Todd A. Brun

Quantum error correction

Quantum computers are able to efficiently perform tasks such as solving various optimization problems and simulating physical systems; problems that are believed to be impossible to solve in a reasonable time with classical computers. The road towards building a large-scale quantum computer is, however, hindered by many obstacles, the most significant being the fragile nature of quantum systems. The delicacy of quantum information makes its storage and manipulation much more challenging than classical information. This, as well as the inability to completely isolate the building-blocks of the quantum computer from its surroundings, introduce errors, which, if are not accounted for, make the computation unfeasible. In this report, we will survey the field of Quantum Error Correction (QEC). We will begin by discussing in more detail why is QEC necessary and what has to be accomplished. We will present a few examples of error correcting codes such as the surface code [1] and discuss their implementation in current state-of-the-art experiments [2]. Finally we will explain the Quantum Threshold Theorem [3] and how it makes large-scale quantum computing possible. The goal of this paper is to introduce the concepts of QEC and several of its most promising applications.

Quantum Error Correction: List of contributors

Quantum computers are able to efficiently perform tasks such as solving various optimization problems and simulating physical systems; problems that are believed to be impossible to solve in a reasonable time with classical computers. The road towards building a large-scale quantum computer is, however, hindered by many obstacles, the most significant being the fragile nature of quantum systems. The delicacy of quantum information makes its storage and manipulation much more challenging than classical information. This, as well as the inability to completely isolate the building-blocks of the quantum computer from its surroundings, introduce errors, which, if are not accounted for, make the computation unfeasible. In this report, we will survey the field of Quantum Error Correction (QEC). We will begin by discussing in more detail why is QEC necessary and what has to be accomplished. We will present a few examples of error correcting codes such as the surface code [1] and discuss their implementation in current state-of-the-art experiments [2]. Finally we will explain the Quantum Threshold Theorem [3] and how it makes large-scale quantum computing possible. The goal of this paper is to introduce the concepts of QEC and several of its most promising applications.

Quantum Error Correction: Alternative quantum computation approaches

Quantum computers are able to efficiently perform tasks such as solving various optimization problems and simulating physical systems; problems that are believed to be impossible to solve in a reasonable time with classical computers. The road towards building a large-scale quantum computer is, however, hindered by many obstacles, the most significant being the fragile nature of quantum systems. The delicacy of quantum information makes its storage and manipulation much more challenging than classical information. This, as well as the inability to completely isolate the building-blocks of the quantum computer from its surroundings, introduce errors, which, if are not accounted for, make the computation unfeasible. In this report, we will survey the field of Quantum Error Correction (QEC). We will begin by discussing in more detail why is QEC necessary and what has to be accomplished. We will present a few examples of error correcting codes such as the surface code [1] and discuss their implementation in current state-of-the-art experiments [2]. Finally we will explain the Quantum Threshold Theorem [3] and how it makes large-scale quantum computing possible. The goal of this paper is to introduce the concepts of QEC and several of its most promising applications.

Quantum Error Correction: Advanced quantum codes

Quantum computers are able to efficiently perform tasks such as solving various optimization problems and simulating physical systems; problems that are believed to be impossible to solve in a reasonable time with classical computers. The road towards building a large-scale quantum computer is, however, hindered by many obstacles, the most significant being the fragile nature of quantum systems. The delicacy of quantum information makes its storage and manipulation much more challenging than classical information. This, as well as the inability to completely isolate the building-blocks of the quantum computer from its surroundings, introduce errors, which, if are not accounted for, make the computation unfeasible. In this report, we will survey the field of Quantum Error Correction (QEC). We will begin by discussing in more detail why is QEC necessary and what has to be accomplished. We will present a few examples of error correcting codes such as the surface code [1] and discuss their implementation in current state-of-the-art experiments [2]. Finally we will explain the Quantum Threshold Theorem [3] and how it makes large-scale quantum computing possible. The goal of this paper is to introduce the concepts of QEC and several of its most promising applications.

Quantum Error Correction: Critical evaluation of fault tolerance

Quantum computers are able to efficiently perform tasks such as solving various optimization problems and simulating physical systems; problems that are believed to be impossible to solve in a reasonable time with classical computers. The road towards building a large-scale quantum computer is, however, hindered by many obstacles, the most significant being the fragile nature of quantum systems. The delicacy of quantum information makes its storage and manipulation much more challenging than classical information. This, as well as the inability to completely isolate the building-blocks of the quantum computer from its surroundings, introduce errors, which, if are not accounted for, make the computation unfeasible. In this report, we will survey the field of Quantum Error Correction (QEC). We will begin by discussing in more detail why is QEC necessary and what has to be accomplished. We will present a few examples of error correcting codes such as the surface code [1] and discuss their implementation in current state-of-the-art experiments [2]. Finally we will explain the Quantum Threshold Theorem [3] and how it makes large-scale quantum computing possible. The goal of this paper is to introduce the concepts of QEC and several of its most promising applications.

Quantum Error Correction: Advanced dynamical decoupling

Quantum computers are able to efficiently perform tasks such as solving various optimization problems and simulating physical systems; problems that are believed to be impossible to solve in a reasonable time with classical computers. The road towards building a large-scale quantum computer is, however, hindered by many obstacles, the most significant being the fragile nature of quantum systems. The delicacy of quantum information makes its storage and manipulation much more challenging than classical information. This, as well as the inability to completely isolate the building-blocks of the quantum computer from its surroundings, introduce errors, which, if are not accounted for, make the computation unfeasible. In this report, we will survey the field of Quantum Error Correction (QEC). We will begin by discussing in more detail why is QEC necessary and what has to be accomplished. We will present a few examples of error correcting codes such as the surface code [1] and discuss their implementation in current state-of-the-art experiments [2]. Finally we will explain the Quantum Threshold Theorem [3] and how it makes large-scale quantum computing possible. The goal of this paper is to introduce the concepts of QEC and several of its most promising applications.

Quantum Error Correction: Background

Quantum computers are able to efficiently perform tasks such as solving various optimization problems and simulating physical systems; problems that are believed to be impossible to solve in a reasonable time with classical computers. The road towards building a large-scale quantum computer is, however, hindered by many obstacles, the most significant being the fragile nature of quantum systems. The delicacy of quantum information makes its storage and manipulation much more challenging than classical information. This, as well as the inability to completely isolate the building-blocks of the quantum computer from its surroundings, introduce errors, which, if are not accounted for, make the computation unfeasible. In this report, we will survey the field of Quantum Error Correction (QEC). We will begin by discussing in more detail why is QEC necessary and what has to be accomplished. We will present a few examples of error correcting codes such as the surface code [1] and discuss their implementation in current state-of-the-art experiments [2]. Finally we will explain the Quantum Threshold Theorem [3] and how it makes large-scale quantum computing possible. The goal of this paper is to introduce the concepts of QEC and several of its most promising applications.

Quantum Error Correction: Generalized approaches to quantum error correction

Quantum computers are able to efficiently perform tasks such as solving various optimization problems and simulating physical systems; problems that are believed to be impossible to solve in a reasonable time with classical computers. The road towards building a large-scale quantum computer is, however, hindered by many obstacles, the most significant being the fragile nature of quantum systems. The delicacy of quantum information makes its storage and manipulation much more challenging than classical information. This, as well as the inability to completely isolate the building-blocks of the quantum computer from its surroundings, introduce errors, which, if are not accounted for, make the computation unfeasible. In this report, we will survey the field of Quantum Error Correction (QEC). We will begin by discussing in more detail why is QEC necessary and what has to be accomplished. We will present a few examples of error correcting codes such as the surface code [1] and discuss their implementation in current state-of-the-art experiments [2]. Finally we will explain the Quantum Threshold Theorem [3] and how it makes large-scale quantum computing possible. The goal of this paper is to introduce the concepts of QEC and several of its most promising applications.

Quantum Error Correction: Topological methods

Quantum computers are able to efficiently perform tasks such as solving various optimization problems and simulating physical systems; problems that are believed to be impossible to solve in a reasonable time with classical computers. The road towards building a large-scale quantum computer is, however, hindered by many obstacles, the most significant being the fragile nature of quantum systems. The delicacy of quantum information makes its storage and manipulation much more challenging than classical information. This, as well as the inability to completely isolate the building-blocks of the quantum computer from its surroundings, introduce errors, which, if are not accounted for, make the computation unfeasible. In this report, we will survey the field of Quantum Error Correction (QEC). We will begin by discussing in more detail why is QEC necessary and what has to be accomplished. We will present a few examples of error correcting codes such as the surface code [1] and discuss their implementation in current state-of-the-art experiments [2]. Finally we will explain the Quantum Threshold Theorem [3] and how it makes large-scale quantum computing possible. The goal of this paper is to introduce the concepts of QEC and several of its most promising applications.

Quantum Error Correction: Applications and implementations

Quantum computers are able to efficiently perform tasks such as solving various optimization problems and simulating physical systems; problems that are believed to be impossible to solve in a reasonable time with classical computers. The road towards building a large-scale quantum computer is, however, hindered by many obstacles, the most significant being the fragile nature of quantum systems. The delicacy of quantum information makes its storage and manipulation much more challenging than classical information. This, as well as the inability to completely isolate the building-blocks of the quantum computer from its surroundings, introduce errors, which, if are not accounted for, make the computation unfeasible. In this report, we will survey the field of Quantum Error Correction (QEC). We will begin by discussing in more detail why is QEC necessary and what has to be accomplished. We will present a few examples of error correcting codes such as the surface code [1] and discuss their implementation in current state-of-the-art experiments [2]. Finally we will explain the Quantum Threshold Theorem [3] and how it makes large-scale quantum computing possible. The goal of this paper is to introduce the concepts of QEC and several of its most promising applications.