We introduce Qulacs, a fast simulator for quantum circuits intended for research purpose. To explore the possibilities of a near-term intermediate-scale quantum algorithm and long-term fault-tolerant quantum computing, a fast and versatile quantum circuit simulator is needed. Herein we show the main concepts of Qulacs, explain how to use its features via examples, and demonstrate its performance with numerical benchmarks.

Excited states of molecules lie in the heart of photochemistry and chemical reactions. The recent development in quantum computational chemistry leads to inventions of a variety of algorithms which calculate the excited states of molecules on near-term quantum computers, but they require more computational burdens than the algorithms for the ground states. In this study, we propose a scheme of supervised quantum machine learning which predicts excited state properties of molecules only from its ground state wavefunction and results in reducing the computational cost for calculating the excited states. Our model is comprised of a quantum reservoir and a classical machine learning unit which processes the results of measurements of single-qubit Pauli operators. The quantum reservoir effectively transforms the single-qubit operators into complicated multi-qubit ones which contain essential information of the system, so that the classical machine learning unit may decode them appropriately. The number of runs for quantum computers is saved by training only the classical machine learning unit and the whole model requires modest resources of quantum hardwares which may be implemented in current experiments. We illustrate the predictive ability of our model by numerical simulations for small molecules with and without including noise inevitable in near-term quantum computers. The results show that our scheme well reproduces the first and second excitation energies as well as the transition dipole moment between the ground states and excited states only from the ground state as an input. Our contribution will enhance applications of quantum computers in the study of quantum chemistry and quantum materials.

Quantum reservoir computing provides a framework for exploiting the natural dynamics of quantum systems as a computational resource. It can implement real-time signal processing and solve temporal machine learning problems in general, which requires memory and nonlinear mapping of the recent input stream using the quantum dynamics in computational supremacy region, where the classical simulation of the system is intractable. A nuclear magnetic resonance spin-ensemble system is one of the realistic candidates for such physical implementations, which is currently available in laboratories. In this paper, considering these realistic experimental constraints for implementing the framework, we introduce a scheme, which we call a spatial multiplexing technique, to effectively boost the computational power of the platform. This technique exploits disjoint dynamics, which originate from multiple different quantum systems driven by common input streams in parallel. Accordingly, unlike designing a single large quantum system to increase the number of qubits for computational nodes, it is possible to prepare a huge number of qubits from multiple but small quantum systems, which are operationally easy to handle in laboratory experiments. We numerically demonstrate the effectiveness of the technique using several benchmark tasks and quantitatively investigate its specifications, range of validity, and limitations in detail.

We propose a classical-quantum hybrid algorithm for machine learning on near-term quantum processors, which we call quantum circuit learning. A quantum circuit driven by our framework learns a given task by tuning parameters implemented on it. The iterative optimization of the parameters allows us to circumvent the high-depth circuit. Theoretical investigation shows that a quantum circuit can approximate nonlinear functions, which is further confirmed by numerical simulations. Hybridizing a low-depth quantum circuit and a classical computer for machine learning, the proposed framework paves the way toward applications of near-term quantum devices for quantum machine learning.

The quantum computer has an amazing potential of fast information processing. However, the realization of a digital quantum computer is still a challenging problem requiring highly accurate controls and key application strategies. Here we propose a platform, quantum reservoir computing, to solve these issues successfully by exploiting the natural quantum dynamics of ensemble systems, which are ubiquitous in laboratories nowadays, for machine learning. This framework enables ensemble quantum systems to universally emulate nonlinear dynamical systems including classical chaos. A number of numerical experiments show that quantum systems consisting of 5–7 qubits possess computational capabilities comparable to conventional recurrent neural networks of 100–500 nodes. This discovery opens up a paradigm for information processing with artificial intelligence powered by quantum physics.