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.

Filter by
Sorted by
Tagged with
1 vote
1 answer
56 views

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 ...
Anyon's user avatar
  • 57
2 votes
0 answers
58 views

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 ...
Cuhrazatee's user avatar
4 votes
1 answer
68 views

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/...
Johan-Luca's user avatar
4 votes
3 answers
132 views

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 ...
lm1909's user avatar
  • 93
4 votes
1 answer
191 views

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 ...
lm1909's user avatar
  • 93
2 votes
2 answers
172 views

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 ...
MonteNero's user avatar
  • 2,481
0 votes
2 answers
261 views

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 ...
Dr. T. Q. Bit's user avatar
1 vote
1 answer
324 views

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 ...
IGY's user avatar
  • 361
6 votes
0 answers
104 views

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 ...
biryani's user avatar
  • 966
4 votes
0 answers
54 views

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(...
narip's user avatar
  • 2,984
2 votes
1 answer
92 views

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 ...
More Anonymous's user avatar
1 vote
0 answers
157 views

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 $|...
刘环宇's user avatar
4 votes
0 answers
87 views

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}...
John Doe's user avatar
  • 841
6 votes
1 answer
103 views

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 ...
Dr. T. Q. Bit's user avatar
3 votes
1 answer
59 views

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 ...
Enrique Segura's user avatar
3 votes
2 answers
91 views

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 ...
user820789's user avatar
  • 3,302
3 votes
2 answers
330 views

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 ...
user820789's user avatar
  • 3,302
8 votes
2 answers
275 views

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 ...
user820789's user avatar
  • 3,302
25 votes
1 answer
2k views

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 $B$ ...
DaftWullie's user avatar
  • 57.9k
8 votes
3 answers
656 views

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 ...
peterh's user avatar
  • 897