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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,…
The fragile nature of quantum information limits our ability to construct large quantities of quantum bits suitable for quantum computing. An important goal, therefore, is to minimize the amount of resources required to implement quantum…
Quantum teleportation is a foundational protocol for sending quantum information through entanglement distribution and classical communication. Assuming ideal classical communication, the reliability of quantum teleportation is limited by…
A classical coding across a block of logical qubits is presented. We characterize subgroups of the product stabilizer group on a block of logical qubits corresponding to dual codes of classical error correcting codes. We prove conditions on…
We propose a method for universal fault-tolerant quantum computation using concatenated quantum error correcting codes. Namely, other than computational basis state preparation as required by the DiVincenzo criteria [1], our scheme requires…
The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this…
The purpose of this paper is to explore the applications of quantum computing to energy systems optimization problems and discuss some of the challenges faced by quantum computers with techniques to overcome them. The basic concepts…
Quantum simulation of molecular electronic structure is one of the most promising applications of quantum computing. However, achieving chemically accurate predictions for strongly correlated systems requires quantum phase estimation (QPE)…
In this paper, we use open-source tools to perform quantum resource estimation to assess the requirements for industry-relevant quantum computation. Our analysis uses the problem of industrial shift scheduling in manufacturing and the…
In the shallow sub-threshold regime, fault-tolerant quantum computation requires a tremendous amount of qubits. In this paper, we study the error correction in the deep sub-threshold regime. We estimate the physical error rate for achieving…
The purpose of this little survey is to give a simple description of the main approaches to quantum error correction and quantum fault-tolerance. Our goal is to convey the necessary intuitions both for the problems and their solutions in…
We identify optimal quantum error correction codes for situations that do not admit perfect correction. We provide analytic n-qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant…
Active quantum error correction is a central ingredient to achieve robust quantum processors. In this paper we investigate the potential of quantum machine learning for quantum error correction in a quantum memory. Specifically, we…
We analyze the effect of a quantum error correcting code on the entanglement of encoded logical qubits in the presence of a dephasing interaction with a correlated environment. Such correlated reservoir introduces entanglement between…
We estimate the resource requirements for the quantum simulation of the ground state energy of the one dimensional quantum transverse Ising model (TIM), based on the surface code implementation of a fault tolerant quantum computer. The…
If a quantum computer is stabilized by fault-tolerant quantum error correction (QEC), then most of its resources (qubits and operations) are dedicated to the extraction of error information. Analysis of this process leads to a set of…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…
Recent progress in quantum information has led to the start of several large national and industrial efforts to build a quantum computer. Researchers are now working to overcome many scientific and technological challenges. The program's…
Qubit loss and gate failure are significant problems for the development of scalable quantum computing. Recently various schemes have been proposed for tolerating qubit loss and gate failure. These include schemes based on cluster and…