Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient quantum imaginary time evolution by drifting real time
  evolution: an approach with low gate and measurement complexity   Quantum imaginary time evolution (QITE) is one of the promising candidates
for finding eigenvalues and eigenstates of a Hamiltonian. However, the original
QITE proposal [Nat. Phys. 16, 205-210 (2020)], which approximates the imaginary
time evolution by real time evolution, suffers from large circuit depth and
measurements due to the size of the Pauli operator pool and Trotterization. To
alleviate the requirement for deep circuits, we propose a time-dependent
drifting scheme inspired by the qDRIFT algorithm [Phys. Rev. Lett 123, 070503
(2019)], which randomly draws a Pauli term out of the approximated unitary
operation generators of QITE according to the strength and rescales that term
by the total strength of the Pauli terms. We show that this drifting scheme
removes the depth dependency on size of the operator pool and converges inverse
linearly to the number of steps. We further propose a deterministic algorithm
that selects the dominant Pauli term to reduce the fluctuation for the ground
state preparation. Meanwhile, we introduce an efficient measurement reduction
scheme across Trotter steps, which removes its cost dependence on the number of
iterations, and a measurement distribution protocol for different observables
within each time step. We also analyze the main error source of our scheme due
to the correlation length both theoretically and numerically. We numerically
test its validity of depth reduction, convergence performance, and faithfulness
of measurement reduction approximation on $\rm{LiH}$, $\rm{BeH_2}$, $\rm{H_6}$
and $\rm{NH_3}$ molecules. In particular, the results on $\rm{LiH}$ molecule
give the circuit depths comparable to that of the advanced adaptive variational
quantum eigensolver (VQE) methods.

30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th