6 research outputs found
Multi-Level Variational Spectroscopy using a Programmable Quantum Simulator
Energy spectroscopy is a powerful tool with diverse applications across
various disciplines. The advent of programmable digital quantum simulators
opens new possibilities for conducting spectroscopy on various models using a
single device. Variational quantum-classical algorithms have emerged as a
promising approach for achieving such tasks on near-term quantum simulators,
despite facing significant quantum and classical resource overheads. Here, we
experimentally demonstrate multi-level variational spectroscopy for fundamental
many-body Hamiltonians using a superconducting programmable digital quantum
simulator. By exploiting symmetries, we effectively reduce circuit depth and
optimization parameters allowing us to go beyond the ground state. Combined
with the subspace search method, we achieve full spectroscopy for a 4-qubit
Heisenberg spin chain, yielding an average deviation of 0.13 between
experimental and theoretical energies, assuming unity coupling strength. Our
method, when extended to 8-qubit Heisenberg and transverse-field Ising
Hamiltonians, successfully determines the three lowest energy levels. In
achieving the above, we introduce a circuit-agnostic waveform compilation
method that enhances the robustness of our simulator against signal crosstalk.
Our study highlights symmetry-assisted resource efficiency in variational
quantum algorithms and lays the foundation for practical spectroscopy on
near-term quantum simulators, with potential applications in quantum chemistry
and condensed matter physics
Symmetry enhanced variational quantum eigensolver
The variational quantum-classical algorithms are the most promising approach
for achieving quantum advantage on near-term quantum simulators. Among these
methods, the variational quantum eigensolver has attracted a lot of attention
in recent years. While it is very effective for simulating the ground state of
many-body systems, its generalization to excited states becomes very resource
demanding. Here, we show that this issue can significantly be improved by
exploiting the symmetries of the Hamiltonian. The improvement is even more
effective for higher energy eigenstates. We introduce two methods for
incorporating the symmetries. In the first approach, called hardware symmetry
preserving, all the symmetries are included in the design of the circuit. In
the second approach, the cost function is updated to include the symmetries.
The hardware symmetry preserving approach indeed outperforms the second
approach. However, integrating all symmetries in the design of the circuit
could be extremely challenging. Therefore, we introduce hybrid symmetry
preserving method in which symmetries are divided between the circuit and the
classical cost function. This allows to harness the advantage of symmetries
while preventing sophisticated circuit design.Comment: 14 pages, 7 figure
Variational quantum simulation of long-range interacting systems
Current quantum simulators suffer from multiple limitations such as short
coherence time, noisy operations, faulty readout and restricted qubit
connectivity. Variational quantum algorithms are the most promising approach in
near-term quantum simulation to achieve quantum advantage over classical
computers. Here, we explore variational quantum algorithms, with different
levels of qubit connectivity, for digital simulation of the ground state of
long-range interacting systems as well as generation of spin squeezed states.
We find that as the interaction becomes more long-ranged, the variational
algorithms become less efficient, achieving lower fidelity and demanding more
optimization iterations. In particular, when the system is near its criticality
the efficiency is even lower. Increasing the connectivity between distant
qubits improves the results, even with less quantum and classical resources.
Our results show that by mixing circuit layers with different levels of
connectivity one can sensibly improve the performance. Interestingly, the order
of layers becomes very important and grouping the layers with long-distance
connectivity at the beginning of the circuit outperforms other permutations.
The same design of circuits can also be used to variationally produce spin
squeezed states, as a resource for quantum metrology.Comment: 11 pages, 7 figure