Noise that exhibits significant temporal and spatial correlations across multiple qubits can be especially harmful to both fault-tolerant quantum computation and quantum-enhanced metrology. However, a complete spectral characterization of the noise environment of even a two-qubit system has not been reported thus far. We propose and experimentally demonstrate a protocol for two-qubit dephasing noise spectroscopy based on continuous-control modulation. By combining ideas from spin-locking relaxometry with a statistically motivated robust estimation approach, our protocol allows for the simultaneous reconstruction of all the single-qubit and two-qubit cross-correlation spectra, including access to their distinctive nonclassical features. Only single-qubit control manipulations and state-tomography measurements are employed, with no need for entangled-state preparation or readout of two-qubit observables. While our experimental demonstration uses two superconducting qubits coupled to a shared, colored engineered noise source, our methodology is portable to a variety of dephasing-dominated qubit architectures. By pushing quantum noise spectroscopy beyond the single-qubit setting, our work heralds the characterization of spatiotemporal correlations in both engineered and naturally occurring noise environments.

Matrix product states form a powerful ansatz for the simulation of a wide range of one-dimensional quantum systems that are in a pure state. Their power stems from the fact that they faithfully approximate states with a low amount of entanglement, the “area law.” However, in order to accurately capture the physics of realistic systems, one generally needs to apply a mixed-state description. In this work, we establish the mixed-state analog of this characterization. We show that one-dimensional mixed states with a low amount of entanglement, quantified by the entanglement of purification, can be efficiently approximated by matrix product density operators.

The Lieb-Robinson (LR) bound rigorously shows that in quantum systems with short-range interactions, the maximum amount of information that travels beyond an effective “light cone” decays exponentially with distance from the light-cone front, which expands at finite velocity. Despite being a fundamental result, existing bounds are often extremely loose, limiting their applications. We introduce a method that dramatically and qualitatively improves LR bounds in models with finite-range interactions. Most prominently, in systems with a large local Hilbert space dimension $D$, our method gives a LR velocity that grows much slower than previous bounds with $D$ as $D\to \mathrm{\infty }$. For example, in the Heisenberg model with spin $S$, we find $v\le \mathrm{const}$. compared to the previous $v\propto S$, which diverges at large $S$, and in multiorbital Hubbard models with $N$ orbitals, we find $v\propto \sqrt{N}$ instead of previous $v\propto N$, and similarly in the $N$-state truncated Bose-Hubbard model and Wen’s quantum rotor model. Our bounds also scale qualitatively better in some systems when the spatial dimension or certain model parameters become large, for example in the $d$-dimensional quantum Ising model and perturbed toric code models. Even in spin-1/2 Ising and Fermi-Hubbard models, our method improves the LR velocity by an order of magnitude with typical model parameters, and significantly improves the LR bound at large distance and early time.

Conventional fault-tolerant quantum error-correction schemes require a number of extra qubits that grow linearly with the code’s maximum stabilizer generator weight. For some common distance-three codes, the recent “flag paradigm” uses just two extra qubits. Chamberland and Beverland [Quantum 2, 53 (2018)] provide a framework for flag error correction of arbitrary-distance codes. However, their construction requires conditions that only some code families are known to satisfy. We give a flag error-correction scheme that works for any stabilizer code, unconditionally. With fast qubit measurement and reset, it uses $\le d+1$ extra qubits for a distance-$d$ code.

Machine learning can help us in solving problems in the context of big-data analysis and classification, as well as in playing complex games such as Go. But can it also be used to find novel protocols and algorithms for applications such as large-scale quantum communication? Here we show that machine learning can be used to identify central quantum protocols, including teleportation, entanglement purification, and the quantum repeater. These schemes are of importance in long-distance quantum communication, and their discovery has shaped the field of quantum information processing. However, the usefulness of learning agents goes beyond the mere reproduction of known protocols; the same approach allows one to find improved solutions to long-distance communication problems, in particular when dealing with asymmetric situations where the channel noise and segment distance are nonuniform. Our findings are based on the use of projective simulation, a model of a learning agent that combines reinforcement learning and decision making in a physically motivated framework. The learning agent is provided with a universal gate set, and the desired task is specified via a reward scheme. From a technical perspective, the learning agent has to deal with stochastic environments and reactions. We utilize an idea reminiscent of hierarchical skill acquisition, where solutions to subproblems are learned and reused in the overall scheme. This is of particular importance in the development of long-distance communication schemes, and opens the way to using machine learning in the design and implementation of quantum networks.