Quantum machine learning

Abstract: Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the physical dimension grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state preparation based on ansatze and classical optimization. We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry--calculating the ground-state molecular energy for He-H(+). The proposed approach drastically reduces the coherence time requirements, enhancing the potential of quantum resources available today and in the near future.

Abstract: Recent progress implies that a crossover between machine learning and quantum information processing benefits both fields. Traditional machine learning has dramatically improved the benchmarking an ...

Abstract: The ground-state energy of small molecules is determined efficiently using six qubits of a superconducting quantum processor. Quantum simulation is currently the most promising application of quantum computers. However, only a few quantum simulations of very small systems have been performed experimentally. Here, researchers from IBM present quantum simulations of larger systems using a variational quantum eigenvalue solver (or eigensolver), a previously suggested method for quantum optimization. They perform quantum chemical calculations of LiH and BeH2 and an energy minimization procedure on a four-qubit Heisenberg model. Their application of the variational quantum eigensolver is hardware-efficient, which means that it is optimized on the given architecture. Noise is a big problem in this implementation, but quantum error correction could eventually help this experimental set-up to yield a quantum simulation of chemically interesting systems on a quantum computer. 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 computers1. 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 helium2,3,4,5,6,7,8. 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 Hamiltonians9 and a robust stochastic optimization routine10. 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.

Abstract: We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit that implements the algorithm consists of unitary gates whose locality is at most the locality of the objective function whose optimum is sought. The depth of the circuit grows linearly with p times (at worst) the number of constraints. If p is fixed, that is, independent of the input size, the algorithm makes use of efficient classical preprocessing. If p grows with the input size a different strategy is proposed. We study the algorithm as applied to MaxCut on regular graphs and analyze its performance on 2-regular and 3-regular graphs for fixed p. For p = 1, on 3-regular graphs the quantum algorithm always finds a cut that is at least 0.6924 times the size of the optimal cut.