Dave Wecker

Gate-count estimates for performing quantum chemistry on small quantum computers

As quantum computing technology improves and quantum computers with a small but non-trivial number of N > 100 qubits appear feasible in the near future the question of possible applications of small quantum computers gains importance. One frequently mentioned application is Feynmans original proposal of simulating quantum systems, and in particular the electronic structure of molecules and materials. In this paper, we analyze the computational requirements for one of the standard algorithms to perform quantum chemistry on a quantum computer. We focus on the quantum resources required to find the ground state of a molecule twice as large as what current classical computers can solve exactly. We find that while such a problem requires about a ten-fold increase in the number of qubits over current technology, the required increase in the number of gates that can be coherently executed is many orders of magnitude larger. This suggests that for quantum computation to become useful for quantum chemistry problems, drastic algorithmic improvements will be needed.

Elucidating reaction mechanisms on quantum computers

Significance Our work addresses the question of compelling killer applications for quantum computers. Although quantum chemistry is a strong candidate, the lack of details of how quantum computers can be used for specific applications makes it difficult to assess whether they will be able to deliver on the promises. Here, we show how quantum computers can be used to elucidate the reaction mechanism for biological nitrogen fixation in nitrogenase, by augmenting classical calculation of reaction mechanisms with reliable estimates for relative and activation energies that are beyond the reach of traditional methods. We also show that, taking into account overheads of quantum error correction and gate synthesis, a modular architecture for parallel quantum computers can perform such calculations with components of reasonable complexity. With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.

Hybrid Quantum-Classical Approach to Correlated Materials

Recent improvements in control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure problems and idealized model Hamiltonians, the highly relevant problem of directly solving a complex correlated material appears to require a prohibitive amount of resources. Here, we show that by using a hybrid quantum-classical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer. In our approach, the quantum computer solves a small effective quantum impurity problem that is self-consistently determined via a feedback loop between the quantum and classical computation. Use of a quantum computer enables much larger and more accurate simulations than with any known classical algorithm, and will allow many open questions in quantum materials to be resolved once a small quantum computer with around one hundred logical qubits becomes available.

Progress towards practical quantum variational algorithms

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.

Solving strongly correlated electron models on a quantum computer

Researchers propose a step-by-step quantum recipe to find the ground state of models of strongly interacting electrons.

TRAINING A QUANTUM OPTIMIZER

We study a variant of the quantum approximate optimization algorithm [ E. Farhi, J. Goldstone, and S. Gutmann, arXiv:1411.4028] with slightly different parametrization and different objective: rather than looking for a state which approximately solves an optimization problem, our goal is to find a quantum algorithm that, given an instance of MAX-2-SAT, will produce a state with high overlap with the optimal state. Using a machine learning approach, we chose a “training set” of instances and optimized the parameters to produce large overlap for the training set. We then tested these optimized parameters on a larger instance set. As a training set, we used a subset of the hard instances studied by E. Crosson, E. Farhi, C. Yen-Yu Lin, H.-H. Lin, and P. Shor (CFLLS) [arXiv:1401.7320]. When tested on the full set, the parameters that we find produce significantly larger overlap than the optimized annealing times of CFLLS. Testing on other random instances from 20 to 28 bits continues to show improvement over annealing, with the improvement being most notable on the hardest instances. Further tests on instances of MAX-3-SAT also showed improvement on the hardest instances. This algorithm may be a possible application for near-term quantum computers with limited coherence times.

Technology and data-intensive science in the beginning of the 21st century.

This article is a summary of the technology issues and challenges of data-intensive science and cloud computing as discussed in the Data-Intensive Science (DIS) workshop in Seattle, September 19-20, 2010.

Design automation for quantum architectures

We survey recent strides made towards building a software framework that is capable of compiling quantum algorithms from a high-level description down to physical gates that can be implemented on a fault-tolerant quantum computer. We discuss why compilation and design automation tools such as the ones in our framework are key for tackling the grand challenge of building a scalable quantum computer. We then describe specialized libraries that have been developed using the LIQUi|〉 programming language. This includes reversible circuits for arithmetic as well as new, truly quantum approaches that rely on quantum computer architectures that allow the probabilistic execution of gates, a model that can reduce time and space overheads in some cases. We highlight why these libraries are useful for the implementation of many quantum algorithms. Finally, we survey the tool Revs that facilitate resource efficient compilation of higher-level irreversible programs into lower-level reversible circuits while trying to optimize the memory footprint of the resulting reversible networks. This is motivated by the limited availability of qubits for the foreseeable future.