470 research outputs found
Finding the ground state of the Hubbard model by variational methods on a quantum computer with gate errors
A key goal of digital quantum computing is the simulation of fermionic
systems such as molecules or the Hubbard model. Unfortunately, for present and
near-future quantum computers the use of quantum error correction schemes is
still out of reach. Hence, the finite error rate limits the use of quantum
computers to algorithms with a low number of gates. The variational Hamiltonian
ansatz (VHA) has been shown to produce the ground state in good approximation
in a manageable number of steps. Here we study explicitly the effect of gate
errors on its performance. The VHA is inspired by the adiabatic quantum
evolution under the influence of a time-dependent Hamiltonian, where the -
ideally short - fixed Trotter time steps are replaced by variational
parameters. The method profits substantially from quantum variational error
suppression, e.g., unitary quasi-static errors are mitigated within the
algorithm. We test the performance of the VHA when applied to the Hubbard model
in the presence of unitary control errors on quantum computers with realistic
gate fidelities.Comment: 5+1 pages, 2 figures, 3 table
Emulating the one-dimensional Fermi-Hubbard model by a double chain of qubits
The Jordan-Wigner transformation maps a one-dimensional (1D) spin-
1
/
2
system onto a fermionic model without spin degree of freedom. A double chain of quantum bits with
X
X
and
Z
Z
couplings of neighboring qubits along and between the chains, respectively, can be mapped on a spin-full 1D Fermi-Hubbard model. The qubit system can thus be used to emulate the quantum properties of this model. We analyze physical implementations of such analog quantum simulators, including one based on transmon qubits, where the
Z
Z
interaction arises due to an inductive coupling and the
X
X
interaction due to a capacitive interaction. We propose protocols to gain confidence in the results of the simulation through measurements of local operators
Quantum simulation of the spin-boson model with a microwave circuit
We consider superconducting circuits for the purpose of simulating the
spin-boson model. The spin-boson model consists of a single two-level system
coupled to bosonic modes. In most cases, the model is considered in a limit
where the bosonic modes are sufficiently dense to form a continuous spectral
bath. A very well known case is the ohmic bath, where the density of states
grows linearly with the frequency. In the limit of weak coupling or large
temperature, this problem can be solved numerically. If the coupling is strong,
the bosonic modes can become sufficiently excited to make a classical
simulation impossible. Here, we discuss how a quantum simulation of this
problem can be performed by coupling a superconducting qubit to a set of
microwave resonators. We demonstrate a possible implementation of a continuous
spectral bath with individual bath resonators coupling strongly to the qubit.
Applying a microwave drive scheme potentially allows us to access the
strong-coupling regime of the spin-boson model. We discuss how the resulting
spin relaxation dynamics with different initialization conditions can be probed
by standard qubit-readout techniques from circuit quantum electrodynamics.Comment: 23 pages, 10 figure
Post-processing noisy quantum computations utilizing N-representability constraints
We propose and analyze a method for improving quantum chemical energy
calculations on a quantum computer impaired by decoherence and shot noise. The
error mitigation approach relies on the fact that the one- and two-particle
reduced density matrices (1- and 2-RDM) of a chemical system need to obey
so-called N-representability constraints. We post-process the result of an RDM
measurement by projecting it into the subspace where certain N-representability
conditions are fulfilled. Furthermore, we utilize that such constraints also
hold in the hole and particle-hole sector and perform projections in these
sectors as well. We expand earlier work by conducting a careful analysis of the
method's performance in the context of quantum computing. Specifically, we
consider typical decoherence channels (dephasing, damping, and depolarizing
noise) as well as shot noise due to a finite number of projective measurements.
We provide analytical considerations and examine numerically three example
systems, \ch{H2}, \ch{LiH}, and \ch{BeH2}. From these investigations, we derive
our own practical yet effective method to best employ the various projection
options. Our results show the approach to significantly lower energy errors and
measurement variances of (simulated) quantum computations
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