Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets

By Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, M. Takita, M. Brink, Jerry M. Chow, Jay M. Gambetta. Nature, 2017

3,380 citations recorded by the source corpus.

Quantum computers can be used to address electronic-structure problems and problems in materials science and condensed matter physics that can be formulated as interacting fermionic problems, problems which stretch the limits of existing high-performance computers. Finding exact solutions to such problems numerically has a computational cost that scales exponentially with the size of the system, and Monte Carlo methods are unsuitable owing to the fermionic sign problem. These limitations of classical computational methods have made solving even few-atom electronic-structure problems interesting for implementation using medium-sized quantum computers. Yet experimental implementations have so far been restricted to molecules involving only hydrogen and helium. Here we demonstrate the experimental optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms, determining the ground-state energy for molecules of increasing size, up to BeH2. We achieve this result by using a variational quantum eigenvalue solver (eigensolver) with efficiently prepared trial states that are tailored specifically to the interactions that are available in our quantum processor, combined with a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. We demonstrate the flexibility of our approach by applying it to a problem of quantum magnetism, an antiferromagnetic Heisenberg model in an external magnetic field. In all cases, we find agreement between our experiments and numerical simulations using a model of the device with noise. Our results help to elucidate the requirements for scaling the method to larger systems and for bridging the gap between key problems in high-performance computing and their implementation on quantum hardware.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/5676184605224be5d89bbf18ef8b992bea6f768f

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Citations in the corpus

Coherent quantum annealing in a programmable 2,000 qubit Ising chain (2022, methodology): “Using a dimensionless annealing parameter s to control the Hamiltonian in equation (1) with J = 1, the system is tuned through its QPT at Γ (sc) = J (sc) for sc ≈ 0.”
Noise-Adaptive Compiler Mappings for Noisy Intermediate-Scale Quantum Computers (2019, background): “QC algorithms show potential to significantly impact areas such as quantum chemistry [31, 50], cryptography [61], machine learning [4], and others.”
An adaptive variational algorithm for exact molecular simulations on a quantum computer (2018, methodology): “The re-optimization subroutine in step 8 can be implemented on either a classical or quantum processor using any of the gradient- or non-gradient-based optimization routines that have been proposed or demonstrated for VQE [12, 15, 16, 18].”
Predicting many properties of a quantum system from very few measurements (2020, background): “Potential applications include quantum chemistry [41] and lattice gauge theory [44]. d. Predicting expectation values of global observables (non-example).”
QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits (2021, methodology): “The variational method has shown huge potentials in applications such as quantum machine learning [4], [7], [56], [63], numerical analysis [37], [39], quantum simulation [30], [31], [52], and optimizations [18], [47].”