Guest contribution by Yuval Boger, Chief Commercial Officer, Quera Computing
Quantum error correction (QEC) is an essential discipline in the quantum computer that aims to protect the quantum information from the inherent errors that occur during the calculation. Since quantum systems are very susceptible to intoxication and decoration, effective QEC techniques for the implementation of scalable and reliable quantum computer technologies are of crucial importance. In 2024 we changed a decisive shift in the focus – from the mere count of physical quBITs to implement and improve an increasing number of logical quBits. What was achieved in 2024 and what can we expect in 2025?
Historical context
In the nineties, pioneers such as Peter Shor, Andrew Steans and Daniel Gottesman laid the basis for the quantum error correction by adapting the classic error correction principles to the quantum area. The Landmark code from SHOR introduced in 1995 showed physically Quibits so that bit flop and phase error errors can be corrected without a collapse of the quantum state.
At the center of QEC is the challenge of achieving fault tolerance and that the quantum calculations remain reliable even in the event of errors in every component of the system. The fault tolerance is based on the threshold, which determines that errors can be effectively corrected as long as the error rate remains below a certain threshold. This principle underpins the continuous development of QEC strategies, with which mistakes should recognize and correct faster than they can accumulate.
Key parameters for comparing different QEC codes
Different QEC codes have unique properties that influence their effectiveness and practicality in different quantum hardware architectures. The most important parameters used for comparison include:
· Cod removal (D): Represents the robustness of a quantum error correction code by measuring the minimum number of physical qubit errors required to damage a logical qubit. For example, a code with D = 3 can correct a single error, d = 7 can correct three errors, while D = 2 can recognize a single error, but cannot correct it.
· Qubit -overhead: The number of physical quBITs that are necessary to encodes a single logical qubit.
· Connectivity request: Whether only local (closest neighbors) or long-distance interactions between qubits and the required qubit degree are required for a code.
· Threshold: The physical error rate, under which logical errors can be suppressed exponentially by increasing the code spacing.
· Accessible logical goals: How easily fault-tolerant logical gates (including non-clifford goals) can be implemented.
· Measuring and decoding complexity: The number of syndromm measurements and the amount of classic calculation that is required to decrypt errors in real time.
2024: The dawn of the logical qubit -era
Several commercial and academic groups have shown impressive results in quantum error correction. Some of the most important publications include:
Advances in the surface code and logical qubit operations
A publication “Logical Quantum Processor based on reconfiguring atomic arrays” (here) has intensified the focus on logical quBITs. It showed an improvement in the surface code with two qubit logic gates by scaling the code spacing of d = 3 to d = 7, fault-tolerant logical GHz states and realized calculated compensationally sophisticated circles with up to 48 logical quables. This research shows some unique functions for neutral computer computers such as reconfiguring connectivity and parallel multi-quit operations.
Google published “Quantum error correction below the surface code threshold” (here), which describes its new Supercondited Willow chip. Google has shown an error correction scheme under the threshold on Willow. Your physical error rates are now low that adding more quBITs for QEC reduces the logical error rate instead of strengthening errors. This is an important milestone in QEC.
Error tolerance innovations in different qubit modalities
IBM published “high-threshold value and low-overhead error-tolerant quantum space” (here), which presented the gross code for superconducting qubits, with simulations indicated by the assumption of a physical error rate of 0.1%.
Microsoft and Quantinuum published “Demonstration of the quantum calculation and error correction with a tesser act code (here) on the 56-qubit-ion computer from Quantinuum. They showed 12 logical quables with an error rate of 0.0011, which is 22 times better than the corresponding circuit error rate of 0.024.
Regardless of this, Microsoft and Atom Computing published “logical calculation with a neutral nuclear quantum processor” (here), which demonstrated 24 and 28 logical quants on a neutral atom computer.
AWS and other published “Hardware -efficient quantum error correction using chained Bosonic quBITs” (here), which was implemented a logical qubit, which was formed from the chain of coded Bosonic cat quibits with an external repeat code of far d = 5.
Algorithmic fault tolerance and magical state distillation
A work carried out by Quera, “algorithmic fault tolerance for the fast quantum computer” (here) (here) shows a new fault tolerance strategy, a transverse algorithmic fault tolerance that a 10-100-time reduction of the time required by QEC by considering the complete algorithmic context in The time reaches decoding, building on a paper led by Harvard, correlated decoding of logical algorithms with transversal goals ”(here). This is contrary to conventional QEC methods, in which a repeated syndrome extraction requires for every logical operation, which leads to a logical clock speed that is considerably slower (often 30 -times in relevant regimens) than the physical clock speed.
A team led by Quera published “Experimental Demonstration of Distillation Logical Magic State” (here), which achieves a key milestone for Quantum Computing on a large scale: Logical Magic State Distillation (MSD). Magic State distillation is a basic building block for large quantum computers. Stabilizer states and clifford operations are often easy to implement on an error-corrected quantum computer. However, such conditions can also be classically simulated and is not sufficient for the universal quantum calculation. Magical conditions come into play here. “Magic”, which describes how far a quantum state is from a stabilizer state. The Magic State distillation creates high-quality magic resource states by refining several lower liquids. MSD showed this work at a logical level using 2D color codes for D = 3 and D = 5 codes.
Special techniques and high -quality operations
Quantinuum had several indications of a note such as “highly fidelity teleportation of a logical quBIT using transversal gates and grating surgery” (here) and “Benchmarking Logical Dre-Qubit Quantum Fourier transformation, which are coded in the steane code on a quantum computer with trapped ions” (( Here).
Beyond the quantum computers
QEC is not only a quantum challenge-es is strongly based on high-performance classical computing to identify, decode and correct mistakes in real time.
An approach to do this is the use of FPGAS or ASICS. For example, see Yales “FPGA-based distributed Union-Find decoder for surface codes (here) or” Quantum error correction in real time and low latency with superconducting quBITs “(here) by Riverlane and Co authors.
Alternatively, some believe that GPUs are more suitable in this phase because they offer high performance in parallel workmanship and flexibility.
Emerging directions and strategies
Despite these progress, the field faces significant challenges, especially in the scaling of the number of physical quables that are necessary to present logical quBITs, a process that can lead to increased resource requirements and complications in maintaining coherence. In addition, reaching the logical error quotas remains a critical hurdle, as the researchers strive for only 1 to million rates to facilitate practical quantum applications. With a view to the future, some instructions are expected in 2025:
Research in logical algorithms: Instead of concentrating exclusively on the code construction, the researchers are now implementing logical algorithms for real hardware. This enables empirical knowledge-necessary decler, fault-tolerant gate designs and the use of noise properties. Early results suggest that gates, especially on reconfiguring platforms such as neutral atoms, can significantly improve algorithmic performance.
A wealth of codes: Surface codes remain a main support for their high threshold (~ 1%), alternatives such as color codes and high rate QLDPC codes win for their potentially lower overheads or simpler logical gate implementations. If the hardware variety is expanded – super -condemning qubits, trapped ions, neutral atoms, photonics – different codes will probably find special niches.
Noise feed: Not all errors are created equally. Practical QEC can benefit from the modeling of specific error channels – bias, extinguishing or photon loss – to adapt correction strategies. Hardware that follows these different noise processes can provide this information back into decoder and improve logical loyalty.
Machine learning in QEC: See “Artificial intelligence for quantum error correction: a comprehensive overview” (here) for a comprehensive review of AI for QEC. Machine learning techniques are used to accelerate decoding algorithms, optimize stabilizer and adjust QEC strategies in real time. This could prove to be invaluable to manage large qubit arrays in which manual coordination is impractical.
A new era for Qec
If QEC has once been considered a distant challenge, it is now the most active limit of the field. The transition from experimental demonstrations to really scalable, fault -tolerant quantum calculation appears to be increasingly feasible. If the number and quality of the logical qubits improves, we approach the goal of using quantum technologies for real applications
Recognition: Harry Zhou, quantum error correction architecture lead at Quera Computing, provided very helpful comments and suggestions for this article.