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.

Dynamic nuclear polarization (DNP), a means of transferring spin polarization from electrons to nuclei, can enhance the nuclear spin polarization (hence the NMR sensitivity) in bulk materials at most 660 times for 1 H spins, using electron spins in thermal equilibrium as polarizing agents. By using electron spins in photo-excited triplet states instead, DNP can overcome the above limit. We demonstrate a 1 H spin polarization of 34%, which gives an enhancement factor of 250,000 in 0.40 T, while maintaining a bulk sample (∼0.6 mg, ∼0.7 × 0.7 × 1 mm 3 ) containing >10 19 1 H spins at room temperature. Room temperature hyperpolarization achieved with DNP using photo-excited triplet electrons has potentials to be applied to a wide range of fields, including NMR spectroscopy and MRI as well as fundamental physics.N uclear spin is a useful probe for noninvasive analysis of bulk materials such as chemical compounds, industrial products, biological samples, and human bodies. The signal from a spin ensemble is proportional to the polarization P. In thermal equilibrium in a magnetic field B at temperature T, P for spin-1/2 particles is given bywhere Z is the Planck constant, k is the Boltzmann constant, and γ is the gyromagnetic ratio. In a magnetic field of several teslas at room temperature, the nuclear spin energy ZγB=2 is much smaller than the thermal energy kT, so nuclear spins are only slightly polarized. This is the major reason why the sensitivity of NMR spectroscopy and MRI is so low. Dynamic nuclear polarization (DNP) is a means of transferring spin polarization from electrons to nuclei. As a method to enhance the bulk nuclear polarization, DNP has been successfully applied to areas ranging from fundamental physics (1-3) to materials science (4), biology (5-7), and medical science (8), since it was discovered 60 y ago (9, 10). As long as electron spins in thermal equilibrium are used as polarizing agents, the upper limit of the polarization enhancement is 660 for 1 H spins and cryogenic temperatures of around 4.2 K are required for hyperpolarization in the order of 10% even in the strong magnetic fields used for NMR. Hyperpolarization at room temperature will simplify instrumentation and expand the sample variety to materials that prefer ambient temperatures. Other techniques such as optical pumping in semiconductors (11) and the Haupt effect (12) also require cryogenic temperature for increasing bulk polarization beyond 10%.One solution for overcoming the upper limit of the enhancement factor of the conventional DNP, γ e =γ n , is to use nonthermalized electron spins as polarizing agents. A number of organic molecules have photo-excited triplet states where, due to the selection rule in the intersystem crossing from the excited singlet state to the triplet state, the population distribution is highly biased. DNP using electron spins in the photo-excited triplet state can achieve hyperpolarization independent of the magnetic field strength and temperature (13)(14)(15)(16). In this work, we have achieved a bulk hy...

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.