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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What are some resources to get started in quantum computing for nuclear and high-energy physics?
One of the big hopes for quantum computing is to simulate quantum many-body systems with quantum systems and thereby solve many outstanding problems that are otherwise intractable in nuclear and high-...
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Qiskit general amplitude embedding leads to long circuits
I am trying to use Qiskit to simulate many-body systems. Hence I calculate the ground state of Hamiltonians a lot. There are 2 ways I do them.
1: Calculate the ground state classically, then do state ...
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MPS in (2+1) D quantum many body system (QMBS)
Can the Matrix Product State (MPS) simulator of the QISKIT be used to solve (2+1) D problems? I have seen this paper using the MPS simulator for a (2+1) D problem. However, my understanding is that an ...
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The no fast forwarding theorem and exponential advantage for many body Hamiltonians
When simulating Hamiltonians in first quantization there are $\eta$ particles occupying a grid of $N$ grid points. In the first quantization, you directly discretize the differential operators onto a ...
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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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