Progress towards practical quantum variational algorithms

By Dave Wecker, M. B. Hastings, Matthias Troyer. 2015

699 citations recorded by the source corpus.

The preparation of quantum states using short quantum circuits is one of the most promising near-term applications of small quantum computers, especially if the circuit is short enough and the fidelity of gates high enough that it can be executed without quantum error correction. Such quantum state preparation can be used in variational approaches, optimizing parameters in the circuit to minimize the energy of the constructed quantum state for a given problem Hamiltonian. For this purpose we propose a simple-to-implement class of quantum states motivated by adiabatic state preparation. We test its accuracy and determine the required circuit depth for a Hubbard model on ladders with up to 12 sites (24 spin orbitals), and for small molecules. We find that this ansatz converges faster than previously proposed schemes based on unitary coupled clusters. While the required number of measurements is astronomically large for quantum chemistry applications to molecules, applying the variational approach to the Hubbard model (and related models) is found to be far less demanding and potentially practical on small quantum computers. We also discuss another application of quantum state preparation using short quantum circuits, to prepare trial ground states of models faster than using adiabatic state preparation.

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

View Paper: https://www.semanticscholar.org/paper/06895e65af2602ce15ac0ad015720871418f0827

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Leakage reduction in fast superconducting qubit gates via optimal control (2020, background): “[34] Wecker, D.”
Quantum variational algorithms are swamped with traps (2022, neutral): “We also consider the training performance of VQE in ﬁ nding the ground state of a Heisenberg XYZ Hamiltonian 43 .”
A Practical Quantum Instruction Set Architecture (2016, neutral): “I Introduction 1”
Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity (2018, background): “More recently, experimental demonstrations [11 – 15] have focused on the development of variational algorithms [16,17], which are often [18,19], but not always [20,21], inspired by time-evolution primitives.”
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator (2018, background): “For instance, it has been argued that a parameterized Trotter approximation [7, 81], to the adiabatic state preparation algorithm may serve as an effective ansatz [40, 41, 51].”
Barren plateaus in variational quantum computing (2024, positive): “By understanding the connections between these different origins of BPs, we will see that one should be able to predict whether a model will exhibit an exponentially concentrated loss.”
Connecting ansatz expressibility to gradient magnitudes and barren plateaus (2021, background): “For instance, the quantum alternating operator ansatz [21] (or the Hamiltonian variational ansatz [25]), encode information of an appropriate adiabatic transformation.”
Variational quantum algorithms (2020, methodology): “Indeed, early estimations of resource requirements suggested that the number of measurements that would be required for interesting quantum chemistry VQE problems would be astronomical, making addressing this issue essential for quantum advantage [26].”
Scalable Quantum Simulation of Molecular Energies (2015, background): “While the unitary variant has no efficient preparation scheme on a classical computer, scalable methods of preparation for a fixed set of parameters on a quantum device have now been documented several times [19,20,22,23].”
Variational Quantum Computation of Excited States (2018, background): “[23] in the context of VQE, and UCCGSD has since been investigated numerically [18, 41].”