The field of quantum computing is advancing rapidly, with two key milestones referred to as **quantum supremacy** and **quantum advantage**. But what do these terms actually mean and what’s the difference between them?

**Defining Quantum Supremacy**

**Quantum supremacy** refers to the point where a quantum computer can carry out a task that is practically impossible for even the most powerful classical supercomputer.

More specifically, quantum supremacy is achieved when:

- A quantum computer successfully performs a specific computational task
- The same task cannot be performed in a reasonable amount of time by any classical (non-quantum) computer, no matter how powerful

The key word here is **practically**. Quantum supremacy does not mean quantum computers are “supreme” in all forms of computation. Rather, it indicates quantum computers can beat the best classical computers at certain tasks.

**Origins of the term “Quantum Supremacy”**

The concept of quantum supremacy was first proposed in 2012 by John Preskill, a theoretical physicist at Caltech. Here’s a quick excerpt from Preskill’s paper:

“Quantum computers, if large enough, would be capable of performing computations beyond the reach of any classical computer. We propose a set of criteria for achieving quantum supremacy, and argue that the task of performing such a computation is within the reach of existing quantum hardware.”

The specific term **“quantum supremacy”** was coined by Preskill to describe the milestone of having a quantum computer cross this threshold.

**Google’s Quantum Supremacy claim**

In October 2019, Google made headlines when it announced its 53-qubit quantum computer named Sycamore had achieved quantum supremacy.

Specifically, Google claimed Sycamore took 200 seconds to perform a randomized benchmarking task that would take the world’s most powerful supercomputer 10,000 years to complete. This announcement was published in the journal Nature.

However, IBM disputed Google’s claim, arguing that the benchmark was flawed and a classical computer could actually perform the task much faster than Google estimated.

So while Sycamore’s feat was a major milestone, there is still debate around whether it constitutes true quantum supremacy. The quest continues!

**Why is quantum supremacy important?**

Demonstrating quantum supremacy is a key milestone because it proves quantum computers can beat classical computers at certain tasks. This has major implications for fields like:

- Cryptography – Shor’s algorithm allows quantum computers to easily crack encryption codes used today
- Quantum simulation – Modeling molecular interactions far beyond classical capabilities
- Optimization – Finding optimal solutions for logistics, financial modeling, machine learning, and more

Quantum supremacy shows these applications are possible using quantum machines. It opens the doors to real-world quantum advantage.

**What is Quantum Advantage?**

The next milestone beyond quantum supremacy is referred to as **quantum advantage**.

While supremacy is about beating classical computers at specialized tasks, **quantum advantage is about quantum computers solving real-world problems better or faster than classical computers**.

Some examples of potential quantum advantage include:

**Material science**: Discovering new materials for batteries, solar cells, medicines, etc**Logistics**: Finding optimal routes and schedules for fleets like airlines and parcel delivery**Financial modeling**: Complex risk analysis, portfolio optimization, derivative pricing, and more**Machine learning**: Pattern recognition, classification, and clustering on very complex datasets

To achieve quantum advantage for these applications, stability and scaleability will be key. So supremacy experiments on small proof-of-concept computers will need to translate to real performance gains on larger machines.

**NISQ era vs fault tolerant quantum computing**

To understand the path to quantum advantage, we need to distinguish between two eras of quantum computing hardware:

**NISQ era**

The **Noisy Intermediate Scale Quantum (NISQ) era** refers to today’s state-of-the-art quantum computers with around 50-100 qubits. NISQ devices are very prone to errors and can only run small, simple algorithms before losing coherence. But they are already entering major research institutions and some businesses. Quantum supremacy will emerge in the NISQ era.

**Fault tolerant era**

The **fault tolerant era** will follow, likely in the late 2020’s or 2030’s, with much more advanced error corrected qubits. At this stage we’ll see quantum computers that can maintain stability for long complex computations on 1000’s of logical qubits. This will enable quantum advantage breakthroughs across many industries like finance, medicine, AI, and more.

So in summary:

**Supremacy**: Possible now with NISQ machines**Advantage**: Requires future fault tolerant computers

**Recent developments toward quantum advantage**

While fullfault tolerant quantum computers are still some years away, researchers arealready starting to demonstrate elements of quantum advantage on NISQhardware. Here are some examples from 2021 and 2022:

**Quantum machine learning**: In March 2021, IonQ ran a quantum algorithm for principal component analysis (PCA) on its trapped ion quantum computer. PCA is an important machine learning technique for pattern recognition. The researchers demonstrated a clear quantum advantage over leading classical algorithms – both in accuracy and running time.**Quantum simulation**: Researchers at Harvard and MIT simulated the binding energy of a water molecule on a 27-qubit trapped ion device made by Quantinuum. This small simulation matched state of the art classical results, demonstrating potential for modeling useful chemical systems.**Quantum algorithms**: In March 2022, researchers from UC Berkeley, AWS, and Caltech published results showing quantum algorithms outperformed classical techniques for eigenvalue estimation – an important component in many applications like machine learning and optimization. They tested on quantum processors from IonQ, Rigetti, Oxford Quantum Circuits, and others.

These are all small examples but important steps toward real-world quantum advantage.

**When will we reach quantum advantage?**

Most experts predict quantum advantage is still some years away, likely in the late 2020’s. And it will emerge gradually over time, rather than a single “Eureka!” moment.

Barriers to overcome include:

- Hardware challenges – Improving qubit count, coherence times, and gate fidelities
- Identifying “killer apps” – Finding commercially valuable use cases that play to quantum’s strengths
- Algorithms and applications research – Continuing to develop novel quantum techniques

As hardware and software continue rapidly maturing, we should see some initial glimpses of quantum advantage this decade. But widespread impact likely awaits the arrival of fault tolerant quantum computers.

**Quantum advantage vs exponential speedup**

One final distinction worth noting is **quantum advantage vs exponential speedup**:

**Quantum advantage**means achieving practical performance gains over classical hardware for real-world problems. These gains may be only 2-4x faster in some cases.**Exponential speedup**refers to asymptotic improvements in computational complexity and runtime. For example, Grover’s search algorithm has quadratic speedup and Shor’s algorithm achieves exponential speedup relative to the best known classical approaches.

Early quantum advantage will be modest – perhaps shaving hours off a process rather than achieving 100,000x speedup. But over time, as hardware scales, certain applications should achieve exponential improvements.

**The road ahead**

Quantum computing is advancing rapidly and we’re on the path from quantum supremacy to practical quantum advantage. But it will likely take until the late 2020’s before quantum computers start making an impact outside research labs. In the years ahead, businesses across many industries are laying the foundations to be “quantum ready” – preparing applications, building skills, and exploring partnerships. Exciting times are ahead!

**Conclusion**

Quantum supremacy and quantum advantage are two eagerly anticipated milestones on the quantum computing roadmap. Supremacy will demonstrate quantum computers can beat classical supercomputers at niche tasks. This is close to being achieved with the latest 50-100 qubit systems. The more valuable goal is quantum advantage – where quantum systems solve highly complex real-world problems intractable for classical computers. This likely remains some years away, awaiting the emergence of fault tolerant quantum computers.

**FAQs**

**What was the Sycamore computer that Google built?**

Sycamore was a 53-qubit quantum processor developed by Google in 2019. Google claimed it achieved quantum supremacy by using Sycamore to perform a randomly sampling task in 200 seconds that would take 10,000 years on the world’s most powerful supercomputer. However, IBM disputed Google’s benchmark and said a classical computer could actually perform the task much faster than estimated.

**When did John Preskill first propose the concept of quantum supremacy?**

The concept of quantum supremacy was first proposed in 2012 by John Preskill in a paper titled “Quantum Computing and the Entanglement Frontier.” Preskill defined quantum supremacy and argued that achieving it was within reach of near-term quantum hardware.

**What are some examples of potential quantum advantage applications?**

Some examples of potential real-world quantum advantage applications include:

- Material science – Discovering new materials for batteries, solar cells, etc
- Logistics – Optimized routing and scheduling for delivery fleets
- Financial modeling – Complex risk analysis and portfolio optimization
- Machine learning – Pattern recognition on very large, complex datasets

**What hardware improvements are needed to achieve widespread quantum advantage?**

The key hardware improvements needed are:

- Increased qubit counts
- Longer coherence times
- Lower gate error rates
- Full implementation of quantum error correction

These improvements will emerge with the arrival of fault tolerant quantum computers, likely in the late 2020s/early 2030s. This will enable the stability and scalability required for commercial quantum advantage.

**What is the difference between quantum advantage and exponential speedup?**

Quantum advantage refers to any practical performance gains over classical systems for real-world applications. Exponential speedup describes asymptotic improvements in computational complexity, e.g. Grover’s algorithm has quadratic speedup and Shor’s achieves exponential speedup. Early quantum advantage may offer modest gains, but over time certain applications will achieve exponential speedup.

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