Awesome Quantum Computing Experiments: Benchmarking Experimental Progress Towards Fault-Tolerant Quantum Computation
Achieving fault-tolerant quantum computation (FTQC) demands simultaneous progress in physical qubit performance and quantum error correction (QEC). This work reviews and benchmarks experimental advancements towards FTQC across leading platforms, including trapped ions, superconducting circuits, neutral atoms, NV centers, and semiconductors. We analyze key physical metrics like coherence times, entanglement error, and system size (qubit count), fitting observed exponential trends to characterize multi-order-of-magnitude improvements over the past two decades. At the logical level, we survey the implementation landscape of QEC codes, tracking realized parameters \([[n, k, d]]\) and complexity from early demonstrations to recent surface and color code experiments. Synthesizing these physical and logical benchmarks reveals substantial progress enabled by underlying hardware improvements, while also outlining persistent challenges towards scalable FTQC. The experimental databases and analysis code underpinning this review are publicly available at .
1 Introduction
The realization of algorithms offering quantum advantage1,2,3,4 demands quantum processors operating not just with a large number of qubits5,6,7,8, but with qubits exhibiting high fidelity, often called “algorithmic qubits” (qubits meeting the fidelity requirements for useful algorithms)9,10. Early physical qubit implementations11,12,13, while demonstrating fundamental quantum phenomena, suffered from significant error rates, far exceeding the requirements for complex computations14,15. The primary strategy to bridge this gap lies in quantum error correction (QEC)14,16,17, where quantum information is redundantly encoded across multiple physical qubits to protect it from local errors, effectively creating robust logical qubits.
Progress towards fault-tolerant quantum computation18,19,20,21,22,23 is thus intrinsically multi-faceted, requiring simultaneous improvements across all layers of the hardware stack. Key areas include extending the fundamental lifetimes (\(T_1\)) and coherence times (\(T_2\)) of physical qubits, minimizing errors in single- and multi-qubit gate operations, dramatically increasing the number of addressable and interconnected physical qubits, and successfully implementing and scaling QEC codes of increasing complexity and distance.
While individual metrics offer valuable insights into specific aspects of a given quantum computing platform’s maturity24, a holistic view combining physical-level benchmarks with logical-level QEC implementation progress25 is crucial for evaluating the trajectory towards fault tolerance and utility scale. The primary aim of this paper is therefore to present and analyze key performance metrics derived from experimental realizations of both physical qubit and QEC implementations. To provide the necessary context for interpreting these metrics, we first review the essential concepts at the physical qubit level for various platforms and their associated metrics in Section 2 followed by an overview of QEC principles and experimental code implementations at the logical level in Section 3 analyzing trends in complexity, and the platforms used.
Given the rapid pace of experimental advancement in the field, tracking progress requires dynamic tools. To facilitate ongoing tracking and analysis of this rapid progress, we have developed an open-source repository containing the databases of experimental results underpinning this review. This resource, available at , is designed to be easily updated by the community with new publications26. Adding new experimental realizations allows for the automatic regeneration of the figures presented herein, providing a continuously evolving snapshot of the state-of-the-art in physical qubit performance and QEC implementation across different platforms and codes.
Therefore, this work provides the following three key advances: (1) A unified benchmarking framework aggregating physical and logical qubit metrics across platforms, (2) Characterization of platform-specific improvement trends through analysis of 25-year experimental data, and (3) Open-source repository enabling tracking of documented quantum experiments through community contributions.
2 Physical Qubit Benchmarks
This section delves into the fundamental building blocks of quantum processors: the physical qubits. As outlined by Nielsen and Chuang27, the physical realization of quantum computation necessitates fulfilling four fundamental requirements: robustly representing quantum information, performing a universal family of unitary transformations, state preparation, and measurement. Within this context, critical metrics for assessing performance include the robustness of quantum states against environmental noise, often quantified by \(T_1\) and \(T_2\) coherence times, and the precision in implementing quantum operations, particularly concerning the controllability required to generate and manipulate entangled states accurately.
We will thus examine key benchmarks used to assess the quality and progress of qubits across various leading experimental platforms24,28,29,30,31. We begin by outlining the platforms considered and the basic concept of how quantum information is encoded within these physical systems. We will then analyze the physical-level metrics that quantify performance, including qubit stability via \(T_1\) and \(T_2\) times, the fidelity of multi-qubit operations through entanglement error, and the progress towards large-scale systems indicated by physical qubit counts.
2.1 Physical Platforms and Qubit Encoding
To provide essential context for the analysis of performance metrics in this section, we briefly outline the physical encoding of quantum information within the hardware platforms considered. Our focus targets platforms demonstrating significant experimental progress towards QEC implementation. These include trapped ion systems28,32, various superconducting circuits24,33, neutral atoms held in dipole traps29, Nitrogen vacancy (NV) centers31 and semiconductors30.
Quantum information is fundamentally encoded in the state of two-level quantum systems, known as qubits. The choice of which two levels within a larger physical system’s Hilbert space represent the computational basis states \(\ket{0}\) and \(\ket{1}\) varies significantly across different hardware platforms, each choice presenting distinct advantages and challenges concerning qubit stability, control fidelity, readout efficiency, and scalability potential.
For instance, both trapped ions28,32 and neutral atoms held in dipole traps29 commonly encode qubits in specific internal electronic energy levels. Often, two stable hyperfine ground states are selected, leveraging their long intrinsic lifetimes. Manipulation in trapped ions, which uses specific ionic species, typically involves precisely tuned microwave fields or lasers (depending on whether hyperfine or optical transitions are used). Neutral atoms, trapped using laser light (e.g., optical tweezers), also use laser or microwave fields for control, frequently employing highly excited Rydberg states to mediate strong interactions required for multi-qubit gates. While both platforms leverage atomic energy levels, the charged nature of ions allows for strong confinement via electric fields, whereas neutral atoms rely on trapping via induced dipole moments which can be accomplished with optical potentials.
Distinctly, superconducting circuits24,33 realize qubits not within natural atoms, but as the two lowest quantized energy eigenstates of macroscopic electrical circuits incorporating non-linear elements like Josephson junctions. These engineered “artificial atoms” (e.g., transmons, fluxoniums) have customizable energy level structures, with \(\ket{0}\) and \(\ket{1}\) corresponding to distinct energy levels manipulated primarily by microwave pulses. More complex encodings using higher energy levels or multiple circuit modes (bosonic codes) offer alternative pathways within this platform.
Another major approach displayed in the metrics of this section relies on spin degrees of freedom. NV centers31, which are point defects within a diamond lattice, typically encode the qubit in the electron spin ground state, and control is achieved via microwave fields. The inherent solid-state environment also allows nearby nuclear spins, such as those of the Nitrogen atom forming the NV center itself (typically \(^{14}\)N or \(^{15}\)N) or nearby carbon-13 atoms (\(^{13}\)C) naturally present within the diamond lattice, to serve as qubits or long-lived memories, often offering longer coherence times than the NV electron spin. Similarly leveraging spin in a solid-state environment, semiconductor qubits30 typically encode information in the spin state (spin-up \(\ket{\uparrow}\) representing \(\ket{0}\) and spin-down \(\ket{\downarrow}\) representing \(\ket{1}\), or vice-versa) of individual charge carriers (electrons or holes) confined in nanoscale structures like quantum dots, or alternatively, using the nuclear or electron spin of donor atoms (e.g., phosphorus) implanted in a host material like silicon. While both NV centers and semiconductor qubits utilize spin, they differ significantly in their host material and the specific nature of the spin carrier (defect electron spin vs. confined electron/hole or donor spin).
As we will see in the next section, each encoding strategy profoundly influences the qubit’s characteristics, including its susceptibility to different noise sources.
2.2 Physical Level Metrics
Evaluating the hardware platforms requires quantifiable benchmarks. We now detail several key metrics commonly used to characterize the quality of individual physical qubits and the scale of experimental systems.
2.2.1 Bitflip and Coherence times
The stability of a physical qubit is fundamentally limited by two characteristic times: the energy relaxation time (\(T_1\), or bitflip time) and the dephasing time (\(T_2\), or coherence time). \(T_1\) quantifies the timescale over which the system incoherently exchanges energy with its environment. However, the practical factor limiting this timescale can vary by platform. For example, in neutral atom qubits where the intrinsic decay between the hyperfine qubit states used is often negligible, the relevant timescale analogous to \(T_1\) is typically determined by off-resonant scattering of trapping light rather than spontaneous emission between \(\ket{1}\) and \(\ket{0}\). Nevertheless, for the purpose of comparative analysis in this review, such dominant qubit loss timescales are generally categorized and plotted under the \(T_1\) metric. \(T_2\) measures the timescale over which the relative phase between \(\ket{0}\) and \(\ket{1}\) in a superposition state is lost. Long \(T_1\) and \(T_2\) times are essential for preserving quantum information.
The physical_qubits dataset26 compiles this key information on physical qubits developed from 1999 to 2024, documenting their evolution across various platforms. For each experiment, the dataset records the code name, the corresponding research article title and link, the publication year, the platform type, and the coherence metrics including \(T_1\) and \(T_2\) times. Figure 1 plots this data, illustrating significant improvements over the past decades, particularly for superconducting circuits24. References are, in chronological order, for superconducting circuits24 based on Josephson junctions13,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52, and based on bosonic encodings39,47,48,50,51,53,54,55,56, for semiconductors57,58,59, for trapped ions60,61,62,63, for neutral atoms64,65,66,67,68 and for graphene69. The last two decades have seen substantial improvements in physical qubit stability, with typical coherence times increasing by one or more orders of magnitude in several leading experimental platforms. Exponential fits to this data (see Section 7.3 for goodness-of-fit analysis) reveal characteristic doubling times ranging from approximately 0.9 years for semiconductor \(T_1\) to around 5.9 years for neutral atom \(T_1\). It should be noted that for the superconducting circuit platform in particular, this overall trend analysis combines data from distinct qubit encodings, such as transmons and those based on bosonic codes, which inherently possess different characteristics and may exhibit varied individual scaling trajectories but they are fitted collectively here for simplicity.
2.2.2 Entanglement Error
Beyond single-qubit stability, the ability to create high-fidelity multi-qubit entanglement is paramount for quantum computation and QEC. For the purpose of this analysis and depending on the available data, we consider both Bell state preparation error (the error associated with generating a maximally entangled state) and two-qubit gate error as equivalent metrics for quantifying entanglement error, as both provide a measure of the system’s ability to create and manipulate entangled states. The entangled_state_error_exp dataset tracks the evolution of error rates in entanglement across multiple quantum computing platforms from 1998 to 2025. For each experiment, the dataset records the entanglement error rate (entangled state error or two-qubit gate error), corresponding research article title, publication year, and implementation platform. Figure 2 plots the reported entanglement error over time for leading platforms. The references are, in chronological order, for superconducting circuits70,71,72,73,74,75, for neutral atoms76,77,78,79,80,81,82,83,84,85,86, for trapped ions12,87,88,89,90,91,92,93,94, for semiconductor spins95,96,97 and for NV center98. We observe a consistent trend of decreasing entanglement error across ion traps, neutral atoms, and superconducting circuits, all below the sub-percent level. Exponential fits to the data indicate characteristic error halving times ranging from approximately 1.2 years for semiconductor spins to 2.6 years for superconducting circuits, reflecting a consistent trend of rapid improvement over the past years (see Section 7.3 for more details). However, recent experimental results are above their respective fits which indicates that progress seems to be recently slowing down for ion traps, superconducting circuits and neutral atoms.
2.2.3 Qubit Count for Scale up
Achieving fault tolerance requires a large number of physical qubits to encode logical information and perform QEC5,6. Scaling the number of individually controllable, high-quality qubits is therefore a major engineering challenge. The qubit count metric serves thus as a critical link between physical qubit progress and the resources available for implementing QEC codes. It is important to note that for neutral atom platforms, while trapping large numbers of atoms in optical lattices is relatively straightforward, the reported qubit counts specifically refer to systems demonstrating essential quantum computing capabilities such as site-resolved readout and internal-state manipulation, rather than just the raw number of trapped atoms. The qubit_count dataset displays experiments from 1998 to 2024, tracking the increasing number of qubits in experimental quantum systems across various platforms. For each realization, the dataset records the qubit count, corresponding research article title, publication year, and implementation platform.
Figure 3 illustrates the growth in the maximum number of physical qubits reported. The references are, in chronological order, for ion traps12,87,99,100,101, neutral atoms77,102,103,104,105,106,68,107,108, superconducting circuit70,109,110,111,112, semiconductor spins113,114,115, and NV centers116. The data highlights platform-specific scaling trajectories, with neutral atoms demonstrating the largest qubit counts (6,100 qubits), followed by superconducting circuits (127 qubits), and ion traps (100 qubits). Fitting exponential trends to this data reveals different scaling rates, with neutral atoms exhibiting the fastest approximate doubling time at 1.4 years, compared to 2.6 years for superconducting circuits and 5.0 years for ion traps.
Section 2 detailed the remarkable advancements in physical-qubit technologies over the past decades, showcasing multi-order-of-magnitude improvements in coherence times, entanglement fidelity, and achievable system sizes across various platforms. However, as the analysis of entanglement error (Section 2.2.2) illustrates, even state-of-the-art physical qubits possess inherent error rates and face scaling challenges that currently preclude the direct execution of large-scale, fault-tolerant quantum algorithms. The physical error rates, while dramatically reduced over the past decades, remain significantly higher than what complex computations demand, and bridging this fidelity gap is the primary motivation for QEC. Therefore, translating the physical qubit advancements reviewed previously into reliable computational power depends critically on the effective implementation and scaling of QEC protocols. Therefore, we now transition from the physical layer benchmarks to the logical layer, by first delving into the principles of QEC and then surveying the experimental landscape of QEC code implementations designed to protect quantum information and ultimately enable fault-tolerant computation.
3 QEC Code Implementation
Inspired by Gottesman’s prioritization of specific QEC codes based on their resource requirements for early fault-tolerance demonstrations117, numerous experimental efforts have successfully implemented many of these codes, see Table 1. These realizations affirm the viability of using smaller, experimentally accessible codes as the initial steps towards achieving robust, fault-tolerant quantum computation.
| Quantum Code Name | Minimum Qubits for Fault Tolerance | Number of Ancilla Qubits |
|---|---|---|
| \([[4, 2, 2]]\) code | 5 | 1 |
| \([[6, 4, 2]]\) code | 7 | 1 |
| \([[8, 6, 2]]\) code | 9 | 1 |
| 9-qubit Bacon-Shor code | 10 | 1 |
| 5-qubit code | 11 | 6 |
| 7-qubit code | 12 | 5 |
| Surface code | \(\geq\) 13 | - |
| 2D NN 9-qubit Bacon-Shor code | 13 | 1 |
Building upon these early demonstrations, this section provides a detailed examination of the broader landscape of experimental QEC code implementations. We will explore the underlying concepts, survey the range of codes and platforms utilized, and analyze key metrics tracking progress towards fault tolerance.
3.1 Concept of QEC
QEC provides a strategy to protect fragile quantum information from noise inherent in physical systems and gate operations. The core principle involves encoding the state of one or more logical qubits into a carefully chosen subspace within a larger Hilbert space spanned by many physical qubits. QEC codes are specifically designed such that common types of physical errors (e.g., single-qubit bit flips or phase flips) map the encoded logical state onto distinguishable, mutually orthogonal error subspaces. This structure enables to extract information about the error that occurred, called error syndrome, through measurements, often involving ancillary qubits. This process reveals the error type and location without directly measuring, and thus collapsing, the encoded logical information itself, allowing for subsequent correction.
The fundamental properties and capabilities of a QEC code are concisely described by the parameters \([[n, k, d]]\). Here, \(n\) represents the total number of physical qubits utilized in the code block, \(k\) denotes the number of logical qubits robustly encoded, and \(d\) is the code distance. The distance \(d\) is a crucial metric quantifying the code’s error detection and correction power. It corresponds to the minimum number of arbitrary single-qubit errors that could potentially transform one encoded logical state into another, or cause an undetectable error. A code possessing distance \(d\) is guaranteed to detect any combination of up to \(d-1\) physical errors and correct any combination of up to \(\lfloor (d-1)/2 \rfloor\) physical errors occurring within a code block. Consequently, achieving higher code distances offers enhanced protection against noise, but this typically comes at the cost of requiring a significantly larger number of physical qubits \(n\).
With the fundamental concepts of encoding, error detection, and code parameters \([[n,k,d]]\) established, we now survey the key experimental efforts realizing these principles. This review concentrates on the platforms and specific QEC codes where significant progress has been documented in the scientific literature, including both peer-reviewed publications and widely accessible preprints (e.g., via arXiv), providing the basis for the analysis presented in the following sections.
3.2 Experiments Considered
Our analysis focuses on the platforms that have demonstrated the most significant experimental progress in multi-qubit operations and the implementation of QEC. These include established approaches like trapped ions28,32 and various superconducting circuits24,33, alongside rapidly advancing systems such as arrays of neutral atoms held in optical traps29. We also consider photonic systems118, which often leverage different computational models based on linear optics or integrated circuits, and solid-state spin systems like NV centers in diamond31. For historical context and early demonstrations, results from Nuclear Magnetic Resonance (NMR) are also included.
The experimental exploration of QEC spans a wide spectrum of codes, reflecting different strategies and complexities. Earliest work often implemented simple Repetition Codes119 (distance \(d\), realizing \([[d, 1, d]]\) parameters for either bit-flip or phase-flip protection) as building blocks or initial demonstrations11,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134. Significant effort has also focused on early stabilizer codes like the \([[5, 1, 3]]\) Perfect Code135,136,137, as well as various small error detecting codes like the \([[4, 1, 2]]\) or \([[4, 2, 2]]\) variants138,139,140,141,142,143,144,145,146,147,131,148,149,150,151,152. More recent research increasingly targets codes with topological properties or higher potential for fault tolerance, such as Surface Codes153 implemented with various distances and configurations, often encoding \(k=1\)154,155,132,66,156,133,157,158, or \(k=2\)66 logical qubits, and Color Codes (e.g., \([[7, 1, 3]]\), \([[19, 1, 5]]\), potentially encoding \(k=1, 2,\) or even \(3\) logical qubits)159,66,157,160,161. Subsystem codes, notably the Bacon-Shor code18,162,163 (e.g., \([[9, 1, 3]]\))164,165,152, offer alternative structures for fault tolerance. Additionally, numerous demonstrations use simpler entangled states like Bell states166,167,168, primarily for error detection protocols rather than full correction, or employ Cluster States66, as resources for measurement-based quantum computation which also possess inherent error detection properties. The specific implementations of these codes across the aforementioned platforms form the core dataset analyzed in this section.
Beyond identifying the specific platforms and codes explored, quantifying the progress in QEC experiments requires analyzing dedicated metrics related to these implementations.
3.3 Logical Level Metrics
Evaluating the progress in experimental QEC necessitates to track specific metrics that capture the type of code implemented, the hardware platform, the \([[n, k, d]]\) code parameters, and the achieved performance, often assessed through logical error rates and proximity to fault-tolerance accuracy thresholds. The analysis presented in this section is based on the qec_exp dataset, which compiles information on experimental QEC implementations spanning from the earliest demonstrations in 199811 up to recent results in 2024. This dataset covers a diverse range of platforms mentioned above, including superconducting circuits, trapped ions, neutral atoms, NMR systems, and photonic devices.
For each documented implementation, the dataset records key details: the specific QEC code family (e.g., Repetition Code, Surface Code, Color Code), the corresponding publication reference, year of publication, the code’s \([[n, k, d]]\) parameters, and the hardware platform employed. Examining the data chronologically reveals a clear trajectory of progress: beginning with three-qubit repetition codes primarily in NMR systems, the field has advanced significantly to implementing sophisticated codes like surface codes that leverage up to 49 physical qubits on neutral atom arrays and superconducting circuits. Notably, recent milestones captured in the dataset include demonstrations of error correction operating below the fault-tolerance threshold using surface codes133.
3.3.1 Cumulative Growth and Platform Distribution
The field has witnessed substantial growth in experimental QEC activity over the past quarter-century. Figure 4 plots the cumulative count of documented QEC experiments since 1998, broken down by the physical platform employed. The overall trajectory demonstrates significant and accelerating growth in research activity. While NMR platforms hosted the earliest demonstrations, trapped ion systems began contributing consistently around 2004 and show steady growth. Superconducting circuits emerged shortly thereafter and have since become the dominant platform in terms of cumulative experimental output, exhibiting particularly rapid growth in the last decade. Neutral atom platforms represent a more recent but fast-growing contributor to the field, alongside consistent contributions from photonic systems and nascent efforts in NV centers. This cumulative view highlights the increasing investment and progress across multiple hardware modalities in tackling the challenges of QEC. A non-cumulative, year-by-year breakdown is provided in Figure 6 in the Appendices.
3.3.2 \([[n, k, d]]\) Representation
As mentioned above, the \([[n, k, d]]\) parameters provide a concise summary of a QEC code’s resource requirements (\(n\)), encoded information capacity (\(k\)), and error correction strength (\(d\)). Figure 5 visualizes the landscape of experimentally realized QEC codes by plotting the number of physical qubits (\(n\)) against the achieved code distance (\(d\)). Each point represents a documented experiment, labeled by the code type and the number of logical qubits encoded (\(k\)).
The plot reveals that a significant portion of experimental work has focused on codes with relatively low distance (\(d \le 3\)) and using fewer than 50 physical qubits. These implementations often serve as crucial demonstrations of QEC principles, stabilizer measurements, or specific code components. Notably, simple repetition codes (\(k=1\), various \(d\)) and early stabilizer codes like the \([[5,1,3]]\) code are represented in this region. However, the figure also clearly illustrates the ongoing effort to push towards higher code distances, which offer protection against a greater number of physical errors, which is a prerequisite for fault tolerance. Milestones include implementations of surface codes and color codes reaching \(d=3\), \(d=5\) and even \(d=7\), requiring substantially more physical qubits (approaching \(n=50\) for \(d=7\)).
3.3.3 QEC Performance Benchmarks
While Section 3.3 introduces logical level metrics such as the cumulative count of experiments and the \([[n, k, d]]\) parameters realized, a dedicated analysis of the performance of implemented QEC codes is essential for benchmarking progress towards fault tolerance. Key performance indicators include the suppression of logical errors relative to physical errors, often quantified by the suppression factor \(\Lambda\), demonstrations of logical qubit lifetime extension beyond the physical qubit limit (break-even), and operation below theoretical fault-tolerance thresholds. Recent experiments have made significant strides in these areas. For instance, logical error suppression when increasing code distance has been quantified, scaling from distance-3 to distance-5, suppression factors of approximately \(2.15(2)\), \(1.69(6)\), and \(1.56(2)\) were measured for different dynamic surface code implementations158, and a factor of \(\Lambda = 1.56(4)\) was observed for the color code, which simulations indicated was below threshold160. While an earlier surface code experiment showed only modest improvement between distance-3 and distance-5 logical qubits (logical error per cycle of \(2.914\%\) vs \(3.028\%\))132, the following demonstration achieved significant suppression (\(\Lambda = 2.14 \pm 0.02\)) when scaling from distance-5 to distance-7133. This latter work also reported operating both distance-5 and distance-7 surface codes below the fault-tolerance threshold, achieving a logical error rate per cycle of \(0.143\% \pm 0.003\%\) for the 101-qubit distance-7 code133. Furthermore, this distance-7 logical memory surpassed the break-even point, exhibiting a lifetime \(2.4 \pm 0.3\) times longer than its best constituent physical qubit133. Although these recent achievements mark critical milestones, the overall number of such demonstrations remains insufficient to establish statistically significant trends in logical error suppression or performance scaling across different codes and platforms at this time.
4 Conclusion
In this work, we have introduced an online and open-source tool26 to track the progress of several chosen metrics in the quantum computing stack, from low-level characteristics like relaxation and coherence times to higher-level ones like QEC code parameters.
Our analysis reveals remarkable advances: physical-qubit coherence and gate fidelity have improved by orders of magnitude, while processor scale has grown exponentially, enabling access to hundreds and even thousands of qubits68,112. Concurrently, experimental QEC has progressed from foundational demonstrations11,120 to implementing sophisticated codes like surface and color codes with increasing scale \(n\) and distance \(d\) across multiple leading platforms133,156,157.
Despite the impressive progress, achieving robust fault-tolerant quantum computation requires overcoming persistent critical challenges. Three key obstacles include: (1) The resource overhead problem: QEC requires encoding information across multiple physical qubits, dramatically increasing hardware complexity. For instance, factorizing a 2048-bit RSA integer using Shor’s algorithm would require approximately one million superconducting qubits despite only needing 1,537 algorithmic qubits, with each algorithmic qubit requiring at most 1,352 physical qubits for noise suppression (\(d=25\))7, (2) The processing of encoded information: Logical gates must operate directly on encoded qubits without decoding, requiring complex physical operations where a single logical two-qubit gate can involve thousands of state preparations and physical gate operations. Achieving universal gate sets adds further overhead through magic state distillation169 or cultivation170, which can consume a significant fraction of logical qubits151,161,160, and (3) The decoding problem: Decoders must process error syndrome data at quantum computer clock speeds, potentially handling gigabit-per-second data rates per logical qubit, requiring scalable decoding algorithms that balance accuracy, latency, and scalability for these thousands of logical qubits involved.
While long \(T_1\) and \(T_2\) times are essential for preserving quantum information, the comparison with gate and QEC cycle times ultimately determines how many operations can be performed before quantum information is lost. Future work will thus focus on incorporating finer-grained metrics essential for fault-tolerance such as the QEC cycle time but also logical qubit performance under repeated correction cycles, logical error suppression factors \(\Lambda\), post-selection rates, detailed ancilla qubit counts, logical qubit half-lives, alongside benchmarks for key subroutines including magic state distillation151,161,160 and GHZ state preparation171,172,173,157,174,152. Synthesizing multi-layered progress, facilitated by the presented resource, is vital for navigating this rapidly evolving field towards the ultimate goal of impactful fault-tolerant quantum computation.
Designed for flexibility and community contribution, our tool provides a unified resource that will be developed as the field continues to grow. We hope it proves valuable for physicists and QEC researchers by having all the resources in one place to make fair comparisons between technologies.
5 Acknowledgements
We thank Pascal Scholl and Antoine Browaeys for insightful discussions during the preparation of this manuscript. We thank Julius de Hond and Louis Vignoli for reading a draft of this paper and providing useful feedback. We thank the Pasqal team, and in particular Lucas Lassablière and Adrien Signoles, for cultivating an environment that enabled this work.
6 References
7 Appendices
7.1 Reaching the Utility Scale
To contextualize the physical qubit benchmarks within the broader goal of useful quantum computation175, we project potential timelines towards a ‘utility scale’ regime, employing a working definition of achieving both a Physical Qubit Count (PQC) of 10,000 and an Entanglement Error (EE) below 0.1% to be a factor 10 below the threshold of the surface code. These metrics are chosen somehow arbitrarily as being hard to reach but not impossible in near future and should be thought of as one possible scenario rather than the definition of utility. While individual gate errors (such as the two-qubit gate error) are commonly used to evaluate the distance to the accuracy threshold in QEC simulations, we use the entangled state error when it is the only available metric as it benchmarks the system’s capability to produce the high-fidelity entangled states essential for QEC, providing a functionally relevant and cross-platform comparable proxy for approaching fault-tolerance requirements. Besides, while one might specifically track the number of physical qubits directly employed within QEC code experiments (the focus of Section 3), examining the maximum reported physical qubit count remains a vital benchmark, as it reflects the underlying platform’s overall progress in fabrication, control, and potential scale, providing the resource pool from which future, larger QEC implementations must draw. By extrapolating the observed exponential improvement rates (halving times for EE, doubling times for PQC) summarized in Table Table 2, we can estimate when each platform might reach these specific thresholds.
| Platform | Best EE | Best EE Year | EE ÷2 factor | US EE | Best PQC | Best PQC Year | PQC ×2 factor | US PQC |
|---|---|---|---|---|---|---|---|---|
| Ion traps | 0.0003 | 2024 | 2.4 | 2024 | 100 | 2023 | 5.0 | 2056 |
| Neutral atoms | 0.0020 | 2023 | 2.3 | 2025 | 6,100 | 2024 | 1.4 | 2024 |
| Superconducting circuits | 0.0030 | 2020 | 2.6 | 2024 | 127 | 2023 | 2.6 | 2039 |
| Semiconductor spins | 0.0035 | 2022 | 1.2 | 2024 | 6 | 2022 | 2.6 | 2050 |
This analysis projects that neutral atom platforms could satisfy both criteria as early as 2025, substantially sooner than trapped ions (projected for 2038) and superconducting circuits (2039). Within the assumptions of this model, the rapid PQC scaling factor currently observed for neutral atoms is the primary driver for this accelerated timeline.
However, several critical caveats apply to these projections. Firstly, let us emphasize again that the definition of ‘utility scale’ based solely on PQC and EE is a simplification: true utility will depend on a complex interplay of metrics including logical qubit fidelity, connectivity, gate speeds, and the ability to execute fault-tolerant protocols (as discussed in Section 3), not just raw physical qubit counts and error rates. The 10k and 0.1% target serves as one specific, potentially arbitrary, milestone. Secondly, the projection relies heavily on the assumption that current exponential scaling trends will continue for years or decades. Such extrapolations are inherently speculative, as technological progress may encounter unforeseen plateaus due to fundamental physics or engineering hurdles (as it seems to be already the case for the EE), or conversely, accelerate due to breakthroughs not captured by historical data. Factors like increasing crosstalk at scale, limitations in control systems, or shifts in research focus could significantly alter these trajectories. Therefore, while illustrative, these projections should be interpreted cautiously as reflecting potential timelines if current rates of progress persist and if the chosen PQC/EE targets adequately capture the requirements for utility.
7.2 Additional Visualisations
7.2.1 Yearly Experiment Counts by Platform
Complementing the cumulative view in Figure 4, Figure 6 displays the number of documented QEC-related experiments on a year-by-year basis, categorized by the experimental platform used. This non-cumulative representation highlights the annual research output and reveals trends in platform activity over time, such as the peak and subsequent decline of NMR contributions, the sustained output from trapped ions, and the recent acceleration of research using superconducting circuits and neutral atoms.
7.2.2 Cumulative Growth of QEC Implementations by Code Family
Figure 7 illustrates the cumulative number of reported experimental implementations specifically categorized by the family of QEC code employed, tracked over time. This view highlights which code families have received sustained attention. Early activity is visible for central concepts demonstrated using Bell states and the \([[5,1,3]]\) code. The plot shows significant recent growth in implementations of surface codes and repetition codes (often used as building blocks or testbeds for surface codes), along with substantial effort dedicated to four-qubit codes.
7.2.3 Timeline of Implementations
Figure 8 provides a detailed chronological perspective, mapping specific QEC code implementations (y-axis) to their publication year (x-axis) and indicating the platform used via color and shape. This visualization clearly shows the pioneering role of NMR in early demonstrations, the consistent contributions from trapped ion systems over many years, and the significant surge of activity in superconducting circuits and neutral atoms, particularly in the last decade. It also illustrates the progression towards implementing more complex codes, such as surface and color codes, primarily on these latter platforms.
7.2.4 Distribution of Implementations Across Platforms and Codes
qec_exp database.
The distribution of QEC experimental efforts across different hardware platforms and code types is summarized in the sunburst chart presented in Figure 9. The inner rings represent the physical platforms, while the outer rings show the specific QEC codes implemented, with segment sizes proportional to the number of documented experiments (indicated by counts). This reveals that superconducting circuits have hosted the largest volume and diversity of QEC experiments to date, followed by trapped ions and, more recently, neutral atoms. It also highlights that certain codes, notably repetition codes and four-qubit codes, have been realized across multiple platforms, offering opportunities for cross-platform comparison. In contrast, implementations of larger-scale topological codes (e.g., surface, color codes with higher distances) are currently concentrated on platforms demonstrating higher available qubit counts.
7.3 Goodness of Fit for Exponential Trends
This appendix details the methodology used to assess how well the exponential trend lines, presented in Section 2.2 for physical qubit benchmarks (Figure 1, Figure 2, Figure 3), fit the collected historical experimental data.
7.3.1 Methodology
To model the observed trends in coherence times (\(T_1\), \(T_2\)), entanglement error, and physical qubit count over time (year, \(x\)), we assumed an exponential relationship of the form: \(y = A \cdot B^x\) where \(y\) represents the metric being analyzed. This exponential model can be linearized by applying a (base-10) logarithm: \(\log_{10}(y) = \log_{10}(A) + x \cdot \log_{10}(B)\) This transformation yields a linear equation \(Y = c + m \cdot x\), where \(Y = \log_{10}(y)\), the intercept \(c = \log_{10}(A)\), and the slope \(m = \log_{10}(B)\).
Standard linear regression was performed on this transformed data (year vs. \(\log_{10}(\text{metric})\)) using the scipy.stats.linregress function from the SciPy library176. This function calculates the best-fit line parameters (slope \(m\) and intercept \(c\)) and also returns the Pearson correlation coefficient, denoted as \(r\).
The goodness of fit for this linear regression in log-space is quantified by the coefficient of determination, \(R^2\), which is simply the square of the Pearson correlation coefficient (\(R^2 = r^2\)). The \(R^2\) value represents the proportion of the variance in the dependent variable (\(\log_{10}(\text{metric})\)) that is predictable from the independent variable (year). An \(R^2\) value ranges from 0 to 1, where 1 indicates that the linear model perfectly explains the variance in the transformed data (corresponding to a perfect exponential fit for the original data), and 0 indicates no linear correlation. Values close to 1 suggest that the exponential model provides a good description of the observed historical trend.
7.3.2 Results
The calculated \(R^2\) values obtained from the linear regression fits performed for Figure 1, Figure 2, Figure 3, are summarized in Table 3 below. Fits were only calculated where sufficient data points (at least three) were available for a given platform and metric.
| Metric | Platform | R\(^2\) | Time Scale | Std Error |
|---|---|---|---|---|
| Coherence Time (\(T_1\)) | Semiconductor | 0.954 | ×2 every 0.86y | 0.077 |
| Superconducting circuit | 0.809 | ×2 every 0.99y | 0.032 | |
| Neutral atoms | 0.122 | ×2 every 5.89y | 0.079 | |
| Coherence Time (\(T_2\)) | Neutral atoms | 0.880 | ×2 every 2.38y | 0.033 |
| Ion traps | 0.860 | ×2 every 1.92y | 0.045 | |
| Superconducting circuit | 0.418 | ×2 every 1.94y | 0.045 | |
| Entanglement Error | Semiconductor spins | 0.981 | ÷2 every 1.16y | 0.036 |
| Ion traps | 0.952 | ÷2 every 2.40y | 0.011 | |
| Superconducting circuits | 0.933 | ÷2 every 2.56y | 0.016 | |
| Neutral atoms | 0.889 | ÷2 every 2.30y | 0.015 | |
| Physical Qubit Count | Semiconductor spins | 0.983 | ×2 every 2.62y | 0.015 |
| Ion traps | 0.955 | ×2 every 5.03y | 0.007 | |
| Neutral atoms | 0.948 | ×2 every 1.37y | 0.019 | |
| Superconducting circuit | 0.877 | ×2 every 2.58y | 0.025 |
7.3.3 Discussion
The \(R^2\) values presented in Table 3 are generally high (many above 0.85), suggesting that the exponential model captures a significant portion of the variance in the historical trends for most platforms and metrics analyzed. This supports the visual impression from Figure 1, Figure 2, Figure 3 and provides quantitative justification for using exponential fits to characterize the rates of progress (doubling/halving times).
However, certain caveats should be noted:
- The \(R^2\) value for Superconducting Circuit \(T_2\) time (0.418) is notably lower than others, reflecting that we included different families of implementations within the “superconducting qubits” category (transmons vs cavities), and an outlier with particularly small \(T_2\) breaks the exponential fit for this platform.
- Similarly, the lower \(R^2\) value for Neutral atoms \(T_1\) (0.122) reflects the inclusion of different atomic species (Rubidium, Cesium, and Strontium) with inherently different characteristics.
- A high \(R^2\) value confirms that the exponential model fits the historical data well but does not guarantee that the trend will continue into the future, as discussed in Section 7.1 regarding the limitations of extrapolation.
Overall, the analysis of \(R^2\) values reinforces the observation of strong historical exponential trends in key physical qubit metrics across major platforms, while also highlighting specific cases where the model fit is weaker or based on limited data.