Variational ansatz-based quantum simulation of imaginary time evolution

By Sam McArdle, Tyson Jones, Suguru Endo, Ying Li, Simon C. Benjamin, Xiao Yuan. npj Quantum Information, 2018

615 citations recorded by the source corpus.

Imaginary time evolution is a powerful tool for studying quantum systems. While it is possible to simulate with a classical computer, the time and memory requirements generally scale exponentially with the system size. Conversely, quantum computers can efficiently simulate quantum systems, but not non-unitary imaginary time evolution. We propose a variational algorithm for simulating imaginary time evolution on a hybrid quantum computer. We use this algorithm to find the ground-state energy of many-particle systems; specifically molecular hydrogen and lithium hydride, finding the ground state with high probability. Our method can also be applied to general optimisation problems and quantum machine learning. As our algorithm is hybrid, suitable for error mitigation and can exploit shallow quantum circuits, it can be implemented with current quantum computers.

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

View Paper: https://www.semanticscholar.org/paper/bcc7928a9016c9b0ba8411b49ae80a14c83e61cb

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Estimating the gradient and higher-order derivatives on quantum hardware (2020, background): “This tensor plays a crucial role in the implementation of the quantum natural gradient optimizer [26] and in the variational quantum simulation of imaginary-time evolution [27].”
Challenges and opportunities in quantum machine learning (2022, background): “Finally, a quantum advantage for generative modelling may be achieved when one can generate ground states [112], equilibrium states [47, 113], or quantum dynamics [114], using generative models incorporating QNNs, in a way where the distribution cannot be sampled classically, and yields more…”
Challenges and opportunities in quantum optimization (2023, neutral): “Similar to the quantum adiabatic algorithm, QITE assumes an initial state ψ ⟩ 0 ∣”
General parameter-shift rules for quantum gradients (2021, methodology): “The metric can also be computed analytically without parameter shifts via a linear combination of uni-taries (LCU) [57, 58], which also employs Hadamard tests.”
Quantum Natural Gradient (2019, background): “Variational imaginary-time evolution on hybrid quantum-classical devices has been previously investigated in [18, 12, 13].”
Variational Quantum Computation of Excited States (2018, methodology): “Here we study hybrid quantum-classical algorithms, which dramatically reduce the required gate depth to run and somewhat mitigate errors, by closely integrating classical and quantum subroutines [2, 9, 14, 15, 21, 23, 26, 40].”
Diagnosing Barren Plateaus with Tools from Quantum Optimal Control (2021, background): “[10] Sam McArdle, Tyson Jones, Suguru Endo, Ying Li, Simon C Benjamin, and Xiao Yuan, “Variational ansatzbased quantum simulation of imaginary time evolution,” npj Quantum Information 5, 1–6 (2019).”
Variational quantum algorithms for nonlinear problems (2019, methodology): “Recently, the concept of variational quantum computing (VQC) attracted considerable interest [19–32] for solving optimization problems.”