Quantum computing is on the cusp of a major revolution, a shift that could redefine the boundaries of computation and problem-solving. At the heart of this revolution is the transition to the logical qubit era in which errors in quantum computers will be dramatically reduced. To appreciate the significance of this development, we first need to understand the fundamental building blocks of quantum computers — the physical qubits — and their susceptibility to errors.

What Is a Logical Qubit?

A logical qubit is encoded using a collection of physical qubits to protect against errors. Unlike a physical qubit, which represents the actual quantum hardware, a logical qubit is a higher-level abstraction used in fault-tolerant quantum computing. It provides a way to perform reliable quantum computations even in the presence of noise and errors. A logical qubit can be thought of as the quantum version of a classical repetition code in which the information of a single physical qubit is spread amongst multiple physical qubits, creating some redundancy and error protection. 

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The Problem With Qubits

Qubits (quantum bits) have two properties important to their computational power. The first is that they can exist in a state of superposition, where they can be both zero and one simultaneously. The second is entanglement, a state in which multiple objects, such as a pair of electrons or photons, share a single and inseparable quantum state. These qualities endow quantum computers with the potential to solve certain problems that were considered intractable. These physical qubits, regardless of their implementation, whether as superconducting circuits, trapped ions, or neutral atoms, are notoriously sensitive and prone to errors.

These errors arise from a variety of factors, including environmental noise, imperfect control mechanisms, and the intrinsic fragility of quantum states. A qubits susceptibility to error significantly limits the practical utility of quantum computers. Even with a so-called state-of-the-art fidelity of 99.9 percent, an error still occurs in one out of every 1000 operations. In the realm of quantum computing, where complex algorithms require many thousands or even millions of qubit operations, such error rates are prohibitively high. Conducting long calculations becomes practically impossible without accumulating significant errors that render the results unreliable.

By contrast, classical computers exhibit minuscule error rates. Thanks to highly reliable semiconductor technology and sophisticated error correction techniques, classical computers achieve error rates as low as one error per quintillion operations (that’s one in 1018). This remarkable reliability is a cornerstone of modern computing, enabling everything from simple arithmetic calculations to complex simulations and data processing.


How Logical Qubits Solve Errors in Quantum Computing

To make quantum computers truly useful and competitive with classical ones, we have to drastically improve their error rates. Simply enhancing the fidelity of physical qubits seems unlikely to bridge this substantial gap, however. This is where the concept of quantum error correction and logical qubits comes into play.

Logical qubits are akin to the repetition code used in traditional computing. In a classical repetition code, information is duplicated across multiple bits to guard against errors. Unfortunately, the no-cloning theorem in physics prohibits simply replicating qubits. Thus, in quantum error correction, the state of a logical qubit is spread across multiple physical qubits. This redundancy allows for the detection and correction of errors that might occur in individual physical qubits, thereby preserving the overall integrity of the quantum information and substantially reducing the error rate.

What is the No-Cloning Theorem in Quantum Mechanics?

The no-cloning theorem, a key principle in quantum mechanics, asserts that the exact duplication of an unknown quantum state is impossible. In classical computing, by contrast, data can be precisely cloned. This poses challenges in quantum computing, especially for error correction, as traditional methods relying on data replication are inapplicable.

Conversely, in quantum communications, the theorem enhances security: any attempt to copy quantum states used in cryptographic keys becomes detectable due to the unavoidable disturbance caused by measurement, providing robust protection against eavesdropping.

With logical qubits, we can begin to tap into the real potential power of quantum computers. By grouping several physical qubits to form a single logical qubit, quantum error correction introduces a level of fault tolerance. If one or more of the physical qubits undergoes an error, the overall state of the logical qubit can still be preserved and determined based on the state of the remaining, unaltered physical qubits. This approach significantly enhances the stability and reliability of quantum computers, enabling them to perform more complex and longer computations without succumbing to errors. Generally speaking, the more physical qubits make up each logical qubit, the lower the error rate is.

The field of logical qubits and quantum error correction is still an ongoing area of research, however. Questions remain about the most efficient error correction codes, the optimal ratio of physical to logical qubits, and the practical challenges of implementing these systems. Researchers continue to explore various strategies and designs to maximize the effectiveness of logical qubits.


Are We Entering the Logical Qubit Era?

Despite these challenges, recent results like those from Harvard University (in collaboration with QuEra Computing, MIT, NIST and UMD) mark the beginning of the logical qubit era. Harvards achievement in performing complex, error-corrected quantum algorithms on 48 logical qubits represents a significant milestone in quantum computing, as previous reports demonstrated only one, two, or sometimes three logical qubits. This advancement not only demonstrates the technology’s feasibility but also brings us one major step closer to realizing quantum computers that are truly useful and impactful. This work is now the basis of new, error-corrected quantum computers.

IBM and Harvard/QuEra also demonstrated that more efficient logical qubits (i.e., requiring fewer physical qubits) can be constructed if each physical qubit can interact with a greater number of nearby qubits. This is significant because, with this implementation, a machine with a certain number of physical qubits can support more logical qubits, enabling it to perform more complex calculations than would be possible with fewer logical qubits.

In the context of building practical quantum computers, the question of how many logical qubits are necessary to achieve truly useful applications is crucial. According to the Microsoft paper Assessing Requirements to Scale to Practical Quantum Advantage, the number of logical qubits required for impactful quantum applications varies depending on the specific use case. For instance, tasks such as simulating complex chemical processes or solving large-scale optimization problems may require hundreds to thousands of logical qubits. The paper provides a framework for estimating the quantum resources needed for various applications, taking into account factors such as error rates and computational complexity.

This research underscores the importance of continuing to develop scalable and robust logical qubit architectures, as reaching the necessary number of logical qubits is key to unlocking the transformative potential of quantum computing. In a few years, users probably won’t care how many physical qubits a quantum computer has — just like they don’t care how many transistors make up the newest phone — but rather focus on the number of logical error-corrected qubits. This is because the number of error-corrected logical qubits determines the complexity and depth of the calculations that can be performed, regardless of how a logical qubit is constructed from physical qubits.

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The Logical Qubit May Unlock Quantum Advantage

The transition to the logical qubit era is a critical development in the quest to harness the full power of quantum computing. By addressing the fundamental challenge of error correction, logical qubits pave the way for more reliable, stable, and practical quantum computers. As research in this area continues to advance, we can expect quantum computing to start making significant contributions to various fields, including drug discovery, optimization problems, artificial intelligence, and beyond. The era of logical qubits is not just a scientific milestone; its a harbinger of the transformative potential that quantum computing holds.

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