Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonian quantum computer in one dimension   Quantum computation can be achieved by preparing an appropriate initial
product state of qudits and then letting it evolve under a fixed Hamiltonian.
The readout is made by measurement on individual qudits at some later time.
This approach is called the Hamiltonian quantum computation and it includes,
for example, the continuous-time quantum cellular automata and the universal
quantum walk. We consider one spatial dimension and study the compromise
between the locality $k$ and the local Hilbert space dimension $d$. For
geometrically 2-local (i.e., $k=2$), it is known that $d=8$ is already
sufficient for universal quantum computation but the Hamiltonian is not
translationally invariant. As the locality $k$ increases, it is expected that
the minimum required $d$ should decrease. We provide a construction of
Hamiltonian quantum computer for $k=3$ with $d=5$. One implication is that
simulating 1D chains of spin-2 particles is BQP-complete. Imposing translation
invariance will increase the required $d$. For this we also construct another
3-local ($k=3$) Hamiltonian that is invariant under translation of a unit cell
of two sites but that requires $d$ to be 8.

27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg