Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
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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 BeH 2. 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.
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Pauli strings that commute qubit-wise can be measured at the same time.
“Pauli strings that commute qubit-wise, i.e. the Pauli operators on each qubit commute, can be measured at the same time (Kandala et al. , 2017; McClean et al. , 2016).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Kandala et al., 2017
A class of hardware-efficient ansätze has been proposed to accommodate device constraints.
“Aclass of hardware-efficient ansätze (see Fig. 3(b)) has been proposed to accommodate device constraints (Kandala et al. , 2017).”
From Noisy intermediate-scale quantum algorithms (2022) · cites this paper as Kandala et al., 2017
#BQP has been defined and shown to contain important physical problems, but it is of equal complexity to #P.
“While the quantum analog of #P , #BQP , has been defined and has been shown to contain important physical problems, it turns out to be of equal complexity to #P 67 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [67]
VQE is the most prominent hybrid algorithm for electronic structure, providing a variational heuristic for upper-bounding ground-state energy.
“The most prominent example of this class of algorithms relevant for electronic structure calculations is the variational quantum eigensolver (VQE), which presents a variational (and thus heuristic) algorithm to upper bounding the ground state energy problem.[126][127][128]”
From Quantum Computing for Molecular Biology** (2023) · cites this paper as [127]
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A review on Quantum Approximate Optimization Algorithm and its variants
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Generalized Unitary Coupled Cluster Wave functions for Quantum Computation
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Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
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Quantum-classical computation of Schwinger model dynamics using quantum computers
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An initialization strategy for addressing barren plateaus in parametrized quantum circuits
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Cloud Quantum Computing of an Atomic Nucleus
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Superconducting quantum computing: a review
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Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
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A generative modeling approach for benchmarking and training shallow quantum circuits
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Towards practical quantum computers: transmon qubit with a lifetime approaching 0.5 milliseconds
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The randomized measurement toolbox
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Self-citationVariational Quantum Linear Solver
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Potential of quantum computing for drug discovery
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Quantum Simulation for High-Energy Physics
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A dissipatively stabilized Mott insulator of photons
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Ground-state energy estimation of the water molecule on a trapped-ion quantum computer
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Mitigating measurement errors in multiqubit experiments
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Self-citationSubspace-search variational quantum eigensolver for excited states
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QAOA for Max-Cut requires hundreds of qubits for quantum speed-up
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Low-Depth Quantum Simulation of Materials
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The future of quantum computing with superconducting qubits
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Self-citationVariational quantum algorithms for nonlinear problems
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Strawberry Fields: A Software Platform for Photonic Quantum Computing
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Layerwise learning for quantum neural networks
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Barren plateaus in variational quantum computing
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Quantum Computer Systems for Scientific Discovery
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Probabilistic error cancellation with sparse Pauli–Lindblad models on noisy quantum processors
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Self-citationSimulating quantum many-body dynamics on a current digital quantum computer
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Thermodynamics and Kinetics of Drug-Target Binding by Molecular Simulation
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A crossbar network for silicon quantum dot qubits
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High-Coherence Fluxonium Qubit
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Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer
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On the complexity and verification of quantum random circuit sampling
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Shuttling a single charge across a one-dimensional array of silicon quantum dots
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Quantum Computation of Electronic Transitions Using a Variational Quantum Eigensolver
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Differentiable learning of quantum circuit Born machines
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Obstacles to Variational Quantum Optimization from Symmetry Protection
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Option Pricing using Quantum Computers
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Scalable Mitigation of Measurement Errors on Quantum Computers
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Self-citationQuantum Information Scrambling on a Superconducting Qutrit Processor
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Measurement optimization in the variational quantum eigensolver using a minimum clique cover
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Improving Variational Quantum Optimization using CVaR
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Simulating Large Quantum Circuits on a Small Quantum Computer
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Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator
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Quantum Long Short-Term Memory
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Information-Theoretic Bounds on Quantum Advantage in Machine Learning
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Variational quantum algorithms for discovering Hamiltonian spectra
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Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers
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Quantum Computing for High-Energy Physics: State of the Art and Challenges
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Self-citationSuppression of Qubit Crosstalk in a Tunable Coupling Superconducting Circuit
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Fermionic neural-network states for ab-initio electronic structure
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Self-citation
- Authors
- Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J. M., & Gambetta, J. M.
- Affiliations
- IBM (United States) (US)
- Corresponding author
- Kandala, Abhinav
- Mezzacapo, Antonio
- ORCID
- Venue
- Nature
- Published
- 2017-09
- Volume
- 549
- Issue
- 7671
- Pages
- 242-246
- ISSN
- 0028-0836 (ISSN-L)
- 1476-4687
- OpenAlex
- W2755255888
- Cited by
- 2,982
- References
- 43
- Citations by year
- 2026: 334 · 2025: 423 · 2024: 439 · 2023: 419 · 2022: 386 · 2021: 405 · 2020: 284 · 2019: 173 · 2018: 101 · 2017: 15 · 2014: 1
- FWCI
- 93.44
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Nature (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Keywords
- variational quantum eigensolver, quantum simulation, ground state energy, small molecules, lithium hydride, beryllium hydride, Heisenberg model, quantum magnetism, superconducting qubits, stochastic optimization, quantum chemistry, quantum error correction, noise modeling
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