Related papers: Linear Logic and Quantum Error Correcting Codes
In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local…
By taking into account the physical nature of quantum errors it is possible to improve the efficiency of quantum error correction. Here we consider an optimisation to conventional quantum error correction which involves exploiting…
I give an overview of the basic concepts behind quantum error correction and quantum fault tolerance. This includes the quantum error correction conditions, stabilizer codes, CSS codes, transversal gates, fault-tolerant error correction,…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
We generalize the construction of quantum error-correcting codes from GF(4)-linear codes by Calderbank et al. to p^m-state systems. Then we show how to determine the error from a syndrome. Finally we discuss a systematic construction of…
Given a logic presented in a sequent calculus, a natural question is that of equivalence of proofs: to determine whether two given proofs are equated by any denotational semantics, ie any categorical interpretation of the logic compatible…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…
This paper presents a simple notion of proof net for multiplicative linear logic with units. Cut elimination is direct and strongly normalising, in contrast to previous approaches which resorted to moving jumps (attachments) of par units…
Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…
We study cut elimination for a multifocused variant of full linear logic in the sequent calculus. The multifocused normal form of proofs yields problems that do not appear in a standard focused system, related to the constraints in grouping…
Motivated from the theory of quantum error correcting codes, we investigate a combinatorial problem that involves a symmetric $n$-vertices colourable graph and a group of operations (colouring rules) on the graph: find the minimum sequence…
It is possible to reduce some types of quantum computation errors by symmetrizing the quantum state of a redundant array. Various models are discussed.
Quantum metrology has been making amazing progress in the past decades. It is always in researchers' interest to search for new optimal states that improve parameter estimation. In this paper, we point out a connection between the code's…
We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph…
The potential of quantum computers to outperform classical ones in practically useful tasks remains challenging in the near term due to scaling limitations and high error rates of current quantum hardware. While quantum error correction…
Quantum error mitigation is expected to play a crucial role in the practical applications of quantum machines for the foreseeable future. Thus it is important to put the numerous quantum error mitigation schemes proposed under a coherent…
We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem…
We present a method for quantum error mitigation on partially error-corrected quantum computers - i.e., computers with some logical qubits and some noisy qubits. Our method is inspired by the error cancellation method and is implemented via…
It is shown that quantum tomography can detect and correct unlimited number of errors during the evaluation of quantum algorithms on quantum computer.
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…