Quantum decodes series

This post is about decoding the recent Quantum chip Willow launched by Google. I will take you through the technical concepts behind achieving this groundbreaking innovation. The post will take sentences from Google website and explain underlying concepts.

You might feel the difficulty in understanding. The best way to read this post is to just understand the concepts explained rather than finding a flow.

Who should read this post?

• This post is absolutely beginner friendly.
• Any experts can read this post and can give suggestions.
• Beginners to Experts in various domain can read this post.

Image source: Google

Willow is the name of a quantum chip which is launched by Google in Dec 2024.

Reducing error exponentially

In order to understand error correction one need to understand different types of errors. Below image summarizes the types of error in quantum computing.

Summary of Types of errors

Major cause of errors

• Stray electromagnetic fields from nearby electronic equipment, radio waves or power lines
• Heat from surrounding environment
• Vibrational or acoustic noise (sound waves)
• Magnetic field disruptions.
• Random fluctuations in charge due to defective materials.
• Light from environment or leaks from optical setup.
• Humidity and Air pressure variations in surrounding environments.

We are aware that there is a high possibility of error occurrence when qubits are increased. The usual case is when you scale qubits (increase), these errors won’t reduce rather error significantly increase. Willow has shown to exponentially reduce the errors as we scale up qubits.

Exponential error reduction is possible when you are using a logical qubit created through quantum error correction and not just individual physical qubits. It's important to understand the difference between Physical qubits and logical qubits.

Physical qubits

• Physical qubits are a two-state quantum system which means there are two quantum states 0 and 1.
• A physical qubit is the actual physical system used to represent quantum information in a quantum computer.
• It's the basic building blocks of quantum computer.
• But remember that physical qubits are prone to errors, and they are implemented in noisy hardware.
• Complex computations are impossible with this error prone physical qubits because error correction is not used here.

Examples of different types of physical qubits are

• Superconducting qubits
• Trapped Ion
• Spin qubits
• Neutral atoms

Logical qubits

• Logical qubits are the one which are error corrected.
• A logical qubit is an abstract qubit which is formed by grouping of physical qubits together and applied quantum error correcting codes to it.
• Logical qubits are reliable in fault tolerant quantum computers.
• A single logical qubit can consist of dozens of physical qubits depending upon the error correction scheme used.

Examples of different types of logical qubits:

• Steane code.
• Surface code.
• Shor code.

The reason for exponential error reduction is owing to the usage of logical qubits. The reason for actual reduction in error rate is the usage of specific error correction code.

Image source: Google

In order to achieve this exponential error reduction, the researchers have used array of physical qubits encoded as logical qubits. This involved grouping multiple physical qubits into a grid configuration. Each grid consists of one logical qubits that is error corrected.

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Some of the grids used in this experiment is:

• 3×3 grid: This grid contains 3×3=9 physical qubits.
• 5×5 grid: This grid contains 5×5=25 physical qubits.
• 7×7 grid: This grid contains 7×7=49 physical qubits.

The basic idea behind error correction technique is:

• The more physical qubits (larger grids), the better the system can detect and correct errors.
• As the grid size increases, logical error rates decrease exponentially because the likelihood of undetectable errors drops sharply.

Code distance (d)

Code distance measures how many errors an error correction code can handle. Also the code distance depends upon the specific error correction scheme.

Lets consider 3x3 qubits encoded with surface codes,

For a square grid of d×d qubits, the code distance equals the side length of the grid,

Thus 3×3 grid → d =3.

Larger grids in quantum error correction codes mean larger code distances. Larger code distance means increase in error correction. Now we can mildly understand how exponential error correction has been achieved with increase in qubits.

This historic accomplishment is known in the field as “below threshold” — being able to drive errors down while scaling up the number of qubits.

The threshold is the maximum allowable error rate for physical qubits at which quantum error correction (QEC) can effectively reduce logical errors. If the physical error rate is below the threshold, the logical error rate decreases exponentially as the code distance increases. If the physical error rate is above the threshold, QEC fails, and logical errors increase regardless of the grid size.

Image source: Google

Metrics in the above image describes how the Willow chip operates below the error correction threshold, making quantum error correction effective.

Key metric related to threshold

We can discuss how the key metrics is compared with threshold.

Single-Qubit Gate Error: 0.035%±0.029%

• The average error rate for single-qubit gates is extremely low ranging between < 0.1%-0.5%
• Whereas the single qubit gate error here is 0.035% which is far below the typical thresholds of 0.1% — 0.5%.

Two-Qubit Gate Error: 0.33%±0.18%

• Two-qubit gates, such as controlled-Z (CZ) gates, are more error-prone but still below the 1%-2% threshold.
• These gates are critical for entangling qubits, a fundamental operation in quantum error correction. Keeping the error rate this low is essential for scalable quantum error correction.

Measurement Error: 0.77%±0.21%

• The error rate is below 1% and the typical threshold for measurement error is 1–3%

Error Correction Cycles per Second: 909,000

• The system performs nearly a million error correction cycles per second, allowing frequent detection and correction of errors before they accumulate.
• This rapid error correction is key to maintaining below-threshold performance.

Coherence time (T1): 68±13μs

Coherence time is a measure of how long a qubit can hold its quantum state before decaying.

• Coherence time of Willow shows that the chip can maintain coherence long enough to perform many gate operations and error correction cycles.
• Typical benchmarks for Superconducting circuit is 50–100 μs. Willows value is well within the acceptable range for superconducting qubits and supports reliable error correction.

As a measure of Willow’s performance, we used the random circuit sampling (RCS) benchmark. Pioneered by our team and now widely used as a standard in the field, RCS is the classically hardest benchmark that can be done on a quantum computer today. You can think of this as an entry point for quantum computing — it checks whether a quantum computer is doing something that couldn’t be done on a classical computer. Any team building a quantum computer should check first if it can beat classical computers on RCS.

Random Circuit Sampling (RCS)

RCS is a benchmark used to evaluate the computational power of a quantum computer by testing its ability to perform tasks that are classically intractable which means the tasks that are so complex which cant be efficiently solved by a classical computer.

When the information increases, classical computers struggle with exponential growth of information. In order to check whether the quantum computer is efficient we use a technique called RCS which means random circuit with more depth and volume is given. And quantum computer should process this circuit. If the quantum computer performs better than the classical supercomputer, then the quantum computer is said to be efficient.

In short, RCS is a benchmark tool to test quantum computer. Literally quantum computer undergoes a stress test for evaluation.

Willow’s performance on this benchmark is astonishing: It performed a computation in under five minutes that would take one of today’s fastest supercomputers 1025 or 10 septillion years. If you want to write it out, it’s 10,000,000,000,000,000,000,000,000 years.

10 septillion years shows demonstration of how much faster Willow’s quantum chip is for a task than time taken for a supercomputer to perform.

In this post we went through the types of errors and the reasons for error occurrence, Random circuit sampling as a benchmark tool, discussed about threshold metrics and ended on a positive note that Willow can perform 10 septillion times faster than a supercomputer.

Uff..All is well that ends well. I went through the concepts in brief with required circuit depth (😜). Please let me know if I want to cover some other topic.

Please dont forget to follow me. I will come up with the sword to decapitate the mysteries of quantum.

Well. Bye for now!!