# Logical Qubit

A Logical Qubit refers to a qubit that 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.

Logical qubits are central to quantum error correction schemes, where multiple physical qubits are entangled to encode a single logical qubit. This encoding allows errors in individual physical qubits to be detected and corrected without disturbing the information stored in the logical qubit. For example, a common encoding might use seven physical qubits to represent one logical qubit, allowing for the correction of certain types of errors.

Logical qubits are essential for building large-scale, fault-tolerant quantum computers. While current Noisy Intermediate-Scale Quantum (NISQ) devices often operate directly on physical qubits, future quantum computers will likely rely on logical qubits to perform complex computations accurately. By providing a layer of protection against errors, logical qubits enable more robust and reliable quantum information processing.

Implementing logical qubits requires significant overhead in terms of additional physical qubits and quantum gates. The complexity of encoding, error detection, and error correction introduces challenges in both hardware and algorithm design. Research into more efficient error correction codes, better physical qubits, and novel encoding schemes continues to be an active area of study, aiming to make logical qubits more practical and accessible.

Logical qubits represent a sophisticated approach to managing the inherent fragility of quantum information. They are a key concept in the ongoing development of quantum computing, bridging the gap between the theoretical promise of quantum computation and the practical challenges of building a quantum computer.

## What is a Logical Qubit?

The answers to a Stack Overflow question “What is the difference between a physical and a logical qubit?” highlight the need for a clear definition. And the simplest distinction of **logical qubit vs physical qubit **is that a logical qubit is a cluster of physical qubits. Within a **logical qubit quantum error correction** will be taking place among the physical qubits. During the execution of algorithms, errors among the noisy physical qubits will be automatically detected and corrected. Therefore, whereas individual physical qubits are too noisy to be useful, with a **logical qubit quantum computing** will become practical.

A Telsy article titled “The logical qubit and the correction of quantum errors” notes that this concept is modality agnostic. There is currently no perfect physical qubit, and therefore error correction remains essential. However, each modality has different properties, and these properties may allow for logical qubits to consist of different counts of physical qubits. For example, neutral atoms naturally maintain their coherence for relatively long times, and therefore may require relatively few atoms per logical qubit. This is important because the complexity of error correction will affect algorithm runtimes and the potential for computational speedups.

The ratio that is commonly given is that each logical qubit will require 1,000 physical qubits. An Everything Explained Today article titled “Physical and logical qubits explained” notes that topological qubits may require as few as one physical qubit per logical qubit. However, topological qubits are still theoretical. Among existing modalities, neutral atoms are among the highest quality.

It is also worth noting that neutral atoms are scalable. At the time this article is being published, the largest publicly-available quantum computer in the world is QuEra’s 256-atom “Aquila” device. Therefore, neutral atoms are a top contender for having enough physical qubits to actually start experimenting with logical qubits. The “logical qubits” of today use too few physical qubits and retain relatively high error rates, therefore they are really just progress toward logical qubits, as opposed to actually being logical qubits.

## The Need for Logical Qubits

Logical qubits are necessary because physical qubits are highly susceptible to errors. The calculations, even where dramatic speedups may be proven, are simply unusable. For quantum computation to eventually become useful, physical qubits will need significant error correction to bring error rates considerably lower than where they are today. And the extent of the overhead that will be required to do that will be packaged as a single logical qubit.

Beyond error rates, another issue is coherence, which is the duration that qubits can retain quantum information. There are algorithms that cannot run today because the physical qubits cannot maintain their quantum states long enough to complete all the operations that need to be performed. Another benefit of logical qubits is that they will be able to maintain their coherence for much longer times, and therefore allow execution of the algorithms that promise to deliver exponential computational speedups.

## Logical Qubits in Quantum Algorithms

To a quantum algorithm, a “Qubit” is an abstraction. It represents the fundamental unit of information without regard as to what it is. It might be a single physical qubit, or it might be a cluster of physical qubits, a logical qubit. It might be one modality, or it might be some other modality. The algorithms are only concerned with the quantum information.

An example of this agnosticism can be found today with qubit mapping. This is an issue with modalities that have limited connectivity, which is not an issue with neutral atoms because the atoms can be shuttled around. Imagine you want to perform operations on qubit0 and qubit2, but qubit1 is in between. The qubits to be operated on need to be connected, and so the states of qubit1 and qubit2 need to be swapped. This swap operation is quite error-prone. So, one solution to this is to map the user’s qubit2 to the physical qubit1. Qubit0 and qubit1 start off connected, and can be operated on without the swap operation, preventing the associated errors. At measurement time, the results of the physical qubit1 are shown to the user as qubit2.

One term being applied to this is “serverless,” although this term goes beyond mapping. The idea is that algorithm designers need only concern themselves with the high-level abstraction known as a “qubit.” Whether that qubit is one atom, a cluster of atoms, or anything else is irrelevant. What ultimately matters is solving real-world problems.