Solving the Max-Cut optimization problem using a method called the QUBO formulation. Today, we’re going to take a different approach and explore how quantum computing can be used for real-world problems.
First, we’ll talk about how we decide which problems might actually benefit from quantum computing. Not every problem needs a quantum solution, so it’s important to understand when quantum computers can be helpful. Then, we’ll look at some recent examples of how people in the quantum computing community have used these ideas in different fields.
By the end of this lesson, you’ll start to get a feel for what kinds of problems quantum computers can solve and how researchers approach them.
Classical vs. quantum difficulty
Understanding Problem Difficulty in Computing
Before we dive into examples, let's first talk about how we classify problems based on their difficulty. Some problems are easy and can be solved quickly with regular (classical) computers. For these, we don’t need quantum computers. But there are also problems that are extremely hard—so hard that even the most powerful classical computers struggle with them. This is where quantum computers might help.
One famous example of a hard problem is finding the prime factors of a huge number (breaking a number into smaller numbers that multiply together to make it). This is important because RSA encryption, which keeps online data secure, relies on how difficult this problem is. However, a quantum algorithm called Shor’s algorithm can solve it much faster than classical computers.
Another example is searching for something in an unsorted list—like finding one specific book in a huge, messy library. Normally, you’d have to check one book at a time, but a quantum algorithm called Grover’s algorithm can speed up the process.
However, most experts believe that for these quantum algorithms to work well, we need error correction—a way to fix mistakes in quantum computers. Right now, the technology isn’t advanced enough.
The "Sweet Spot" for Quantum Computers
So, what kinds of problems can today’s quantum computers actually solve? We’re looking for problems that are too hard for classical computers but not impossible for current quantum computers—problems in the "sweet spot" between easy and extremely hard.
Understanding Complexity Classes
To better understand which problems quantum computers can solve, we look at computational complexity theory—a field of computer science that sorts problems into different categories based on their difficulty. Here are some important ones:
P (Polynomial time): These are easy problems. They can be solved quickly as they get bigger.
NP (Nondeterministic Polynomial time): These problems are harder. They might not be solved quickly, but if someone gives you the answer, you can check it quickly.
NP-complete: These are some of the hardest problems in NP. Examples include the Traveling Salesman Problem (finding the shortest route between cities) and Sudoku.
BPP (Bounded-error Probabilistic Polynomial time): These are problems that classical computers can solve using random guessing, but with a small chance of being wrong.
When quantum computing was developed, scientists wanted to know what kinds of problems quantum computers could solve better than classical ones. They came up with a new category:
BQP (Bounded-error Quantum Polynomial time): These are problems that quantum computers can solve efficiently (in polynomial time) with a small chance of error. BQP is like the quantum version of BPP.
Why This Matters
Understanding these categories helps scientists figure out what quantum computers are good for. Right now, quantum computers aren’t powerful enough to solve the hardest problems, but they could be useful for problems that classical computers struggle with. As technology improves, quantum computing might change the way we solve complex problems in science, finance, and security.
Application Areas and Use Cases
How Quantum Computers Can Be Useful
Quantum computers have the potential to solve problems that regular computers struggle with. Right now, scientists are exploring three main areas where quantum computing might have a big impact:
1.Nature Simulations
- Scientists use computers to simulate atoms and molecules, but regular computers aren’t very good at it. Quantum computers, however, can do this much more efficiently.
- This could help in creating better batteries, capturing carbon dioxide to fight climate change, and even developing new medicines.
- Some special quantum algorithms used in this area are:
VQE (Variational Quantum Eigensolver): Helps find the most stable energy states of materials.
TDS (Time Dynamics Simulation): Helps understand how materials react to different conditions.
SQD (Sample-based Quantum Diagonalization): A new technique that might become important soon.
2.Optimization
- Many real-world problems involve choosing the best solution from many possibilities—this is called optimization.
- Quantum computers could help in finance (choosing the best investments), designing better products, and improving supply chains (like making deliveries faster and cheaper).
- A key algorithm here is QAOA (Quantum Approximate Optimization Algorithm), especially used in finance.
3.Quantum Machine Learning (QML)
Machine learning is when computers learn from data, and quantum computers might make this even more powerful.
Quantum machine learning could help with language translation, spotting fraud in banking, and analyzing internet traffic.
Some important algorithms in this area are:
QSVM (Quantum Support Vector Machine): Helps classify and analyze data.
QNN (Quantum Neural Networks): Inspired by how the human brain works.
QGAN (Quantum Generative Adversarial Networks): Used for creating realistic data, like images or patterns.
Teamwork in Quantum Computing
Because quantum computing is so complex, people work together in different working groups to focus on specific topics. IBM has created teams to study:
- Healthcare & Medicine
- New Materials & Supercomputing
- High Energy Physics (like studying space and tiny particles)
- Optimization (solving business problems more efficiently)
- Sustainability (helping the environment)
Even though quantum computing is still developing, scientists are already solving interesting problems. If you’re curious, you can read research papers on these topics and start learning how quantum computers work!
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Use Case 1: Simulating hadron dynamics
First, we're going to delve into a paper by Martin Savage's group at the University of Washington called Quantum Simulations of Hadron Dynamics in the Schwinger Model Using 112 Qubits.
Exploring Quantum Simulations of Hadron Dynamics
Today, let's talk about an interesting scientific experiment by Martin Savage’s research team at the University of Washington. They used a quantum computer to study tiny particles called hadrons in a simplified model known as the Schwinger model.
What Are Hadrons?
Hadrons are tiny particles made up of even smaller particles called quarks. The most well-known hadrons are protons and neutrons, which make up the nucleus of atoms. You might have heard of the Large Hadron Collider (LHC), a massive machine that smashes particles together to help scientists understand the universe.
Scientists hope that, in the future, quantum computers will be able to fully simulate how particles behave in these experiments. We’re not there yet, but we're making progress!
What is the Schwinger Model?
The Schwinger model is a simplified way to study particle interactions. It focuses on electrons and positrons (a type of antimatter) interacting in a world with just one space dimension (instead of the three we are familiar with). Even though it's simpler, it shares similarities with quantum chromodynamics (QCD), the theory that explains how quarks stick together inside hadrons. Since QCD is too complex to simulate directly, scientists use models like Schwinger’s to test ideas.
Why Did Scientists Think Quantum Computers Could Handle This?
Quantum computers can struggle with long-range interactions between qubits (quantum bits). But in the Schwinger model, particles interact mostly with their nearby neighbors, meaning the quantum computer doesn’t need to manage too many long-range interactions. This makes the problem more manageable for today’s quantum devices.
How Did They Run the Experiment?
1.Prepare the Ground State → The scientists started by creating a "vacuum state" (a state with no particles).
2.Create a Wave Packet → They introduced hadrons by pairing particles and antiparticles at different locations. By carefully arranging these, they formed a moving "wave packet."
3.Let It Evolve → They let the wave packet move forward in time, just like particles moving in a real experiment.
4.Measure the Results → Finally, they measured key properties to understand how the hadrons behaved.
How Did They Make It Work on a Noisy Quantum Computer?
Quantum computers today are still noisy, meaning they make errors. To reduce errors, the scientists used several techniques, including:
Dynamical decoupling → A method to keep qubits stable longer.
Zero noise extrapolation → A way to estimate what the result would be if there were no errors.
Pauli twirling → A technique to make errors more predictable.
Operator decoherence renormalization → A new method for dealing with quantum noise.
The experiment was run on an IBM Quantum Heron device, which is one of IBM’s latest quantum computers.
Why Does This Matter?
High-energy physics is one of the most exciting fields of science. Scientists built the LHC, spending billions of dollars, to explore the fundamental nature of reality. By using quantum computers, researchers hope to simulate these experiments instead of always having to run costly real-world tests. Even though we are only in the early stages, these experiments are pushing the limits of what quantum computers can do!
Above is a figure from the paper showing the observable of interest, the chiral condensate, which is basically a superfluid phase of the hadrons. Now, we can see the wavepacket at the center of the sites that have been designated to run this experiment. The black lines are the error-free results from the (computationally expensive) classical simulation, while the points with error bars are the results from the 133-qubit IBM quantum computer, Torino.
We see two different time steps in the wavepacket evolution. At time t=1, you can see that the chiral condensate is narrow and localized, and it also matches the classical simulation well. At t=14, it is much more spread out. The comparison to the simulator isn't quite as perfect now, but you can still obviously see very good agreement between theory and data, which is encouraging.
In conclusion, this is a very cool example of the type of simulation work you might not initially think of applying quantum computing to, but which shows real promise. It's not perfect but you don't have to be a particle physics expert to see that the quantum computer accurately predicts the outward propagation of the wavepacket, which is exactly what we would expect to find. Hopefully future work in this area will continue and high energy physicists will continue to find ways to incorporate quantum computing into their workstreams. The aim is to solve difficult theoretical problems more precisely and use experiments to accept or reject theories in hopes of discovering new physics, building improved detectors, and leading to a better understanding of nature at its most fundamental level.
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