscopic systems made of a large number of interacting particles as relevant to quantum computing, or simulation of such systems using a quantum computer.
Questions tagged [many-body-systems]
29 questions
26
votes
1 answer
Explicit Lieb-Robinson Velocity Bounds
Lieb-Robinson bounds describe how effects are propagated through a system due to a local Hamiltonian. They are often described in the form
$$
\left|[A,B(t)]\right|\leq Ce^{vt-l},
$$
where $A$ and $B$ are operators that are separated by a distance…
DaftWullie
- 62,671
- 4
- 55
- 140
8
votes
2 answers
How could a quantum network be constructed to handle 10,000 clients concurrently?
The C10k Problem is a classical computing problem whose name (C10k) is a numeronym for concurrently handling ten thousand connections.
How could a quantum network be constructed to handle 10,000 clients concurrently?
user820789
- 3,440
- 13
- 43
8
votes
3 answers
Can we synthesize quantum many body systems with quantum computers quickly in the general case?
Quantum computing can be used to efficiently simulate quantum many-body systems.
Solving such a problem is classically hard because its complexity grows exponentially with the problem size (roughly with the degree of freedoms), which is an inherent…
peterh
- 897
- 2
- 14
- 23
7
votes
0 answers
Tripartite quantum marginal problem
Consider a tripartite quantum system with the three subsystems labeled $A, B,$ and $C$. Now take two states $\rho_{AB}$ on the joint system $AB$ and $\rho_{BC}$ on the joint system $BC$. Under what conditions are these compatible with the same…
biryani
- 1,026
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6
votes
1 answer
Do we know anything about the computational complexity of the exchange-correlation functional?
Density functional theory is based on the Hohenberg-Kohn (HK) theorems and aims to compute the ground-state many-body wavefunction of a physical material and/or molecules.
To put it simply, the HK theorems show that there is a unique one-to-one…
Dr. T. Q. Bit
- 537
- 3
- 13
6
votes
1 answer
Is it known whether the Fermi-Hubbard ground state can be prepared efficiently or not?
Naturally, in general, ground state preparation is QMA-complete. There exists a paper by Andrew Childs, David Gosset & Zak Webb, which shows that ground state preparation for the Bose-Hubbard model is QMA-complete.
However, is it known what the…
lm1909
- 115
- 8
4
votes
2 answers
Hilbert space to accurately represent 3x3 Rubik's Cube
What Hilbert space of dimension greater than 4.3e19 would be most convenient for working with the Rubik's Cube verse one qudit?
The cardinality of the Rubik's Cube group is given…
user820789
- 3,440
- 13
- 43
4
votes
1 answer
How to benchmark approximate random unitary sampling
I'm currently studying a specific sampling "quantum advantage" (sorry for the buzzword) protocol wich consist of periodically driving a random Ising chain (https://iopscience.iop.org/article/10.1088/2058-9565/acbd69), the resulting evolution…
Johan-Luca
- 101
- 7
4
votes
3 answers
Survey of which 'physically interesting' many-body states can be efficiently prepared on a quantum computer?
For digital quantum simulation of many-body problems, efficiently preparing an initial state of 'physical interest' (e.g. ground states, thermal states, topologically ordered states etc.) is very relevant.
There is quite an extensive amount of…
lm1909
- 115
- 8
4
votes
0 answers
How to calculate $\langle\sigma_i^z\rangle$ with the method of symmetry in Heisenberg XXZ model?
The Hamiltonian of Heisenberg's XXY model is given by:
$$
H=\sum_{j=1}^{N}\left[S_{j}^{x} S_{j+1}^{x}+S_{j}^{y} S_{j+1}^{y}+\Delta S_{j}^{z} S_{j+1}^{z}\right]
,$$
where $S_{j}^{u}=\sigma_{j}^{u} / 2(u=x, y, z), \sigma_{j}^{u}$ are the Pauli spin-…
narip
- 3,169
- 2
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4
votes
0 answers
Quantum Ising model correlation function query
In this paper on quantum Ising model dynamics, they consider the Hamiltonian
$$\mathcal{H} = \sum_{j < k} J_{jk} \hat{\sigma}_{j}^{z}\hat{\sigma}_{k}^{z}$$
and the correlation function
$$\mathcal{G} = \langle…
John Doe
- 941
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- 14
3
votes
1 answer
Primer for learning about quantum circuits simulating systems
I am interested in a couple of books or arXiv links to learn how to develop quantum circuits for the purpose of simulating quantum multi-body systems. Moreover, I am interested in learning how to develop an ansatz from a quantum circuit.
Any…
Enrique Segura
- 1,011
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- 9
3
votes
1 answer
Is second quantization related to first quantization as adjacency matrices relate to adjacency lists?
In an introductory classical algorithms class, one learns of a couple of ways to represent an unweighted, $d$-regular graph $G=(V,E)$ on $n=|V|$ vertices and $m=|E|$ edges.
A first way might be the adjacency list representation, which, for each…
Mark Spinelli
- 15,378
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3
votes
2 answers
Combining Different Qunits
Has any work been done on quantum systems which use a combination of types of qunits (eg. using qubits & qutrits simultaneously)?
If work has been done, what kind of work has been done? (eg. in quantum information in general? in quantum computing?…
user820789
- 3,440
- 13
- 43
3
votes
2 answers
The support of the ground state of stoquastic Hamiltonian is connected
A Hamiltonian $H$ is stoquastic in the standard basis if all the off-diagonal terms of the Hamiltonian are non-positive. If we choose $\beta$ small enough, all entries of $I-\beta H$ are non-negative. By the Perron-Frobenius Theorem, the eigenvector…
qmww987
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