Why are physical qubits and logical qubits different in quantum computing?

Physical qubits are the actual hardware components, which are prone to errors and have short coherence times. Logical qubits are an abstraction, representing error-corrected qubits created from many physical qubits, which are ideal for computation but require significant overhead.

How many qubits are needed for a quantum computer to be commercially useful?

Estimates suggest that a few hundred to a few thousand logical qubits would be sufficient to solve commercially interesting problems faster than classical computers. This would likely require hundreds of thousands to millions of physical qubits due to error correction needs.

How can quantum computers break current encryption methods like RSA?

Quantum computers, specifically using Shor's algorithm, can efficiently factor large prime numbers. This ability directly breaks RSA encryption, which relies on the difficulty of factoring large numbers for its security, potentially reducing cracking times from trillions of years to days or seconds.

What are the most promising real-world applications for quantum computers?

The most promising applications include quantum chemistry for developing new materials and drugs, finance for portfolio optimization and risk analysis, and logistics for solving complex routing and location problems. Code-cracking is also a significant, though potentially disruptive, application.

Can quantum computers help solve climate change or improve weather forecasts?

While quantum computers could indirectly aid climate change efforts through better materials for energy storage or carbon capture, they are not suited for running climate or weather models directly. This is because these models involve non-linear equations, while current quantum computers primarily solve linear problems.

When might we see practical applications of quantum computing?

The speaker is skeptical about widespread impact in the next few decades due to the difficulty of error correction. However, quantum chemistry is considered a likely early application once sufficiently stable and numerous logical qubits are available.

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Quantum Computers Could Solve These Problems

Sabine Hossenfelder

Science & Technology4 min read24 min video

Apr 22, 2023|349,634 views|14,840|1,364

quantum computing physics quantum physics quantum computer what is a quantum computer good for quantum computing applications quantum quantum mechanics quantum technology quantum tech hossenfelder science without the gobbledygook

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Key Moments

TL;DR

Quantum computers promise real breakthroughs in specific areas but face significant hurdles before widespread use.

Key Insights

Quantum computers utilize qubits in superposition and entanglement for faster computation on certain problems, unlike classical computers.

The development of practical quantum computers requires a massive number of physical qubits to create fewer, error-corrected logical qubits.

Potential applications include code-breaking (RSA), quantum chemistry for material/drug discovery, financial modeling, and logistics optimization.

Quantum computers excel at linear problems; they are not suitable for non-linear problems like climate or weather modeling.

Significant challenges remain in error correction and scalability, making widespread impact in the near future uncertain.

The transition to quantum-safe cryptography is expected to precede the widespread use of quantum computers for code-breaking.

UNDERSTANDING QUANTUM COMPUTING FUNDAMENTALS

Quantum computers operate on quantum bits (qubits) which, unlike classical bits (0 or 1), can exist in superpositions. This allows them to represent and process a vast number of states simultaneously. Entanglement, another quantum phenomenon, further enhances their computational power. Physical operations on these qubits, governed by quantum mechanics, enable solutions to specific mathematical problems that are intractable for conventional computers. The ability to compute with these non-existent states, as described by wave-functions, is central to their advantage, though observed results are single basis states due to measurement collapse.

PHYSICAL VS. LOGICAL QUBITS AND ERROR CORRECTION

The practical realization of quantum computing hinges on the distinction between physical and logical qubits. Physical qubits are the actual hardware components, which are prone to errors and decoherence, meaning their quantum states decay rapidly. Logical qubits, on the other hand, are error-corrected idealizations. Creating a single logical qubit requires a significant number of physical qubits, akin to the many support staff needed for a flawless film shoot. This overhead for error correction is a major hurdle, as current quantum devices are far from achieving the hundreds or thousands of logical qubits needed for commercially relevant problems.

ECONOMIC INTEREST AND INVESTMENT IN QUANTUM COMPUTING

Despite the hype, significant investment from governments and tech giants like Google, IBM, and Microsoft, along with financial institutions such as Goldman Sachs and JPMorgan, underscores the perceived potential of quantum computing. This heavy investment is driven by the anticipation of breakthroughs that could reshape industries. However, the speaker expresses skepticism about the near-term impact, citing the immense difficulty in controlling errors and the potential for companies to abandon projects if they become too costly before yielding significant returns.

CODE-CRACKING AND THE FUTURE OF CRYPTOGRAPHY

One of the most publicized applications for quantum computers is breaking encryption, particularly RSA, which relies on the difficulty of factoring large prime numbers. While a quantum computer with a few thousand logical qubits could potentially break current RSA keys in days or seconds, this capability is still distant. Importantly, new quantum-safe cryptographic protocols are being developed and are likely to be implemented widely before quantum computers become powerful enough to pose a significant threat to existing encryption, mitigating some of the most dramatic feared consequences.

QUANTUM CHEMISTRY AND MATERIAL SCIENCE ADVANCEMENTS

A more grounded and likely near-term application of quantum computing lies in quantum chemistry. By simulating the behavior of atoms and molecules, quantum computers can predict their properties, such as optical, electrical, and chemical behavior, by solving the Schrödinger equation. This capability could revolutionize the development of new materials, like superconductors or battery components, and aid in drug discovery by efficiently testing molecular interactions and toxicity without the need for extensive physical synthesis and experimentation.

FINANCIAL MODELING AND LOGISTICAL OPTIMIZATION

The financial sector anticipates using quantum computers for complex optimization problems, such as portfolio management and option pricing, which are computationally intensive for classical systems. Similarly, logistics applications, like the traveling salesman problem or vehicle routing, could benefit from quantum speedups in finding optimal routes and resource allocation. These improvements could lead to more efficient supply chains, reduced costs, and environmental benefits, although such optimizations are often tackled with hybrid classical-quantum approaches rather than purely quantum ones.

MISCONCEPTIONS AND THE LIMITATIONS OF QUANTUM COMPUTING

It's crucial to distinguish between realistic applications and overhyped claims. Quantum computers are not expected to offer better graphics or faster general internet speeds. While they can indirectly aid in addressing climate change by optimizing energy storage or material efficiency, they are not suitable for running climate or weather models directly because these involve non-linear equations. Furthermore, quantum computers are limited in their ability to output large volumes of data, making them ill-suited for tasks requiring extensive data processing like weather forecasting.

THE ROAD AHEAD: PRACTICALITY AND TIMELINES

The path to realizing the full potential of quantum computing is fraught with challenges, primarily concerning error correction and scalability. Estimates suggest a need for hundreds of thousands to millions of physical qubits to achieve the few hundred to thousand logical qubits required for impactful applications. While progress is being made, with companies like IBM pushing qubit counts, the ability to perform useful, error-corrected computations is still a significant bottleneck. The timeline for widespread commercial impact remains uncertain, with many experts, including the speaker, expressing skepticism about its realization within the next few decades.

Mentioned in This Episode

●Products

●Software & Apps

●Companies

●Concepts

●People Referenced

Common Questions

A qubit is the basic unit of quantum information, analogous to a bit in classical computers. Unlike classical bits which are either 0 or 1, qubits can exist in a superposition of both states simultaneously, allowing for more complex calculations.

Topics

AI & Machine Learning Technology & Innovation Science & Mathematics Quantum Computing Optimization Problems Quantum Chemistry

Mentioned in this video

Companies

Microsoft

A software giant working on quantum computing.

IBM

A company working on quantum computing and has released the Osprey chip with 433 qubits.

Wells Fargo

A bank investing in quantum computing.

Google

A software giant investing in quantum computing.

Goldman Sachs

A bank investing in quantum computing.

JPMorgan

A bank investing in quantum computing.

Digital Science

The owner of Overleaf, a platform for collaborating on LaTeX documents.

Concepts

traveling salesman problem

A classic optimization problem in logistics that seeks the shortest possible route to visit a set of destinations and return to the origin, difficult for classical computers.

superposition

A quantum mechanical principle allowing qubits to exist in multiple states simultaneously, crucial for quantum computation.

Wave function

In quantum mechanics, a mathematical description representing the state of a quantum system, which includes superpositions of basis states.

entanglement

A quantum phenomenon where qubits are linked, influencing each other instantaneously regardless of distance, contributing to quantum computing's power.

Facility Location Problem

An optimization problem in logistics focused on determining the optimal placement of facilities (e.g., warehouses) to serve a given set of customers.

Qubits

Quantum bits that quantum computers use for calculations, capable of superposition and entanglement.

post-quantum cryptography

Cryptographic protocols designed to be secure against attacks from both classical and quantum computers.

Schrödinger equation

The fundamental equation in quantum mechanics that describes how the quantum state of a physical system changes over time, crucial for understanding molecular properties.

Vehicle Routing Problem

A logistics problem that determines optimal routes for a fleet of vehicles to deliver goods or services to multiple locations.

Software & Apps

Overleaf

A collaborative platform for creating and editing LaTeX documents, sponsored by Digital Science.

Products

IBM Osprey chip

A quantum computing chip with 433 physical qubits developed by IBM.

People

Rivest, Shamir, and Adleman

The inventors of the RSA encryption algorithm.