# The era of logical qubits

## What is all the excitement about?

#### Top-line summary

A Harvard-led team that included QuEra has successfully executed large-scale algorithms on an error-corrected quantum computer with 48 logical qubits. Read the full announcement here. This breakthrough, performed at Harvard's lab, is larger by orders of magnitude than any previous demonstration, and marks a new era in scalable, fault-tolerant quantum computing - it signifies the transition from the era of physical qubits to the era of logical error-corrected qubits.

#### Context

Quantum computers have the potential to solve complex problems in various fields, but noise affecting qubits has been a major hurdle, corrupting the computation before one can get the desired results. These errors can be fixed by combining several physical qubits to represent a single "logical" qubit. This process, called “quantum error correction”, makes the calculations more stable and reliable. With a sufficient number of error-corrected logical qubits, quantum computers can live up to their tremendous promise.

#### What has the team demonstrated?

The Harvard-led team leveraged quantum error correction to enhance computation stability and reliability, solving the error problem. The team achieved quantum computation with 48 logical qubits and hundreds of entangling operations. This is a significant leap from previous demonstrations which showcased only to two logical qubits and one entangling gate. Moreover, the research show that we can operate logical qubits with a fidelity better than the component physical qubits. Impressively, this fidelity improves as the code distance increases.

#### Why is it significant?

The Harvard-led research is the first to show large-scale algorithm execution on an error-corrected quantum computer. It opens the door to quantum devices capable of executing complex computations reliably, unveiling the technology's vast potential.

#### How does this compare to current state of the art?

Previous experiments have been limited to one or two logical qubits. They could only correct a limited number of errors, constrained by small code distances. Our Harvard-led work significantly pushes these boundaries, not only increasing the number of logical qubits to 48 but also extending the code distance up to seven with better error suppression, thus offering more robust error correction capabilities.

#### What made this possible?

This breakthrough is the culmination of many years of research and development in neutral-atom technology. The key developments that made this possible are:

**A large number of qubits**: the system allows to control hundreds of physical qubits (280 in this experiment). Since each logical qubit is made of several physical qubits, the number of physical qubits (and the method by which physical qubits are encoded into logical ones) determines the number of logical qubits. See this Nature paper.

**The ability to shuttle qubits while preserving their computational state**. Unlike quantum modalities such as superconducting qubits which are static and cannot move, neutral atom qubits can be shuttled without losing their quantum state. This ability to move any qubit next to any other qubit enables more efficient error-correction codes (e.g. using fewer physical qubits), and simplified circuits. Specifically, the team succeeded in moving all the physical qubits that make up a logical qubit in unison. See this Nature paper.

**High-fidelity two-qubit gates:**Quantum computations are executed by performing operations (known as gates) on qubits. The accuracy of these operations is crucial. For effective error correction, two-qubit gates should have at least 99% fidelity, or else error-correction codes cannot correct errors fast enough. In prior Harvard-led work, a fidelity of 99.5% was achieved. See this Nature paper.

**Hardware-efficient control:**The system built at Harvard utilizes direct, parallel control over an entire group of logical qubits. This ability to move multiple qubits at once significantly reduces the control overhead and complexity of performing logical operations, such that instead of controlling one physical qubit at a time, we directly control each logical qubit as an individual unit. The number of control signals is important as we think about scaling to thousands or tens of thousands of qubits. In a superconducting architecture, two or three control signals are required for each physical qubit, thus leading to tens of thousands of control signals in large-scale superconducting systems. Despite using up to 280 physical qubits, we require fewer than 10 controls for operations. As system size scales up, the control number will only slightly increase. See this Nature paper.

**Zoned architecture**: Drawing inspiration from classical computer architecture, which has separate memory and computation units, the team introduced a zoned architecture consisting of three different functional zones: storage, entangling, and readout. The storage zone is used for qubit storage, free from gate errors and featuring long coherence times (e.g. the ability of qubits to maintain their state for long periods); the entangling zone is used for high-fidelity parallel entangling gates, operating on the qubits; and the readout zone gives us the capability to measure the quantum state of a subset of qubits without affecting the quantum state of other qubits, which is critical for error correction. See this Nature paper.

**Mid-circuit readout and feedforward**: Using the readout zone, the team achieved high-fidelity, mid-circuit measurements on select qubits and executed feedforward operations (e.g., use the measurements to correct errors), essential for numerous error-corrected quantum computation schemes. See this Nature paper.

#### Could this be done with other modalities?

Perhaps, but it's more difficult.

Our Harvard-led approach stands in contrast to superconducting machines, where several high-performance control lines are typically required for each physical qubit. As such, controlling 280 physical qubits in a superconducting quantum computer would require many hundreds of control signals, as opposed to fewer than 10 controls that we use here. Therefore, it will likely be challenging for other modalities to replicate this soon. To draw an analogy, it's akin to opening your 4K television and finding a dedicated wire for every pixel - clearly impractical. Our approach, on the other hand, allows for an increase in qubits without a proportional rise in control signals, greatly enhancing scalability.

Comparatively, qubits in ion trap quantum computers can be moved, but with limited parallelism.

Of course, neutral atom computers also have limitations, and we'll be happy to discuss them with interested parties.

#### How many logical qubits are necessary to create truly-useful quantum computers?

The question of the requisite number of logical qubits for a truly-useful quantum computer remains a vibrant area of research, eliciting diverse opinions.

Some researchers posit that industrial applications would require quantum computers equipped with thousands of high-quality logical qubits. Conversely, others argue that merely 100 high-quality logical qubits could suffice, provided they are paired with optimized algorithms. Notably, such 100-qubit systems would eclipse the simulation capabilities of classical computers, which are limited to around 50 qubits. In our research, we intentionally capped our logical qubit count at 48. This allowed us to juxtapose our quantum system's results with simulated outcomes, affirming their authenticity.

## Interested in quantum error correction?

#### When will this research be incorporated into a product?

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