Kristan Temme

Quantum optimization using variational algorithms on near-term quantum devices

  1. Nikolaj Moll,
  2. Panagiotis Barkoutsos,
  3. Lev S. Bishop,
  4. Jerry M. Chow,
  5. Andrew Cross,
  6. Daniel J. Egger,
  7. Stefan Filipp,
  8. Andreas Fuhrer,
  9. Jay M. Gambetta,
  10. Marc Ganzhorn,
  11. Abhinav Kandala,
  12. Antonio Mezzacapo,
  13. Peter Müller,
  14. Walter Riess,
  15. Gian Salis,
  16. John Smolin,
  17. Ivano Tavernelli,
  18. and Kristan Temme
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits.
Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed. With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupled-cluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits.
arxiv pdf

Hardware-efficient Quantum Optimizer for Small Molecules and Quantum Magnets

  1. Abhinav Kandala,
  2. Antonio Mezzacapo,
  3. Kristan Temme,
  4. Maika Takita,
  5. Jerry M. Chow,
  6. and Jay M. Gambetta
Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance
computing resources. Finding exact numerical solutions to these interacting fermion problems has exponential cost, while Monte Carlo methods are plagued by the fermionic sign problem. These limitations of classical computational methods have made even few-atom molecular structures problems of practical interest for medium-sized quantum computers. Yet, thus far experimental implementations have been restricted to molecules involving only Period I elements. Here, we demonstrate the experimental optimization of up to six-qubit Hamiltonian problems with over a hundred Pauli terms, determining the ground state energy for molecules of increasing size, up to BeH2. This is enabled by a hardware-efficient quantum optimizer with trial states specifically tailored to the available interactions in our quantum processor, combined with a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. We further demonstrate the flexibility of our approach by applying the technique to a problem of quantum magnetism. Across all studied problems, we find agreement between experiment and numerical simulations with a noisy model of the device. These results help elucidate the requirements for scaling the method to larger systems, and aim at bridging the gap between problems at the forefront of high-performance computing and their implementation on quantum hardware.
arxiv pdf