Related papers: Quantum Error Correction via Convex Optimization
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming…
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…
Multi-valued quantum systems can store more information than binary ones for a given number of quantum states. For reliable operation of multi-valued quantum systems, error correction is mandated. In this paper, we propose a 5-qutrit…
The rotation of trapped molecules offers a promising platform for quantum technologies and quantum information processing. In parallel, quantum error correction codes that can protect quantum information encoded in rotational states of a…
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
We formulate learning of a binary autoencoder as a biconvex optimization problem which learns from the pairwise correlations between encoded and decoded bits. Among all possible algorithms that use this information, ours finds the…
Why do neurons encode information the way they do? Normative answers to this question model neural activity as the solution to an optimisation problem; for example, the celebrated efficient coding hypothesis frames neural activity as the…
Quantum error correcting codes have been developed to protect a quantum computer from decoherence due to a noisy environment. In this paper, we present two methods for optimizing the physical implementation of such error correction schemes.…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical…
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 present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by…
The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. There is a considerable body of mathematical…
Quantum error correction is one of the fundamental building blocks of digital quantum computation. The Quantum Lego formalism has introduced a systematic way of constructing new stabilizer codes out of basic lego-like building blocks, which…
Constructing an efficient and robust quantum memory is central to the challenge of engineering feasible quantum computer architectures. Quantum error correction codes can solve this problem in theory, but without careful design it can…
An error correcting mechanism is proposed in the context of the Quantum Interference Computer approach
The components of a quantum computer are quantum subsystems which have a complex internal structure. This structure is determined by short-range interactions which are appropriately described in terms of local gauge fields of the first…
The standard quantum error correction protocols use projective measurements to extract the error syndromes from the encoded states. We consider the more general scenario of weak measurements, where only partial information about the error…
Quantum error correction (QEC) codes are traditionally defined and searched for without specifying the manner in which its syndrome extraction circuits are executed using elementary gates and measurements. We show how morphing circuits…