Error Correction (in quantum computing)

Extracted Attributes

• Field

  Quantum Computing

• Impact

  Essential for scaling quantum computers to millions of qubits

• Mechanism

  Uses syndrome measurements to diagnose and correct errors

• Primary Goal

  Protect quantum information from errors

• Key Challenge

  Managing errors without disrupting delicate quantum states

• Current Status

  Immense challenge and key area of research

• Secondary Goal

  Achieve fault-tolerant quantum computing

• Types of Errors Addressed

  Bit flips, phase flips, or both (corresponding to Pauli matrix operations)

• Requirement for Fault-Tolerance

  Prevents errors from spreading during correction or computation

• Analogy to Classical Error Correction

  Employs syndrome measurements

• Distinction from Classical Error Correction

  Overcomes no-cloning theorem; deals with qubits in superpositions

Timeline

• Peter Shor discovers the first quantum error correcting code. (Source: Wikipedia)

  1995

Quantum error correction

Quantum error correction (QEC) is a set of techniques used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is theorised as essential to achieve fault tolerant quantum computing that can reduce the effects of noise on stored quantum information, faulty quantum gates, faulty quantum state preparation, and faulty measurements. Effective quantum error correction would allow quantum computers with low qubit fidelity to execute algorithms of higher complexity or greater circuit depth. Classical error correction often employs redundancy. The simplest albeit inefficient approach is the repetition code. A repetition code stores the desired (logical) information as multiple copies, and—if these copies are later found to disagree due to errors introduced to the system—determines the most likely value for the original data by majority vote. For instance, suppose a bit is copied in a given state (for example, the state of "on" also known as one) three times. Suppose further that noise in the system introduces an error that corrupts the three-bit state so that one of the three copied bits becomes zero ("off") but the other two remain equal to one. Assuming that errors are independent and occur with some sufficiently low probability p, it is most likely that the error is a single-bit error and the intended message is three bits in the one state. It is possible that a double-bit error occurs and the transmitted message is equal to three zeros, but this outcome is less likely than the above outcome. In this example, the logical information is a single bit in the one state and the physical information are the three duplicate bits. Creating a physical state that represents the logical state is called encoding and determining which logical state is encoded in the physical state is called decoding. Similar to classical error correction (QEC), QEC codes do not always correctly decode logical qubits, but instead reduce the effect of noise on the logical state. Copying quantum information is not possible due to the no-cloning theorem. This theorem seems to present an obstacle to formulating a theory of quantum error correction. But it is possible to spread the (logical) information of one logical qubit onto a highly entangled state of several (physical) qubits. Peter Shor first discovered this method of formulating a quantum error correcting code by storing the information of one qubit onto a highly entangled state of nine qubits. In classical error correction, syndrome decoding is used to diagnose which error was the likely source of corruption on an encoded state. An error can then be reversed by applying a corrective operation based on the syndrome. Quantum error correction also employs syndrome measurements. It performs a multi-qubit measurement that does not disturb the quantum information in the encoded state but retrieves information about the error. Depending on the QEC code used, syndrome measurement can determine the occurrence, location and type of errors. In most QEC codes, the type of error is either a bit flip, or a sign (of the phase) flip, or both (corresponding to the Pauli matrices X, Z, and Y). The measurement of the syndrome has the projective effect of a quantum measurement, so even if the error due to the noise was arbitrary, it can be expressed as a combination of basis operations called the error basis (which is given by the Pauli matrices and the identity). To correct the error, the Pauli operator corresponding to the type of error is used on the corrupted qubit to revert the effect of the error. The syndrome measurement provides information about the error that has happened, but not about the information that is stored in the logical qubit—as otherwise the measurement would destroy any quantum superposition of this logical qubit with other qubits in the quantum computer, which would prevent it from being used to convey quantum information.

Web Search Results

• Quantum Error Correction: The Key to Quantum Computing

  ‍ What Is Quantum Error Correction? Quantum error correction, or quantum computing error correction, is a set of techniques for protecting quantum information from errors that are caused by noise and decoherence. While classical error correction deals with 1s or 0s, QEC involves qubits that exist in superpositions. This makes it a challenging yet key aspect of quantum computing. [...] Quantum error correction is a method used to detect and fix quantum computing errors caused by environmental interference, hardware imperfections, or measurement noise. Unlike classical error correction, it encodes information across multiple entangled qubits. This allows for detecting and correcting errors without directly observing the qubits’ states. ### What are the three types of error correction? [...] The biggest challenge is managing and correcting these errors without disrupting the delicate quantum state—a problem unique to quantum computing. This is where quantum error correction (QEC) comes in, presenting a way to detect and fix errors while preserving quantum coherence. As the field reaches new heights, QEC remains a key area of research, with major players like Google, IBM, and Microsoft making efforts to overcome these limitations and unleash the full potential of quantum computing.

• What is quantum error correction? | Q-CTRL

  Quantum error correction - or QEC for short - is an algorithm known to identify and fix errors in quantum computers. This error-correcting algorithm is able to draw from validated mathematical approaches used to engineer special “radiation-hardened” classical microprocessors deployed in space or other extreme environments where errors are much more likely to occur. QEC is the source of much of the great promise supporting our community's aspirations for quantum computing at scale. [...] Looking to the future we see that a holistic approach to dealing with noise and errors in quantum computers is essential. Quantum error correction is a core part of the story, and combined with performance-boosting quantum firmware we see a clear pathway to the future of large-scale quantum computers. For a deeper dive into the intersection of QEC and Quantum Firmware. [...] In the context of QEC, quantum firmware actually reduces the number of qubits required to perform error correction. Exactly how is a complex story, but in short, quantum firmware reduces the likelihood of error during each operation on a quantum computer. Better yet, quantum firmware easily eliminates certain kinds of errors that are really difficult for QEC and actually transforms the characteristics of the remaining errors to make them more compatible with QEC. Win-win!

• Quantum Error Correction Codes - Azure Quantum | Microsoft Learn

  Quantum error correction (QEC) is a technique that allows us to protect quantum information from errors. Error correction is especially important in quantum computers, because efficient quantum algorithms make use of large-scale quantum computers, which are sensitive to noise. The basic principle behind quantum error correction is that the number of bits used to encode a given amount of information is increased. This redundancy allows the code to detect and correct errors. [...] Quantum error correction codes work by encoding the quantum information into a larger set of qubits, called the physical qubits. The joint state of the physical qubits represents a logical qubit. The physical qubits are subject to errors due to decoherence and imperfections in quantum gates. The code is designed so that errors can be detected and corrected by measuring some of the qubits in the code.

• Quantum error correction - Microsoft Quantum

  Quantum error correction techniques are being developed and applied to quantum systems to help protect and stabilize quantum computers from these errors, ensuring accurate computation. Quantum error correction works by encoding the quantum information in a way that allows errors to be detected and corrected. This is typically done by encoding the information into a larger set of qubits, called a “quantum error-correcting code,” which is designed to be resilient to errors. Some common quantum [...] Quantum error correction is likely to be a crucial component of practical, scaled quantum computing. The frequency of errors on current quantum computing systems means that long running or large-scale quantum algorithms are unlikely to produce accurate results. Moreover, many promising quantum algorithms, such as Shor’s algorithm for factoring and qubitization for quantum simulation, require a large number of qubits and operations, exacerbating the issue. [...] Quantum error correction techniques enable the construction of logical qubits from multiple physical qubits, reducing the impact of errors on the overall computation and making it possible to scale up quantum computers. Quantum error correction is necessary to ensure the reliability of these algorithms on noisy, imperfect quantum hardware. However, it’s important to note that quantum error correction is not perfect. While it can greatly reduce the rate of errors in a quantum computation, it

• Quantum Error Correction: the grand challenge - Riverlane

  Quantum error correction (QEC) and quantum error mitigation (QEM) are two different schemes to deal with noise in devices, which can cause errors in computation. Quantum error correction methods use multiple physical qubits to represent a single logical qubit. Data is preserved by distributing the information across multiple qubits. Quantum decoders can then detect and correct any errors that occur during computation. Surface code is a popular QEC code. [...] Quantum error correction and fault-tolerant quantum computers are often informally used interchangeably. To experts the terms have slightly difference meanings. Quantum error correction is a scheme for protecting information from noise in device. Fault-tolerance builds on this. Fault-tolerant quantum computers also prevent errors from spreading during the error correction process or during a computation. It is a richer and broader subject. [...] Scaling quantum computers to millions of qubits requires classical systems capable of processing vast amounts of data—up to 100 terabytes per second. Quantum error correction is essential for ensuring reliable quantum operations (QuOps) by identifying and correcting qubit errors. This must scale to millions of quantum operations (MegaQuOps) and ultimately trillions (TeraQuOps) for quantum computers to fulfil their vast potential.