Google’s latest quantum computing chip, “Willow,” has drawn significant attention from the global tech community. This groundbreaking development not only showcases the latest achievements in quantum computing but also raises critical discussions about its potential impact on blockchain security. The foundation of blockchain security lies in complex cryptographic challenges, and advancements in quantum computing may pose a threat to this foundation. This article delves into the potential implications of Google’s “Willow” chip on blockchain security.

A Closer Look at the Quantum Chip “Willow”

According to official reports [1], Google has unveiled its latest quantum computing chip, “Willow,” and announced two major breakthroughs:

1. Advancements in Quantum Error Correction: \
   By increasing the number of qubits, “Willow” has significantly reduced the error rate, addressing a critical issue in quantum computing that has remained unsolved for nearly 30 years.
2. Unprecedented Computational Speed: \
   “Willow” completed a standard benchmark computation in less than five minutes. By comparison, one of the world’s fastest supercomputers would require 1,025 years to perform the same task— a timeframe that far exceeds the age of the universe.

Let’s unpack these achievements. For now, we will set aside the first breakthrough in quantum error correction and focus on the second: computational speed. If “Willow” can complete in five minutes what a supercomputer would take 1,025 years to achieve, it presents a striking comparison to traditional cryptographic challenges.

For instance, consider the time required for a classical computer to brute-force an RSA-2048 encryption key. According to estimates by John Preskill [2], a home computer would need approximately 10¹⁶ years to break RSA-2048.

Given the staggering capabilities of “Willow,” if it can handle tasks that take a supercomputer 1,025 years in just five minutes, it might seem trivial for it to tackle challenges requiring 10¹⁶ years. Does this mean the cryptographic problem of integer factorization, upon which RSA is based, is no longer secure? By the same logic, has the discrete logarithm problem on elliptic curves, another cornerstone of blockchain security, already been solved? These speculations hint at a scenario where blockchain security might collapse in an instant.

But Is That Really the Case?

Let’s delve deeper into the actual implications of these developments for cryptography and blockchain technology. (To be continued…)

What Kind of Quantum Computer is Needed to Break Blockchain Private Keys?

Quantum computers have the theoretical potential to break classical cryptographic challenges, such as the integer factorization problem and the discrete logarithm problem, which underpin many encryption systems. But what level of quantum computing capability is actually required to break specific cryptographic challenges? Let’s explore this through the following examples:

Factoring a large integer from an RSA-2048 public key.

Deriving a private key from a public key on elliptic curves such as Secp256k1, Secp256r1, or Ed25519.

For classical computers, both tasks are computationally infeasible. Based on their respective security parameters, elliptic curve cryptography (ECC) is slightly harder to break than RSA. However, research by Martin et al. [3] suggests that for quantum computers, the situation is reversed: RSA is slightly harder than ECC. For simplicity, we treat both problems as having similar difficulty and focus on the second problem.

The Role of Secp256k1 and Similar Curves in Blockchain Security

Elliptic curves like Secp256k1, Secp256r1, and Ed25519 are widely used in blockchain systems. The discrete logarithm problem (DLP) on these curves forms the backbone of blockchain security, including systems like Bitcoin. If this problem is solved, attackers could forge transactions on the blockchain at will. Clearly, the ability to solve DLP on elliptic curves would directly determine the survival of blockchain security.

Quantum Computing Requirements for Breaking DLP

According to Martin et al. [3], solving the discrete logarithm problem on an elliptic curve defined over a prime-order field (with order size nnn bits) would require:

• Quantum Resources:
  9n+2⌈log⁡2(n)⌉+109n + 2\lceil \log_2(n) \rceil + 109n+2⌈log2​(n)⌉+10 logical qubits.
• Quantum Circuitry:
  448n3log⁡2(n)+4090n3448n^3\log_2(n) + 4090n^3448n3log2​(n)+4090n3 Toffoli gates in the quantum circuit.

Example: Breaking NIST Standard Curve P-256

For the P-256 curve used in many cryptographic systems:

• Logical Qubits: 2,330 high-quality logical qubits are needed for quantum gate operations.
• Toffoli Gates: Approximately 1.26×10111.26 \times 10^{11}1.26×1011 Toffoli gates are required to fully implement Shor’s algorithm.

Implication for Blockchain Security

A quantum computer with just 2,330 logical qubits and capable of executing 1.26×10111.26 \times 10^{11}1.26×1011 Toffoli gates would be enough to compromise blockchain systems. This capability would dismantle the security of Bitcoin, Ethereum, and virtually all other blockchain networks relying on ECC for cryptographic protection.

While these resource requirements are daunting, the rapid advancements in quantum computing technology suggest that achieving such capabilities might not be impossible in the long term. However, current estimates place the realization of such quantum systems 15–20 years into the future, giving the blockchain industry a crucial window to develop and deploy quantum-resistant cryptography.

The Key to Quantum Computing: High-Quality Logical Qubits

The extraordinary computational power of quantum computers, which vastly surpasses that of classical computers, lies in their ability to leverage quantum superposition and quantum parallelism through quantum bits (qubits). Unlike classical computing, which relies on linear processes, quantum computing enables complex calculations by operating on multiple states simultaneously. However, the unique properties of qubits also bring significant challenges.

Qubits are highly sensitive to environmental noise and external interference, making their states unstable and prone to losing their quantum properties (a phenomenon known as decoherence). Errors can occur at virtually every stage of a quantum computation process—during initialization, state maintenance, quantum gate operation, or result measurement. Such errors can render quantum algorithms ineffective or produce incorrect results. Consequently, ensuring the stability and accuracy of qubits to obtain high-quality qubits is one of the core challenges in quantum computing.

Addressing the Challenge: Logical Qubits and Error Correction

One of the key strategies to overcome qubit instability is the construction of logical qubits, which reduce error rates by combining multiple physical qubits with quantum error correction codes. These codes, such as surface codes and Cartesian codes, enable the detection and correction of errors, thereby enhancing the robustness and reliability of quantum systems.

Each logical qubit typically requires dozens to thousands of physical qubits to support it. While logical qubits significantly improve the fault tolerance of quantum computers, they come at the cost of increased physical qubit requirements and complex error correction algorithms.

A critical challenge in quantum error correction has emerged as a major bottleneck. Researchers initially assumed that sacrificing additional physical qubits would improve the accuracy of logical qubits. However, reality has proven otherwise. Due to the inherently high error rates of physical qubits (ranging from 10⁻¹ to 10⁻³), early attempts at error correction often resulted in logical qubits with even higher error rates than the physical qubits themselves.

This paradox can be likened to a chaotic team scenario: “The more people involved, the more chaos ensues.” In quantum error correction, the poor quality of physical qubits meant that error correction mechanisms frequently introduced more errors than they eliminated. This phenomenon, often described as “over-correcting into chaos,” underscores the importance of high-quality physical qubits as a foundation for constructing reliable logical qubits.

Without high-quality logical qubits, practical quantum computing remains out of reach. Addressing this challenge requires not only advancements in physical qubit stability but also breakthroughs in quantum error correction techniques. Achieving this goal is essential to unlock the full potential of quantum computing and overcome its current limitations.

Revisiting the Achievements of Quantum Chip “Willow”

With a solid understanding of the challenges surrounding quantum computing, we can now reevaluate the accomplishments of Google’s quantum chip, “Willow.”

One of the most groundbreaking aspects of “Willow” is its ability to overcome the long-standing obstacles in quantum error correction using surface codes [4][5]. By increasing the number of qubits and optimizing error correction techniques, “Willow” has achieved a historic milestone: transforming error correction from a loss-making process to a net gain.

Surface code performance

Additionally, the “Willow” chip completed the Random Circuit Sampling (RCS) benchmark computation in less than five minutes. RCS is a widely used method for evaluating the performance of quantum computers.

However, it’s important to note that the impressive performance gap between the quantum computer and a classical supercomputer in this test partially arises from the fundamental differences between quantum and classical computing. To better understand this, we can use an imperfect analogy: comparing the “speed of a satellite in space” to the “speed of a car on the ground”.

Furthermore, it should be emphasized that RCS currently lacks practical application scenarios, serving primarily as a performance evaluation tool.

When Will “Willow” Overcome Classical Cryptographic Challenges?

Google Quantum Computing Roadmap

The diagram above illustrates the six stages of Google’s quantum computing development roadmap, highlighting the critical path from experimental breakthroughs to large-scale practical applications.

Stage 1 (2019):

Using the Sycamore processor, the team demonstrated quantum computation surpassing classical computation. In just 200 seconds, the processor completed a task that would take a traditional supercomputer 10,000 years, establishing the foundation for quantum supremacy. This stage’s goals were achieved with a quantum computer featuring 54 physical qubits.

Stage 2 (2024):

The Willow chip was used to demonstrate the first prototype of a logical qubit, proving that quantum error correction can reduce error rates. This breakthrough paved the way for building large-scale practical quantum computers and enabled the possibility of near-term intermediate-scale quantum (NISQ) applications. The goals for this stage were also achieved, with the quantum computer reaching 105 physical qubits and a logical qubit error rate of 10−310^{-3}10−3.

Stage 3:

The aim is to build long-lived logical qubits with an error rate of less than one in a million operations. Achieving this requires more robust quantum error correction and scalable hardware architecture. Quantum computers at this stage are expected to have 10310^3103 physical qubits, with logical qubit error rates reduced to 10−610^{-6}10−6.

Stage 4:

Focus shifts to achieving low-error logical quantum gate operations, enabling meaningful quantum error correction applications. Quantum computers are expected to reach 10410^4104 physical qubits while maintaining a logical qubit error rate of 10−610^{-6}10−6.

Stage 5:

The system will expand to 100 logical qubits and achieve high-precision gate operations, unlocking more than three fault-tolerant quantum applications. Quantum computers are expected to feature 10510^5105 physical qubits, with logical qubit error rates staying at 10−610^{-6}10−6.

Stage 6:

The ultimate goal is to control and connect 1 million qubits, creating a large-scale fault-tolerant quantum computer. This system is envisioned to be broadly applicable in fields such as medicine and sustainable technologies, with over 10 quantum applications transforming various industries. Quantum computers at this stage will have 10610^6106 physical qubits, with logical qubit error rates dropping to 10−1310^{-13}10−13.

As discussed earlier, breaking common blockchain cryptographic challenges, such as the elliptic curve discrete logarithm problem, requires about 2,330 high-quality logical qubits and a quantum circuit with 1.26×10111.26 \times 10^{11}1.26×1011 Toffoli gates. Logical qubits rely on quantum error correction, with each logical qubit typically requiring multiple physical qubits for support. For instance, the Willow chip uses a code distance of 7, requiring 72=497^2 = 4972=49 physical qubits per logical qubit, totaling approximately 114,170 physical qubits.

However, this estimate is optimistic. As the scale and depth of quantum operations increase, stricter requirements for logical qubit error rates will emerge. Currently, Willow’s logical qubit error rate is around 10−310^{-3}10−3, far from the level needed to solve such problems. According to Craig et al. [6], solving the RSA-2048 problem, which has a complexity similar to the elliptic curve discrete logarithm problem, requires a logical qubit error rate of 10−1510^{-15}10−15 and a code distance of at least 27. This means each logical qubit would need 272=72927^2 = 729272=729 physical qubits, totaling over 1,698,570 physical qubits. Additionally, the required logical qubit error rate of 10−1510^{-15}10−15 is not only far below Willow’s 10−310^{-3}10−3 but also two orders of magnitude lower than the logical qubit error rate anticipated for quantum computers in Google’s Stage 6 roadmap.

Based on Google’s development roadmap, it will only be possible to tackle the elliptic curve discrete logarithm problem once quantum computing reaches Stage 6. Achieving this goal will require significant advancements in logical qubit quality, along with efficient management and error correction of massive numbers of physical qubits.

Assuming a five-year interval between Stages 1 and 2 and steady progress, it is estimated that it will take 15 to 20 years for “Willow” to overcome classical cryptographic challenges. Even with an optimistic outlook, it would take at least 10 years to reach the required level.

Future Blockchain Security

Once quantum computers achieve sufficient computational power, they will be able to exploit their asymmetric advantages to quickly compromise the core security mechanisms of cryptocurrencies. This includes stealing users’ private keys and gaining control over their assets. In such a scenario, existing cryptocurrency networks would face systemic collapse, leaving user assets unprotected.

Currently, however, Google’s Willow quantum chip remains in the early stages of quantum computing research and is incapable of solving cryptographic challenges such as large integer factorization and elliptic curve discrete logarithms. As a result, it does not yet pose a substantive threat to blockchain security. Developing a truly practical quantum computer faces numerous technical challenges, making this a long and arduous journey.

While quantum computing technology does not yet directly threaten encrypted assets, its rapid development cannot be ignored. According to forecasts based on current technological trends, quantum computers are expected to overcome several key technical bottlenecks within the next decade, gradually approaching the critical point where they could threaten traditional cryptography. In anticipation of this potential challenge, the blockchain community must proactively plan and prepare to address the technological impact of the quantum era. To ensure the long-term security and stability of blockchain systems, three key measures are essential:

1. Accelerating the Research and Standardization of Quantum-Resistant Algorithms

It is critical to advance research into quantum-resistant cryptography, such as lattice-based algorithms, and to promote their standardized application globally. This is the top priority in addressing quantum threats and is vital for the future security of blockchain technology.

1. Actively Deploying Quantum-Resistant Cryptographic Technologies

Efforts should focus on establishing a robust quantum-resistant cryptographic infrastructure to provide a strong technical foundation for the long-term security of blockchain networks. This will ensure systems can respond effectively to potential quantum threats and maintain stable operations.

1. Exploring the Innovative Potential of Quantum Computing

The blockchain community should also explore the potential applications of quantum computing, such as optimizing on-chain computations, improving resource scheduling efficiency, and enhancing privacy protection. These innovations could inject new growth momentum into blockchain technology.

Although the widespread application of quantum computers has not yet materialized, their eventual arrival is inevitable. In this context, blockchain security frameworks based on traditional cryptography will gradually be replaced by security guarantees grounded in quantum-resistant cryptography.

Companies like Safeheron are already collaborating with academic institutions to actively explore quantum-resistant algorithms, laying the groundwork for the technological evolution of digital asset security. Additionally, the blockchain ecosystem has begun to see public chains integrating quantum-resistant algorithms, demonstrating a forward-thinking trend that alleviates excessive concern.

The development of quantum computing not only presents potential security challenges for blockchain technology but also offers opportunities for technological advancement and efficiency improvements. By actively addressing these changes and embracing transformation, blockchain technology can thrive amidst future waves of innovation, achieving higher levels of maturity and creativity.

References

[1] Meet Willow, our state-of-the-art quantum chip
[2] John Preskill – Introduction to Quantum Information (Part 1) – CSSQI 2012
[3] Quantum Resource Estimates for Computing Elliptic Curve Discrete Logarithms
[4] Suppressing quantum errors by scaling a surface code logical qubit
[5] Quantum error correction below the surface code threshold
[6] How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
[7] Google’s quantum computing roadmap

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