Recent developments have shown the existence of quantum low-density parity check (qLDPC) codes with constant rate and linear distance. A natural question concerns the efficient decodability of these codes. In this paper, we present a linear time decoder for the recent quantum Tanner codes construction of asymptotically good qLDPC codes, which can correct all errors of weight up to a constant fraction of the blocklength. Our decoder is an iterative algorithm which searches for corrections within constant-sized regions. At each step, the corrections are found by reducing a locally defined and efficiently computable cost function which serves as a proxy for the weight of the remaining error.

We reconsider the black hole firewall puzzle, emphasizing that quantum error-correction, computational complexity, and pseudorandomness are crucial concepts for understanding the black hole interior. We assume that the Hawking radiation emitted by an old black hole is pseudorandom, meaning that it cannot be distinguished from a perfectly thermal state by any efficient quantum computation acting on the radiation alone. We then infer the existence of a subspace of the radiation system which we interpret as an encoding of the black hole interior. This encoded interior is entangled with the late outgoing Hawking quanta emitted by the old black hole, and is inaccessible to computationally bounded observers who are outside the black hole. Specifically, efficient operations acting on the radiation, those with quantum computational complexity polynomial in the entropy of the remaining black hole, commute with a complete set of logical operators acting on the encoded interior, up to corrections which are exponentially small in the entropy. Thus, under our pseudorandomness assumption, the black hole interior is well protected from exterior observers as long as the remaining black hole is macroscopic. On the other hand, if the radiation is not pseudorandom, an exterior observer may be able to create a firewall by applying a polynomial-time quantum computation to the radiation.

Multiple mobile device-based collaborative computing emerges with the rapid proliferation of various smart mobile devices such as smartphones and tablets, which provide always-on connectivity, information and communication. However, due to severe resource poverty and poor network connectivity, lots of traditional embedded electronic devices with attracting features cannot be incorporated into this computing paradigm conveniently. In this paper, an uneven-dual-core SoC, which integrates a CPU core and a MCU core on a single chip with multiple operating system support, is proposed to realize loosely-coupled multiple heterogeneous device collaboration. A network file system, MRFS (Multi-client Raindrop File System), and FAT-X (File Allocation Table eXtension) are also proposed to provide client-centric cross-device data consistency and virtual file access respectively. Comprehensive mobile services are enabled by offloading appropriate tasks from existing smart mobile devices to involved traditional embedded devices. The SoC is implemented onto a 16.65 mm2silicon with 65 nm CMOS technology. This paper also presents three typical applications to illustrate the universality and huge potential for innovative usage model of the proposed system.