The mathematics of quantum-based cryptography, and why existing data is already at risk

Noise and instability made quantum computing seem out of reach for decades

Recent advances in error suppression, mitigation, and correction are allowing quantum computers to perform practical tasks that challenge classical machines. IBM’s 2016 launch of its first cloud-accessible quantum computer attracted over 22,000 users in its first month alone.

How quantum computers can empower Shor's algorithm to break digital encryption

Secure communications largely rely on numeric keys generated by multiplying two enormous prime numbers together, and it is computationally impractical to determine these primes by trying to divide by every possible one. While Shor's algorithm can provide better guesses for this brute-force approach, it relies on a number that is difficult to determine on classical computers but much easier to calculate using the simultaneous computations enabled by quantum superposition.

Quantum computers harness weird physics to explore unsolvable problems

Classical computers manipulate bits as either 0 or 1, but quantum computers use qubits to hold combinations of both, enabling new algorithms. This new approach could one day help with breakthroughs in medicine, chemistry, and AI.

Explore a visual guide to how quantum computers can crack RSA encryption

In 1994, Peter Shor introduced an algorithm that showed a quantum computer could efficiently factor the product of two very large prime numbers, undermining the mathematics that makes RSA so secure. While using larger keys can delay the decryption time of quantum computers, this solution increases the time it takes to encrypt data, which may become impractical.

The Majorana 1 chip may provide quantum computing using geometry-based qubits

Traditional quantum computers are incredibly fragile, with encoded information easily disrupted and requiring significant error correction systems. Microsoft’s approach involves storing data on a surface, which is more stable, but involves an elusive particle first theorized in 1938.

Quantum computers can simulate nature more effectively than classical computers

Ordinary computers struggle to simulate quantum fields due to entanglement, but systems built from those elements can model the complexity. Systems using particle in more than two states—qudits—have successfully modeled 2D electromagnetic fields and done so more efficiently.

Quantum computers use qubits to solve problems much faster than classical machines

Unlike regular computers, where each bit is either 0 or 1, quantum computers use qubits, which can simultaneously be both—allowing for massive parallel processing power. Google’s quantum processor once solved a problem in seconds that would have taken a supercomputer 47 years.

Qubits let quantum computers process massive datasets all at once

The quantum phenomena of superposition and entanglement enable qubits to act in 0 and 1 binary states simultaneously and influence each other instantly. These features give quantum computers incredible power, though keeping them stable is a major challenge.

One of five competing qubit technologies may usher in the quantum computing era

No winning qubit technology exists among photonic networks, superconducting circuits, spin qubits, neutral atoms, and trapped ions. Each has significant limitations and unique advantages, such as neutral-atom systems' ability to maintain quantum states for several minutes, far longer than the others.

Misunderstandings about how quantum computing works may have overhyped their ability

Quantum computers are often viewed as machines that can solve all problems instantly by trying every solution simultaneously. Instead, they amplify correct answers and cancel out wrong ones, which only works for specific kinds of problems with special structures.

Efforts to find Majorana particles may finally lead to reliable quantum computers

Though the particle—which is its own antiparticle—remains theoretical, scientists from Microsoft to Google continue developing systems to mimic this property towards building error-resistant quantum computers. Scientists at UCSB have been attempting to get the particle using just pencil lead and Scotch tape.

Lasers, semiconductors, medical imaging, and atomic clocks rely on quantum mechanics

Semiconductors, crucial in electronics, operate based on quantum superposition. Lasers use stimulated emission, a quantum process, and MRI machines leverage the quantum spin of hydrogen atoms for imaging. Atomic clocks measure time with unprecedented precision using quantum transitions.

Transistors in traditional computers are physically limited to atomic scales

As computer parts shrink, transistors—tiny switches that control the path of electrical signals—become obsolete because electrons can quantum tunnel through switch barriers. This makes quantum computers, which take advantage of quantum effects, an enticing alternative.

Superconducting qubits have become foundational to today’s quantum computing efforts

Relying on electrons experiencing no friction across metal, these qubits require extremely low temperatures and behave like artificial atoms. The first superconducting qubit, invented in 1999, was large enough to be seen with the naked eye.

Quantum tunneling allows particles to pass through classically impenetrable barriers

First described in 1928, the phenomenon is the result of probability waves, which represent the location of particles in space as extended objects. Just as sound waves can reflect off of and pass through barriers, these probability waves dictate that solid matter has a chance at passing through obstacles.

Dilution fridges create the colder-than-space environments needed for quantum computers by successively lowering temperatures across layers plated with gold, which reduces heat transfer via radiation and gives them a chandelier-like appearance.

View how AES—the global standard for symmetric encryption—works

Established by the National Institute of Standards and Technology in 2001, the Advanced Encryption Standard transforms plaintext into ciphertext using multiple rounds of processing, including substitution, transposition, and mixing. Larger keys undergo more rounds to produce 16-byte blocks of scrambled data, with 256-bit AES keys taking 3.31 × 10⁵⁶ years to decrypt via brute force.

How entanglement lies at the heart of quantum computing

Theoretical physicist and mathematician Frank Wilczek boils down the complex notion of quantum entanglement into this reasonably understandable summary. Wilczek discusses the concepts of quantum entanglement and how it relates to other ideas like the Many-Worlds Interpretation (MWI) of quantum mechanics. What sounds a bit "science-fictiony" can have actual real-world and concrete applications.

A mathematical breakdown of how RSA encryption uses prime numbers to encrypt data

This form of asymmetric cryptography uses mathematical functions that rely on the product of two large prime numbers. Because traditional computers struggle to factor such products, obtaining the private keys needed to decrypt messages becomes effectively impossible. This security can be reinforced with larger prime numbers, though this makes encryption more computationally taxing.

IBM developed a benchmark to measure the usable performance of a quantum computer

Dubbed "quantum volume," the benchmark tests how well a quantum computer runs complex tasks. It stops when the computer can no longer correctly select the most likely answers, called "heavy outputs," more than two-thirds of the time.

Solid neon mirrors help trap single electrons to create stable quantum bits

Researchers created this new unit of information for a quantum computer by trapping a single electron near the surface of solid neon. The electron was held in its quantum state by attraction to its mirror image.

DNA computing allows for storage and processing of massive amounts of data

Although costly and less efficient for simpler tasks, as of 2025, DNA could hold 455 exabytes of data with near limitless parallel computation potential in small data centers. Every movie ever made would fit inside the volume of a single sugar cube.

As of 2025, there are no federal laws involving privacy and smart city technologies

Advancements in cloud technology and artificial intelligence allow cities to capture, store, and analyze more information than ever before. Experts warn that the unhindered ability to collect and use this data may infringe on residents' rights and endanger them if the data gets into the hands of malicious parties.

Storing data in DNA requires converting binary code into DNA's four-base system

Researchers have suggested that DNA's ability to form compact, dense structures justifies investigating its use for long-term, safe data archiving. This system could fit all of the world's data in a single shoebox, though processing each bit into a nucleotide base takes 2 minutes, as of 2024.

Quantum mechanical principles are responsible for chemical properties

Besides quantization, the wave-particle duality, and probabilistic features, quantum theory's mathematics introduces the exclusion principle, quantum tunneling, quantum entanglement, and other phenomena foreign to our everyday experiences. Some suggest that all possibilities for a quantum system may also occur across the multiverse.

Google’s quantum computer completes a 10,000-year task in about 3 minutes

Google used its 53-qubit processor on an extremely difficult problem for traditional computers to simulate to showcase quantum supremacy. IBM later challenged Google’s claim by arguing that its Summit supercomputer could solve the same problem in just 2.5 days using a more efficient method.

Quantum physics explained in 22 minutes

Brian Cox, Royal Society Professor for Public Engagement in Science, discusses the fundamental principles of quantum mechanics, emphasizing their importance in understanding the nature of reality and their practical applications in emerging technologies like quantum computers.

Emergent quantum phenomena can produce nonfundamental quasiparticles

While physicists have discovered new particles by colliding known ones at high speeds, placing known particles in extreme environments or configurations can allow quantum mechanics to produce bizarre behaviors, making them seem like new types of matter.

The science of cryptography, including methods to encrypt data and how to break encryption

Monoalphabetic ciphers use a set of rules to replace each letter with another consistently, making them susceptible to brute force attacks that try every kind of replacement. While more complex ciphers can transform text in less obvious ways, because certain letters are used more often than others, an analysis of letter frequency may reveal patterns that help uncover the rules that make up a cipher.

Cooling silica nanoparticles lets physicists push the boundary of how large an object can still behave quantum mechanically.

IBM Quantum’s dilution refrigerators keep quantum processors colder than space

In IBM’s quantum lab, quantum processors are kept at a temperature of 15 millikelvin using dilution refrigerators. These refrigerators use nested thermal layers, cryogens like liquid nitrogen and helium, and powerful compressors to maintain the ultra-cold temperatures required for qubit stability and performance.

Explore an optical table to create quantum physics experiments

This interactive teaches users to create quantum experiments through lessons resembling video game levels. Users can also use the virtual lab to visualize landmark quantum experiments like entanglement, teleportation, cryptography, and quantum computing, or create their own experiments with drag-and-drop elements.

Watch how the Enigma machine encrypts messages and learn about its critical design flaw

Using settings selected from a series of rotors and a plugboard that let operators swap letters with any of their choosing, the machine lit up the output letter for each letter typed. While this system could generate messages requiring any of 150 quintillion potential keys, the machine's reflector never encrypted a letter as itself, providing an entry point for exploiting the system.

As of 2025, the internet is entering its fourth phase, with three more to go

Since the inception of the internet as a tool for connecting teams of researchers, technological and infrastructure advancements have progressively increased connectivity. Connections between computers, mobile devices, all devices, and now AI agents will be succeeded by an internet that integrates perception and the senses toward an eventual quantum internet.

In 2018, it took about 2.3 years to develop a way to exploit a software bug for malicious purposes, but as of 2026, AI tools have reduced this time to about 20 hours.

There is a limit to how small transistors can become because they rely on being able to allow or block the flow of electrons, but quantum effects allow electrons to leak through these barriers, generating heat, current loss, and potential data errors.

Four video explainers on quantum fundamentals

Ready to level up your working knowledge of quantum mechanics? Check out these four TED-Ed Lessons written by Chad Orzel, associate professor in the Department of Physics and Astronomy at Union College

Quantum mechanics-based technology may explain the Fermi paradox

It describes the discrepancy between the high likelihood of life beyond Earth given the vastness of the universe and the lack of evidence for such life, since extraterrestrial civilizations have not communicated with us. However, quantum communication—a more information-dense and effective method than classical means—requires massive receivers and very narrow signals, which would easily miss Earth, making a lack of signals expected.

Probability waves govern particles like electrons in the quantum space

Just as waves are extended objects whose heights change across space, quantum waves dictate that the probability of an object existing in different locations across space varies. Like water waves, the probability waves can combine, changing the heights—and therefore probabilities—in different locations.

Quantum mechanics explains how particles behave like both matter and waves

In the quantum world, particles such as electrons are “quantized,” meaning they can only hold specific values of energy or momentum. These particles also behave like waves, with their wave function predicting where they might be found at any moment as probability clouds called orbitals.

Within quantum physics, the order of events across time may not follow causality

Although time is considered a fixed, ordered mapping of events, where the past affects the future, quantum superposition breaks down causality, suggesting that future events can occur simultaneously with past ones. Within the quantum model, the notion of cause and effect is not a fundamental feature of our universe.

One of Einstein's papers challenged quantum theory but helped confirm entanglement

In 1935, Einstein suggested that quantum mechanics was incomplete due to its strange implications about entangled particles. Their challenge led to decades of experiments that eventually proved distant particles could affect each other instantly.

Quantum field theory, which has made predictions accurate to 12 decimal places, explained

Instead of being made of indivisible particles, all visible matter in the universe is built from underlying quantum fields—smooth, invisible entities that behave like waves and extend throughout space and time. The theory suggests these fields are fundamental, and particles are disturbances that move through them.

Google chose Santa Barbara to host its Quantum AI computing project

The project seeks to reduce errors within its quantum computer and integrate 1 million physical qubits (or quantum bits) into the room-sized computer. This powerful device will attempt to solve complex problems in medicine, computing, and more.

The history and operation of SIGABA, the US counterpart of the Nazi Enigma machine

Developed by the US Army and US Navy, over 10,000 of these machines were deployed by the end of World War II to encrypt messages for the armed forces using three series of rotors. The device would continue to be used until the 1950s, while personal computers were shown to possess enough computing power to crack it by 2021.

How end-to-end encryption protects messages, even from service providers

Using symmetric and asymmetric cryptography, data is encrypted on the sender's device before being transmitted across application servers that lack the key needed to decrypt it. The message is not decrypted until it reaches the recipient's device, which uses their private key to recover the plaintext. E2EE's effectiveness has led to its adoption by WhatsApp and Signal.

View a list of the 25 most common passwords according to an analysis of 2.5 terabytes of public data breaches.

Since computers rely on the distribution of electrons in microchips to represent binary code, cosmic rays and ionizing radiation from radioactive elements can introduce software errors by detaching electrons from atoms.

A timeline of how Claude Code was used to execute cyberespionage

In September 2025, a Chinese state-sponsored group targeted 30 large tech companies, financial institutions, chemical manufacturing companies, and government agencies by manipulating Claude Code, having succeeded in infiltrating a small subset. The cyberattack is believed to have been the first of its scale carried out without major human intervention.

Visualizing cyberattacks by country

Cyber crime is expected to cost the global economy trillions per year by 2025. This data illustration showcases the countries with the most severe cyber attacks from 2006-2020.