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We demonstrate, both analytically and experimentally, the usefulness of non-Markovianity for preserving correlations and coherence in quantum systems. For this, we consider a broad class of qubit evolutions, having a decoherence matrix separated from zero for large times. While any such Markovian evolution leads to an exponential loss of correlations, non-Markovianity can help to preserve correlations even in the limit t → ∞. In fact, under general assumptions, eternally non-Markovian evolution naturally emerges as the one that allows for optimal preservation of quantum correlations. For covariant qubit evolutions, we also show that non-Markovianity can be used to preserve quantum coherence at all times, which is an important resource for quantum metrology. We explicitly demonstrate this effect experimentally with linear optics, by implementing the optimal non-Markovian quantum evolution.

The Green’s function has been an indispensable tool to study many-body systems that remain one of the biggest challenges in modern quantum physics for decades. The complicated calculation of the Green’s function impedes the research of many-body systems. The appearance of the noisy intermediate-scale quantum devices and quantum–classical hybrid algorithm inspire a new method to calculate the Green’s function. Here we design a programmable quantum circuit for photons with utilizing the polarization and the path degrees of freedom to construct a highly-precise variational quantum state of a photon, and first report the experimental realization for calculating the Green’s function of the two-site fermionic Hubbard model, a prototypical model for strongly-correlated materials, in photonic systems. We run the variational quantum eigensolver to obtain the ground state and excited states of the model, and then evaluate the transition amplitudes among the eigenstates. The experimental results present the spectral function of the Green’s function, which agrees well with exact results. Our demonstration provides the further possibility of the photonic system in quantum simulation and applications in solving complicated problems in many-body systems, biological science and so on.

An experiment based on a trapped ytterbium ion validates the inertial theorem for the SU (2) algebra. The qubit is encoded within the hyperfine states of the atom and controlled by RF fields. The inertial theorem generates analytical solutions for non-adiabatically driven systems that are ‘accelerated’ slowly, bridging the gap between the sudden and adiabatic limits. These solutions are shown to be stable to small deviations, both experimentally and theoretically. By encoding a two-level system into hyperphine structure of a trapped ytterbium, we explore the high control over the system dynamics in order to validate range of applicability of the inertial theorem in our system. For large deviations from the inertial condition, the experimental results show that the phase remains accurate while the amplitude diverges, so the inertial theorem has good robustness in the phase estimate. As a result, we experimentally showed that the inertial solutions pave the way to rapid quantum control of closed, as well as open quantum systems.

Full quantum state tomography (FQST) plays a unique role in the estimation of the state of a quantum system without a priori knowledge or assumptions. Unfortunately, since FQST requires informationally (over)complete measurements, both the number of measurement bases and the computational complexity of data processing suffer an exponential growth with the size of the quantum system. A 14-qubit entangled state has already been experimentally prepared in an ion trap, and the data processing capability for FQST of a 14-qubit state seems to be far away from practical applications. In this paper, the computational capability of FQST is pushed forward to reconstruct a 14-qubit state with a run time of only 3.35 hours using the linear regression estimation (LRE) algorithm, even when informationally overcomplete Pauli measurements are employed. The computational complexity of the LRE algorithm is first reduced from ∼10 ^19 to ∼10 ^15 for a 14-qubit state, by dropping all the zero elements, and its computational efficiency is further sped up by fully exploiting the parallelism of the LRE algorithm with parallel Graphic Processing Unit (GPU) programming. Our result demonstrates the effectiveness of using parallel computation to speed up the postprocessing for FQST, and can play an important role in quantum information technologies with large quantum systems.