47 research outputs found
Quantum Monte Carlo with Coupled-Cluster wave functions
We introduce a novel many body method which combines two powerful many body
techniques, viz., quantum Monte Carlo and coupled cluster theory. Coupled
cluster wave functions are introduced as importance functions in a Monte Carlo
method designed for the configuration interaction framework to provide rigorous
upper bounds to the ground state energy. We benchmark our method on the
homogeneous electron gas in momentum space. The importance function used is the
coupled cluster doubles wave function. We show that the computational resources
required in our method scale polynomially with system size. Our energy upper
bounds are in very good agreement with previous calculations of similar
accuracy, and they can be systematically improved by including higher order
excitations in the coupled cluster wave function.Comment: Submitted to Physical Review Letter
Faster spectral density calculation using energy moments
Accurate predictions of inclusive scattering cross sections in the linear
response regime require efficient and controllable methods to calculate the
spectral density in a strongly-correlated many-body system. In this work we
reformulate the recently proposed Gaussian Integral Transform technique in
terms of Fourier moments of the system Hamiltonian which can be computed
efficiently on a quantum computer. One of the main advantages of this framework
is that it allows for an important reduction of the computational cost by
exploiting previous knowledge about the energy moments of the spectral density.
For a simple model of medium mass nucleus like Ca and target energy
resolution of MeV we find an expected speed-up of times for
the calculation of the giant dipole response and of times for the
simulation of quasi-elastic electron scattering at typical momentum transfers.Comment: 13 pages, 4 figure
Importance sampling for stochastic quantum simulations
Simulating complex quantum systems is a promising task for digital quantum
computers. However, the depth of popular product formulas scales with the
number of summands in the Hamiltonian, which can therefore be challenging to
implement on near-term as well as fault-tolerant devices. An efficient solution
is given by the stochastic compilation protocol known as qDrift, which builds
random product formulas by sampling from the Hamiltonian according to the
magnitude of their coefficients. In this work, we unify the qDrift protocol
with importance sampling, allowing us to sample from arbitrary distributions
while controlling both the bias as well as the statistical fluctuations. We
show that the simulation cost can be reduced while achieving the same accuracy
by considering the individual simulation cost during the sampling stage.
Moreover, we incorporate recent work on composite channel and compute
rigorous bounds on the bias and variance showing how to choose the number of
samples, experiments, and time steps for a given target accuracy. These results
lead to a more efficient implementation of the qDrift protocol, both with and
without the use of composite channels. Theoretical results are confirmed by
numerical simulations performed on a lattice nuclear effective field theory.Comment: 15 pages, 10 pages supplemental materia