Abstract
Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite coherent lifetimes. Hybrid algorithms, such as the variational quantum eigensolver (VQE), leverage classical resources to reduce the required number of quantum gates. Experimental demonstrations of VQE have resulted in calculation of Hamiltonian ground states, and a new theoretical approach based on a quantum subspace expansion (QSE) has outlined a procedure for determining excited states that are central to dynamical processes. We use a superconducting-qubit-based processor to apply the QSE approach to the molecule, extracting both ground and excited states without the need for auxiliary qubits or additional minimization. Further, we show that this extended protocol can mitigate the effects of incoherent errors, potentially enabling larger-scale quantum simulations without the need for complex error-correction techniques.
- Received 7 August 2017
DOI:https://doi.org/10.1103/PhysRevX.8.011021
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Viewpoint
Quantum Computer Simulates Excited States of Molecule
Published 12 February 2018
Excited-state energies of the hydrogen molecule have been calculated using a two-qubit quantum computer.
See more in Physics
Popular Summary
While universal quantum computers promise significant societal impact through their ability to outperform the best classical devices, the realization of such technology requires significant advances in state-of-the-art quantum hardware. Nascent quantum processors with finite coherence times, modest gate fidelities, and a limited number of qubits may still be leveraged to perform useful tasks by using so-called hybrid quantum-classical algorithms, which subdivide a given computational task into quantum and classical parts and allocate quantum resources only where necessary. We implement one such hybrid protocol and use it to calculate the complete energy spectrum of the hydrogen molecule.
This protocol, the variational quantum eigensolver (VQE), was developed to calculate the ground-state energy of complex chemical systems. It uses a classical optimization routine to minimize the expected energy of candidate wave functions, leveraging the quantum hardware to evaluate the energy. We realize this algorithm using a quantum processor comprised of two superconducting qubits with real-time classical optimization. With this architecture, we demonstrate, for the first time, the ability to calculate the full energy spectrum of a given Hamiltonian (in this case, the molecule) beyond just the ground state.
Our new approach to implementing a VQE suppresses the effects of certain types of errors, making it an attractive choice for future larger-scale calculations.