Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States

By Jarrod R. McClean, M. Schwartz, Jonathan Carter, W. A. Jong. 2016

454 citations recorded by the source corpus.

Author(s): McClean, JR; Kimchi-Schwartz, ME; Carter, J; De Jong, WA | Abstract: © 2017 American Physical Society. Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One powerful example of such a hybrid quantum-classical approach optimized for classically intractable eigenvalue problems is the variational quantum eigensolver, built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed as leaders among the candidates for the first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even nonsystematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we develop a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions by leveraging additional measurements and classical resources. We demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error-correction codes.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/40b9025dba73ae073ddcdeb24680fd947aa2bc17

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Variational quantum algorithms (2020, methodology): “A different approach is to use as ansatz a trainable linear combination of parametrized states |ψ({cμ},θ)〉 = ∑ μ cμ|ψμ(θμ)〉 with {cμ} classically optimizable coefficient [44–50].”
t|ket⟩: a retargetable compiler for NISQ devices (2020, methodology): “For excited-state calculations, one can use methods such as quantum subspace expansion, reduced density matrix approximation, penalty functions, and symmetry constraints [82].”
An adaptive variational algorithm for exact molecular simulations on a quantum computer (2018, methodology): “This was followed by several theoretical studies on VQE [7, 11–17] and demonstrations on other hardware such as superconducting qubits [7, 16, 18] and trapped ions [19, 20].”
QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits (2021, methodology): “Other methods such as quantum subspace expansion [119] and learning-based mitigation [120], [121] are also proposed.”