Questions tagged [many-body-systems]
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.
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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/...
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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 ...
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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 ...
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Can we always simultaneously diagonalize $H_A \otimes \mathbb{1}$ and $\mathbb{1} \otimes H_B$?
Suppose we have systems $A$ and $B$ with respective Hamiltonians $H_A \otimes \mathbb{1}$ and $\mathbb{1} \otimes H_B$. These Hamiltonians commute, so they share the same eigenbasis and hence can be ...
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What is the "physical" Hilbert space for non-local Hamiltonians?
In their 2011 paper, D. Poulin and coauthors show that the size of "physically" accessible states in Hilbert space for local Hamiltonians is exponentially smaller than the total Hilbert ...
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Jordan-Wigner Transform and Trotterization: which goes first?
I've been reading this paper about the procedure to simulate a many-body quantum system on a quantum device. I got confused by Figure 1. on page 3, and the 3 steps explained below the figure.
It seems ...
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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 ...
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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(...
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Lieb-Robinson Bound in 2nd quantized description?
Background
Let us restrict our discussion to bosons and adopt the convention First Quantised $\leftrightarrow $ Second Quantised Theory (we are following these Ashok Sen's Quantum Field Theory I of ...
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Is there a connection between the definitions of one- and two-particle reduced density matrices?
In quantum chemistry, there are concepts about one-particle reduced density matrix (1-RDM) and similarly, the two-particle reduced density matrix (2-RDM).
Generally, for an $n$ particle wavefunction $|...
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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
$$\mathcal{G}...
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votes
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Do we know anything about the computational complexity of the exchange-correlation functional?
Density functional theory is based on the Hohenberg-Kohn (HK) theorems and aims to compute the ground-state many-body wavefunction of a physical material and/or molecules.
To put it simply, the HK ...
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Primer for learning about quantum circuits simulating systems
I am interested in a couple of books or arXiv links to learn how to develop quantum circuits for the purpose of simulating quantum multi-body systems. Moreover, I am interested in learning how to ...
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Combining Different Qunits
Has any work been done on quantum systems which use a combination of types of qunits (eg. using qubits & qutrits simultaneously)?
If work has been done, what kind of work has been done? (eg. in ...
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Hilbert space to accurately represent 3x3 Rubik's Cube
What Hilbert space of dimension greater than 4.3e19 would be most convenient for working with the Rubik's Cube verse one qudit?
The cardinality of the Rubik's Cube group is given by:
Examples
66 ...
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How could a quantum network be constructed to handle 10,000 clients concurrently?
The C10k Problem is a classical computing problem whose name (C10k) is a numeronym for concurrently handling ten thousand connections.
How could a quantum network be constructed to handle 10,000 ...
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answer
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Explicit Lieb-Robinson Velocity Bounds
Lieb-Robinson bounds describe how effects are propagated through a system due to a local Hamiltonian. They are often described in the form
$$
\left|[A,B(t)]\right|\leq Ce^{vt-l},
$$
where $A$ and $B$ ...
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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 ...
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