What is quantum error correction?

What is quantum error correction, and why is it important?

Quantum error correction (QEC) is the process of detecting quantum information errors in qubits caused by noise and decoherence and applying techniques to correct and prevent them. This helps produce more reliable quantum computing systems.

Why do quantum errors occur?

Classical digital logic behavior is highly predictable and reliable because digital logic exists in traditional, steady, logical states -- ones or zeros -- established and maintained using conventional electronic circuitry operating under the persistent effects of stable voltage and current. While errors can and do occur in digital logic devices, those errors are relatively rare and easy to detect.

Quantum environments are far more fragile. Quantum errors occur because qubits -- and their vital sub-atomic characteristics of spin and coherence -- are incredibly delicate and sensitive to the prevailing environment. Further, qubits are rarely just ones or zeros and can exist in a superposition of both states simultaneously. Thus, the very state in which the qubit exists is fragile and difficult to maintain outside a laboratory. These factors disturb qubits easily, leading to interference and decoherence that can disrupt the qubit's quantum state, causing quantum information errors.

Ironically, anything that touches a qubit can cause quantum errors, but there are three broad reasons to consider, including the following:

• Interference. Interference is unavoidable in the real world. Any physical factor can interfere with a qubit. Temperature changes, electromagnetic fields, energy, and even physical obstructions and vibrations can disrupt a qubit's coherence and cause quantum errors.
• Decoherence. Decoherence is a loss of quantum properties -- such as entanglement and superposition. Decoherence can result from interference or interactions with other particles and qubits. A qubit that loses coherence tends to behave like a traditional digital bit -- which is undesirable in quantum computing.
• Quantum gates. Quantum gates are the varied mechanisms used to manage and compute using qubits. While digital gates use transistors, quantum gates use machinery such as lasers, microwave signal sources and sophisticated magnetic fields. These gates are imperfect and prone to errors, leading to unexpected interference and decoherence that result in quantum errors.

Common types of quantum errors

Three general types of quantum errors can challenge qubits and quantum computing, including the following:

• Bit-flip error. This occurs when a qubit changes from a zero to a one or vice versa.
• Phase-flip error. This occurs when a qubit's phase changes unexpectedly. Phase is a characteristic of the qubit's quantum state. It flips the qubit's superposition state somewhere between one and zero.
• Gate errors. This occurs due to the unexpected, improper or unforeseen operation of a quantum gate acting upon a qubit.

The importance of QEC and fault-tolerant quantum computing

All modern technologies are worthless without reliability -- the simple confidence that each device's operation and performance will deliver accurate and repeatable results. Errors can occur, but the techniques and components used to detect and correct errors make modern devices usable.

Quantum computers are incredibly powerful and expensive systems. They allow effective information processing that would be impossible for traditional processor-based computer systems. But without an assurance of reliability, no business or government will use quantum computing for anything more than scientific curiosity. Practical quantum computing demands implementing fault tolerance (FT) and error correction -- especially as quantum computers scale to operate on many qubits simultaneously.

QEC is one part of the answer. It implements an array of available error-correcting codes to support detecting and correcting quantum errors in real time. FT builds on QEC, helping to deliver quantum computer designs that can operate correctly -- even when computational errors occur.

Quantum computing will remain a niche technology until QEC and FT technologies can be applied to ensure predictable and repeatable outcomes in real-world situations on a large computational scale.

Quantum error correction vs. quantum error mitigation

The ideas of mitigation and correction are sometimes used interchangeably, but it's important to distinguish between them.

Mitigation. To mitigate is to reduce the probability of -- or soften the resulting effect of -- an undesirable event. Quantum error mitigation (QEM) seeks to reduce the probability of quantum errors or achieve the best possible results from quantum computing results when errors do occur.

One part of quantum error mitigation is to address the design of quantum gates and the handling of qubits. For example, better operational temperature controls and superior magnetic field shaping hardware can result in more stable qubits and lower gate errors.

The other part of QEM uses techniques to find the best outcome from erroneous quantum information. This is handled through noisy intermediate-scale quantum techniques, including the following:

• Zero noise extrapolation. This is where the quantum gate is operated under varied interference levels until the lowest noise level is found, yielding the best results.
• Probabilistic error cancellation. This is where statistical methods are used to blunt the effects of interference and errors.
• Measurement error mitigation. This technique is used to offset or reduce errors in quantum information measurements.

Correction. To correct is to amend or rectify an undesirable result. QEC seeks to establish more resilience in quantum information, allowing the quantum computer to detect -- and sometimes -- correct quantum errors. There are three fundamental phases to QEC, including the following:

• Encoding. QEC operates by encoding quantum information across multiple qubits, each containing a portion of the overall quantum information. Quantum information is encoded across multiple qubits using specific algorithms -- or QEC codes.
• Detection. When the quantum data from each encoded qubit is measured again, the information is reassembled and processed against the QEC code. This detection process can determine if a quantum error occurred in any qubits containing the quantum information.
• Correction. Once an error is identified, the QEC algorithm can mathematically re-determine the proper state of the erroneous qubit and use quantum hardware devices to restore the afflicted qubit to its original state -- effectively correcting the error in that qubit.

There are many QEC code algorithms available to quantum computer designers.

Techniques for quantum error correction

QEC codes are the algorithms that distribute data across physical qubits. They assemble a logical qubit offering reasonable protection against quantum information errors. Many QEC codes are available today, with more than 540 QEC codes and variations associated with quantum technologies. Each QEC code offers a unique complexity, cost, style and benefits. Here are five common QEC techniques:

• Hastings-Haah code. This QEC code can provide better cost-performance benefits than surface codes when working with Majorana qubits. Majorana qubits are based on Majorana exotic fermion particles to create stable and robust qubits. Surface code can be more efficient for gate-based instruction sets with higher overhead.
• Repetition code. A simple QEC encodes a single data qubit into multiple qubits through simple repetition. In effect, each repeated qubit has the same information. Repetition codes can correct bit-flip errors but not phase-flip errors. A common example is a three-qubit code, where a data qubit is repeated onto three duplicate qubits.
• Shor code. Developed by Peter Shor, this approach encodes one logical qubit into nine physical qubits. The Shor code can detect and correct single-bit- or single-phase-flip errors. However, Shor code cannot correct both types of errors simultaneously.
• Steane code. This seven-qubit code can correct bit-flip and phase-flip errors simultaneously. Steane code is fault-tolerant, so the error correction process doesn't introduce extra errors. This characteristic can make Steane code more reliable and robust than other QEC code types.
• Surface code. This QEC code is designed to operate on a 2D qubit lattice to encode logical qubits. Its high error correction capability is attractive for large-scale, fault-tolerant quantum computing tasks and is used by systems such as the Azure Quantum Resource Estimator.

Challenges of quantum error correction

Quantum error correction is critical to ensure quantum computers' practical and reliable operation. QEC fundamentally encodes portions of data across many physical qubits to create a single logical qubit. Each qubit provides redundancy and can be examined to look for errors. Errors can then be corrected. Still, designers face significant challenges with error correction at the quantum scale, including the following:

• Complexity. QEC multiplies the number of physical qubits handled by a quantum computer system. This demands a multiplication in the number of quantum gates and other hardware needed to support the larger logical qubit that handles the same amount of quantum information that a single physical qubit might otherwise carry. This complexity also multiplies the effective cost of the quantum computer's design, construction, operation and maintenance.
• Measurement errors. Encoding portions of data across multiple physical qubits is key to redundancy and QEC. However, every physical qubit involved in the logical qubit is still subject to the same possibility of errors due to interference and decoherence. Finding errors in fragile quantum states -- without introducing additional errors in those many additional qubits -- poses a fearsome challenge to quantum engineers.
• Code selection. The choice of QEC code influences how quantum information is represented across the entangled states of many qubits. Numerous QEC code algorithms are currently available, but the surface code is the most popular type of QEC code. These operate on a 2D array of qubits, adding helper qubits near the data qubits to support error detection by effectively mimicking traditional parity checks. Other approaches to qubit arrangements may necessitate different QEC codes. Designers must pick the right tool for the job.

Quantum error correction technology

Hardware and software tools for quantum error correction are quickly emerging as quantum computing gains attention and investment. Some noteworthy elements employed in QEC include the following:

• Quantum error decoders. Quantum error decoders are processors designed to filter the information from noisy qubits and remove noise to preserve the underlying quantum information integrity and allow the computation to run. Such decoders are central to fault-tolerant quantum computing and rely on QEC encoding and ancilla qubits to isolate noise from data.
• Quantum firmware. Just as the firmware of traditional digital computers bridges the gap between hardware and operating systems and software, quantum firmware connects the mathematical abstractions of quantum algorithms with the practical physical control of hardware that manipulates the qubits. Designers are increasingly interested in unifying or standardizing quantum firmware to provide proven methodologies to deliver qubit operations with high abstraction with minimal user intervention.
• Quantum dynamic stabilization. Many quantum systems are inherently unstable and quickly decohere into undesirable states. Quantum dynamic stabilization is a set of techniques that periodically manipulate the qubit to counteract destabilizing effects and stabilize the qubit in a desired quantum state. Such technologies are central to error mitigation by improving the quality of qubits -- thus reducing the probability of errors in the first place.
• Quantum error suppression. Quantum error suppression (QES) builds quantum error mitigation. It seeks to reduce hardware errors in quantum computers by creating better quantum control techniques and enhancing the resilience of control hardware -- effectively preventing quantum errors from occurring rather than detecting and correcting errors after they occur. Quantum error suppression often involves designing and implementing advanced quantum hardware capable of more precise control pulses or dynamic feedback techniques. Examples of quantum error suppression include dynamic decoupling, quantum feedback control and predictive machine learning-based quantum error suppression (MLQES).

It's important to note that these techniques are often complementary and not mutually exclusive. For example, QES is complementary to QEC, and both sets of techniques can be implemented in the same quantum computer design.

Stephen J. Bigelow, senior technology editor at TechTarget, has more than 30 years of technical writing experience in the PC and technology industry.