Related papers: A Quantum Analog of Delsarte's Linear Programming …
Recent years have seen rapid development in the subject of quantum coding theory, with breakthroughs on many exciting classes of codes, including quantum LDPC codes, quantum locally testable codes, and quantum codes with interesting…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…
Traditional quantum error-correcting codes are designed for the depolarizing channel modeled by generalized Pauli errors occurring with equal probability. Amplitude damping channels model, in general, the decay process of a multilevel atom…
We propose a fault-tolerant quantum error correction architecture consisting of a linear array of emitters and delay lines. In our scheme, a resource state for fault-tolerant quantum computation is generated by letting the emitters interact…
Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and…
Unambiguous measurements play an important role in quantum information, with applications ranging from quantum key distribution to quantum state reconstruction. Recently, such measurements have also been used in quantum algorithms based on…
Quantum error correction will likely be essential for building a large-scale quantum computer, but it comes with significant requirements at the level of classical control software. In particular, a quantum error-correcting code must be…
The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
We present a universal framework for quantum error-correcting codes, i.e., the one that applies for the most general quantum error-correcting codes. This framework is established on the group algebra, an algebraic notation for the nice…
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…
Several upper bounds on the size of quantum codes are derived using the linear programming approach. These bounds are strengthened for the linear quantum codes.
The Heisenberg limit provides a quadratic improvement over the standard quantum limit, and is the maximum quantum advantage that quantum sensors could provide over classical methods. This limit remains elusive, however, because of the…
We present a novel strategy for obtaining optimal probe states and measurement schemes in a class of noiseless multiparameter estimation problems with symmetry among the generators. The key to the framework is the introduction of a set of…
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…
We take advantage of recent and new results on optimal quantization theory to improve the quadratic optimal quantization error bounds for backward stochastic differential equations (BSDE) and nonlinear filtering problems. For both problems,…
The problem of computing distances of error-correcting codes is fundamental in both the classical and quantum settings. While hardness for the classical version of these problems has been known for some time (in both the exact and…
We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The…
Linear Software Models enable rigorous linear algebraic procedures for modular design of classical software systems. These procedures apply a spectral approach to matrix representations - e.g. the Laplacian - of the software system. Recent…
The realization of scalable fault-tolerant quantum computing is expected to hinge on quantum error-correcting codes. In the quest for more efficient quantum fault tolerance, a critical code parameter is the weight of measurements that…