Quantum Algorithms That Could Change the World Entirely

In 1935, Albert Einstein described in a letter quantum entanglement, one of the strangest foundations of quantum computing, rather brilliantly as “spooky action at a distance.”

Scientists obviously lean toward precision, but here, the word spooky feels almost folkloric or mythical, like something whispered around a campfire.

Its cadence is short, jagged, and almost childlike. Easy to say, yet heavy with unease. You can hear it in a kind of Werner Herzog fatalistic sort of way: stark, unblinking, acknowledging that the universe harbors mysteries so profound they brush against dread.

Quantum Beginnings

For decades, physicists wrestled with the strangeness of a world where particles could be in two places at once, or influence each other instantly across space, a paradox that later became central to discussions of quantum advantage.

And yet, in the quiet corners of academia, this new idea began to emerge. By the 1980s, figures like Yuri Manin in Moscow and David Deutsch at Oxford proposed something audacious: if the universe itself is quantum, perhaps the most natural way to compute is to follow its quantum rules.

Deutsch coined the term “universal quantum computer”. In 1985 he argued that because physical reality is quantum-mechanical, a universal computing device must be able to go beyond classical Turing machines and operate based on quantum theory.

This planted a seed and that seed began to sprout in 1994.

Peter Shor, a mathematician at Bell Labs, published an algorithm that shocked the world of cryptography. Around the same time, another mathematician, Lov Grover, proposed an algorithm for searching unsorted data. 

Now, as companies like QuantumBasel, IBM, Google, IonQ, Rigetti, D-Wave, Xanadu, Pasqal, Quantinuum, and a rising class of startups, coax increasingly stable qubits into action, the promise of practical quantum computing becomes tantalizing. 

So here’s the question: which quantum algorithms matter? Which ones are marketing spin? And which ones might just, if roadblocks don’t get in the way, actually alter the way the world works?

Shor’s Algorithm: The Threat That Sparked a Race

Cryptography is built on hardness. RSA encryption, the system guarding everything from emails to bank transactions, relies on the difficulty of factoring large numbers. For example, on classical computers, factoring a 2,048-bit number would take longer than the age of the universe.

Then came Peter Shor. In 1994, he showed that a quantum computer could solve this task in “polynomial time”. To you and me, this means the bigger the number gets, the time a quantum computer needs to crack it goes up in a manageable way.

Security experts realized the foundations of digital trust could collapse if this ever occurred. Governments took notice and funding for quantum computing began to surge.

According to the thinktank Center for Data Innovation, the U.S. interest in the tech publicly spawned in the 90s when the National Institute of Standards and Technology (NIST), Department of Defense (DOD), and National Science Foundation (NSF) held their first workshops on quantum.

SRI International, the former Stanford Research Institute, reports that public funding for quantum research and innovation globally is now estimated at $44.5 billion.

Shor’s algorithm was never run at full scale because today’s quantum machines remain far too small. But the threat is real enough that a huge amount of investment is going into new systems resistant to quantum attack.

You could say that Shor’s algorithm did more than unsettle cryptographers. It gave quantum computing a purpose. Suddenly, building these machines was urgent.

Grover’s Algorithm: The Elegant Shortcut

Lov Grover’s 1996 discovery was less dramatic than Shor’s but equally groundbreaking. His algorithm tackled the classic search problem of finding an item in an unsorted database of N entries, doing so in roughly √N steps (a speedup that, while not exponential, remains profoundly important).

Imagine a pharmaceutical company searching through billions of molecular structures for a promising drug candidate or a logistics giant optimizing thousands of delivery routes. Grover’s algorithm offers a promising shortcut through complexity, a sort of way to prune the haystack before hunting for the needle.

Grover’s method can accelerate problems reducible to search, which includes optimization, pattern recognition, and even machine learning. While it may not grab headlines like Shor’s, Grover’s algorithm is likely to make its way into countless industries once hardware matures.

VQE and QAOA: The Algorithms for the Noisy Present

While Shor and Grover’s algorithms demand future, error-corrected quantum computers, those machines have not reached their powerful potential. Yet. Enter the variational algorithms for this noisy middle stage of quantum development.

They are clever hybrids that use today’s quantum processors alongside classical computers to get useful results.

The Variational Quantum Eigensolver (VQE), introduced in 2014, often tackles one of the hardest tasks in science: simulating molecules. You can read a full study on the topic here.

Classical supercomputers struggle with even modest molecules because the quantum interactions scale exponentially. VQE uses a quantum processor to approximate solutions, with a classical computer optimizing parameters.

This hybrid approach has already been tested by major pharmaceutical companies to model simple molecules like lithium hydride and hydrogen chains. Read about the study here on arxiv.

The Quantum Approximate Optimization Algorithm (QAOA) also targets optimization tasks and is often employed in combinatorial optimisation. It aims for “good enough” solutions faster than classical methods, offering big cost savings. Unlike Shor’s or Grover’s, such algorithms favor practicality and can work on today’s machines.

Harrow–Hassidim–Lloyd: The Algorithm AI Is Waiting For

In 2009, Aram Harrow, Avinatan Hassidim, and Seth Lloyd introduced what’s now called the HHL algorithm, a quantum method for solving linear systems of equations.

At the time, the revelation prompted MIT News to declare that “quantum might actually be useful.”

It’s interesting for AI because AI is basically math at scale. Training a neural network, making predictions, or finding patterns in data all come down to two big jobs: search and optimization, and linear algebra. It was found that the HHL algorithm may be able to solve those math problems much faster than a normal computer.

If the tech is realized, this algorithm would likely supercharge artificial intelligence, climate modeling, financial forecasting, and more. But like Shor’s, it demands hardware beyond what exists today. Still, its existence suggests an exciting and possible intense future.

Quantum Challenges

Quantum operations might be dazzling, but the obstacles are also pretty stubborn, we have to admit.

At the heart of the center of everything quantum are the qubits. They are to quantum what bits are to classical computers. They give quantum computers their extraordinary potential power. But they’re also ridiculously fragile. And today’s best quantum computers still need more qubit power.

Some say many of the world-changing algorithms will demand millions of qubits. However, in September 2025, researchers reported a new quantum supremacy in a preprint titled “Demonstrating an unconditional separation between quantum and classical information resources”.

IBM has a roadmap to build100,000-qubit systems by 2033. Google first claimed to demonstratequantum supremacy in 2019, showing a quantum processor outperforming the world’s best supercomputers. Startups are experimenting with exotic qubit designs, from trapped ions to topological states, each claiming a pathway to scalability, so progress and the will to make quantum work is undeniable.

Why Quantum Matters?

Quantum algorithms aren’t just academic puzzles in computer science. They hint at transformations across nearly every sector. They exploit the unique properties of the quantum state in ways that classical algorithms cannot:

• Cybersecurity: Shor’s quantum circuit could force a global shift to quantum-safe encryption.
• Healthcare: VQE could shorten drug discovery timelines from decades to years.
• Energy: QAOA might optimize power grids for efficiency and resilience.
• Finance: HHL and Grover could sharpen risk models and trading strategies.
• Climate: Quantum simulations could model Earth’s systems with unprecedented fidelity.

The economic stakes are staggering. A 2022 report by McKinsey estimated that quantum computing could create trillions in value by 2035, with early movers in pharma, chemicals, and finance poised to benefit most.

For computer science, this is not just theory but a frontier where quantum state manipulation and quantum circuit design promise to outpace the reach of classical algorithms, solving problems previously thought impossible.

That said, it’s tempting to believe that quantum will deliver breakthroughs everywhere. And indeed, startups and corporations frequently frame quantum as a near-universal accelerator.

But many of these industries don’t yet map cleanly onto today’s quantum hardware. Current devices are noisy, error correction is still years away, and many algorithms might lose their theoretical speedups once you factor in data preparation.

Names Who Paved the Way for Quantum

While Shor and Grover are household names in quantum circles, others shaped the field in quieter ways.

• Richard Feynman is often considered the one who brought the idea of quantum mechanical systems to the fore. Overshadowed in some areas of the industry by Shor/Grover, but foundational.
• Yuri Manin, a Russian mathematician, may have been the first to suggest quantum computers in 1980, years before Deutsch.
• David Deutsch developed the concept of the universal quantum computer in 1985.
• Paul Benioff at Argonne National Laboratory described a quantum Turing machine in 1981, the earliest concrete model of quantum computation.
• Charles Bennett, an IBM researcher, co-invented quantum cryptography with Gilles Brassard.
• Arthur Ekert introduced entanglement-based quantum cryptography in 1991.
• Love Grover is known for Grover’s algorithm, but also developed quantum database search methods.
• Peter Shor is famous for Shor’s algorithm, but less known is his foundational work on quantum error correction.
• Seth Lloyd, a theorist at MIT, pushed quantum algorithms into new domains from communication to machine learning.
• John Preskill coined the term “quantum supremacy” and developed key ideas in fault-tolerantquantum error correction. Preskill’s role is foundational but often behind the scenes.

The Future of Quantum Computing

Quantum’s influence is clearly seeping from academic pages into the modern world. Governments are funding national initiatives. The European Union has launched its Quantum Europe Strategy.

Universities are producing graduates fluent in quantum information theory. Startups are building prototype machines with potential applications across fields from secure cryptosystems to modeling differential equations.

At QuantumBasel, we are providing neutral multi-vendor quantum hardware access, hybrid quantum and AI solutions, and training to accelerate adoption and real-world use cases.

But the algorithms are the compass in this journey. They tell us where the machines must go and why they matter. Without them, quantum hardware would be little more than expensive curiosities. With them, they could be a tool to reshape how humanity solves its hardest complete problems and reveals the power of quantum computation.

As Deutsch wrote nearly 40 years ago, a universal quantum computer could simulate any system in nature. That vision, once obscure, is now edging closer to reality.

And when it arrives, efficient quantum algorithms, whether designed for a novel search algorithm or to reduce computational complexity, may transform everything from drug discovery and quantum chemistry to AI powered by quantum machine learning. The algorithms conceived in chalk on blackboards decades ago may massively change the world.