Intermediate scalings in holographic RG flows and conductivities

We construct numerically finite density domain-wall solutions which interpolate between two AdS 4 fixed points and exhibit an intermediate regime of hyperscaling violation, with or without Lifshitz scaling. Such RG flows can be realized in gravitational models containing a dilatonic scalar and a massive vector field with appropriate choices of the scalar potential and couplings. The infrared AdS 4 fixed point describes a new ground state for strongly coupled quantum systems realizing such scalings, thus avoiding the well-known extensive zero temperature entropy associated with AdS2×R2. We also examine the zero temperature behavior of the optical conductivity in these backgrounds and identify two scaling regimes before the UV CFT scaling is reached. The scaling of the conductivity is controlled by the emergent IR conformal symmetry at very low frequencies, and by the intermediate scaling regime at higher frequencies

Demonstration of Density Matrix Exponentiation Using a Superconducting Quantum Processor

Quantum computers hold the potential to outperform classical supercomputers at certain tasks. To implement algorithms on a quantum computer, programmers use conventional computers and hardware to create a set of classical control signals that implement a desired quantum algorithm. However, feeding the quantum information forward requires an inefficient conversion: extraction of quantum information, conversion to classical control signals, and reinjection of those signals into the system to implement quantum operations. Here, we demonstrate a more natively quantum strategy to programming quantum computers. Our approach uses the density matrix exponentiation (DME) protocol, a general technique for using a quantum state to enact a quantum operation. It can be thought of as a subroutine with which programmers can turn multiple copies of a quantum state into instructions for next steps in a quantum algorithm.We implement DME using two qubits in a superconducting quantum processor. Our implementation relies on a high-fidelity two-qubit gate and a novel technique called quantum measurement emulation to approximately reset a known quantum state. These developments enable us to demonstrate the DME protocol for the first time on a small-scale quantum processor and benchmark its performance.While DME was originally proposed in the context of a specific quantum machine-learning algorithm, it may also represent a fundamentally different approach to quantum programming. It allows the possibility of encoding quantum algorithms directly into quantum states and executing those algorithms on other quantum states, enabling a new class of efficient quantum algorithms