Related papers: Verifying the Steane code with Quantomatic
Correcting errors in real time is essential for reliable large-scale quantum computations. Realizing this high-level function requires a system capable of several low-level primitives, including single-qubit and two-qubit operations,…
Quantum error correction (QEC) is essential for quantum computers to perform useful algorithms, but large-scale fault-tolerant computation remains out of reach due to demanding requirements on operation fidelity and the number of…
Monoidal algebraic structures consist of operations that can have multiple outputs as well as multiple inputs, which have applications in many areas including categorical algebra, programming language semantics, representation theory,…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
A common assumption in analyses of error thresholds and quantum computing in general is that one applies fault-tolerant quantum error correction (FTQEC) after every gate. This, however, is known not to always be optimal if the FTQEC…
Designing quantum processors is a complex task that demands advanced verification methods to ensure their correct functionality. However, traditional methods of comprehensively verifying quantum devices, such as quantum process tomography,…
Ancilla post-selection is a common means of achieving fault-tolerance in quantum error-correction. However, it can lead to additional data errors due to movement or wait operations. Alternatives to post-selection may achieve lower overall…
We introduce a Steane-like enlargement procedure for entanglement-assisted quantum error-correcting codes (EAQECCs) obtained by considering Euclidean inner product. We give formulae for the parameters of these enlarged codes and apply our…
Quantum error correcting code is a useful tool to combat noise in quantum computation. It is also an important ingredient in a number of unconditionally secure quantum key distribution schemes. Here, I am going to show that quantum code can…
Errors in quantum computers are of two kinds: sudden perturbations to isolated qubits, and slow random drifts of all the qubits. The latter may be reduced, but not eliminated, by means of symmetrization, namely by using many replicas of the…
Building reliable quantum computers requires protecting fragile quantum states from inevitable environmental noise and operational errors. While quantum error correction codes like the Steane $[\![7,1,3]\!]$ code provide elegant theoretical…
In this work we discuss the ability of different types of ancillas to control the decoherence of a qubit interacting with an environment. The error is introduced into the numerical simulation via a depolarizing isotropic channel. After the…
The quantum error correction theory is as a rule formulated in a rather convoluted way, in comparison to classical algebraic theory. This work revisits the error correction in a noisy quantum channel so as to make it intelligible to…
Formal verification of neural networks is an active topic of research, and recent advances have significantly increased the size of the networks that verification tools can handle. However, most methods are designed for verification of an…
Quantum error correction (QEC) is fundamental for suppressing noise in quantum hardware and enabling fault-tolerant quantum computation. In this paper, we propose an efficient verification framework for QEC programs. We define an assertion…
In quantum error correction using imperfect primitives, errors of high weight arising from a few faults are major concerns since they might not be correctable by the quantum error correcting code. Fortunately, some errors of different…
Quantum states can quickly decohere through interaction with the environment. Quantum error correction is a method for preserving coherence through active feedback. Quantum error correction encodes the quantum information into a logical…
Many-electron problems pose some of the greatest challenges in computational science, with important applications across many fields of modern science. Fermionic quantum Monte Carlo (QMC) methods are among the most powerful approaches to…
Quantum Error Correction (QEC) is essential for fault-tolerant quantum copmutation, and its implementation is a very sophisticated process involving both quantum and classical hardware. Formulating and verifying the decomposition of logical…
Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…