# The Quantum Computer

> What a quantum computer is and why it could matter: qubits, superposition, entanglement and interference, Shor’s and Grover’s algorithms, the race to post-quantum encryption, how qubits are built and corrected, and what is real today. With live qubit demos you can play with.

Interactive film: https://www.planetpast.com/stories/quantum-computers/  
Publisher: PlanetPast (https://www.planetpast.com/) · Published 2026-10-13 · Physics, Technology

## Prologue

### The quantum computer
*October 2026 · Physics and technology*

A machine that calculates with the strangest rules in physics. How does it work, and how close is it?

In October 2026 the US defence research agency DARPA moved four quantum computing companies into the final, hands-on stage of a long test. Its question is simple: can anyone build a quantum computer that is worth what it costs by 2033? Machines like this one are kept colder than outer space. At the bottom, a small chip computes with superposition, entanglement and interference. To see why that could matter, and why it is so hard, we start with the smallest piece: a single quantum bit.

Prologue · Why the news matters

#### The quantum computer

In early October 2026 DARPA, the US Defense Advanced Research Projects Agency, announced that Atom Computing, Diraq, IBM and IonQ had reached Stage C of its Quantum Benchmarking Initiative. In this final stage its team physically tests each company’s hardware to see whether it performs as their roadmaps predict. Microsoft and PsiQuantum are in the same stage through an earlier pilot. Behind the test lies a bigger question: what is a quantum computer, what could it do, and how much of the excitement is real?

- **In the final stage**: 4 + 2 four new entrants, plus Microsoft and PsiQuantum

- **Target**: 2033 can any approach reach “utility scale”?

- **DARPA’s definition of utility scale**: The value of what the computer produces exceeds its total capital and operating costs Four different kinds of qubit are in the running: neutral atoms, silicon spins, superconducting circuits and trapped ions

The scene shows a simplified dilution refrigerator, the gold “chandelier” that cools a superconducting quantum chip. Real ones are hidden inside nested metal cans.

How to use: pick a chapter below the scene or press ← → to change step · ▶ plays the step · drag to rotate, scroll or pinch to zoom · buttons on the scene run the quantum demos · “Play the film” runs every step full-screen.

Sources: [DatacenterDynamics: DARPA QBI Stage C (Oct 2026)](https://www.datacenterdynamics.com/en/news/darpa-announces-four-companies-advancing-to-final-stage-of-its-quantum-benchmarking-initiative); [Quantum Computing Report: DARPA selects four companies for Stage C](https://quantumcomputingreport.com/darpa-selects-atom-computing-diraq-ibm-and-ionq-for-final-stage-c-verification-under-quantum-benchmarking-initiative/)

## Chapter I · Bits and qubits

### Bits and qubits
*0 and 1*

An ordinary bit is a switch. A quantum bit is something stranger.

An ordinary computer stores everything as bits. Each bit is either 0 or 1, like a switch that is off or on. Three bits can hold any one of eight patterns, but only one pattern at a time. A quantum bit, or qubit, is described by two numbers called amplitudes: one for 0 and one for 1. Add a qubit and the description doubles. Ten qubits need 1,024 amplitudes. Fifty need about a million billion.

Chapter I · Step 1

#### Bits and qubits

A qubit can be made from any quantum system with two distinct states, such as the spin of an electron or two energy levels of an atom. Its state is written α|0⟩ + β|1⟩, where the **amplitudes** α and β are complex numbers. The word “qubit” was introduced by Benjamin Schumacher in 1995.

- **1 bit**: 0 or 1 one of two values

- **1 qubit**: α|0⟩ + β|1⟩ with |α|² + |β|² = 1

- **n qubits**: 2ⁿ amplitudes one for every pattern of n bits

- **50 qubits**: ~1.1 × 10¹⁵ 2⁵⁰ amplitudes

This is why quantum states are so hard to simulate on ordinary computers. But it does **not** mean a quantum computer stores 2ⁿ answers you can read: measuring n qubits gives back just n ordinary bits (step 3). In the scene each column is one amplitude; its height is the size and its colour is the phase.

Source: [Wikipedia: Qubit](https://en.wikipedia.org/wiki/Qubit)

### An arrow in a sphere
*Superposition*

Every possible state of one qubit is a point on the surface of a sphere.

Physicists picture a qubit as an arrow inside a sphere, the Bloch sphere. Straight up is 0. Straight down is 1. A Hadamard gate tips the arrow onto the equator: an equal superposition of 0 and 1. A Z gate swings it halfway around the vertical axis. The chances of 0 and 1 stay the same, but the phase, a hidden angle, changes. Now another Hadamard sends the arrow all the way down to 1. The phase decided the result. Quantum gates are rotations of this arrow. Try them yourself with the buttons on the scene.

Chapter I · Step 2 · Superposition

#### An arrow in a sphere

The Bloch sphere, named after the physicist Felix Bloch, shows every pure state of one qubit as a point on a sphere. The poles are |0⟩ and |1⟩. Every other point is a superposition. How far the arrow tilts sets the chances of 0 and 1; the angle around the vertical axis is the **relative phase**, which cannot be seen directly but changes what later gates do.

- **X**: half-turn about the x-axis. Swaps |0⟩ and |1⟩, like a classical NOT.

- **H** (Hadamard): half-turn about the diagonal between x and z. Turns |0⟩ into an equal superposition.

- **Z**: half-turn about the vertical axis. Flips the phase, leaves the chances alone.

- **S**: quarter-turn about the vertical axis.

In the scene: |+⟩ and |−⟩ are the two equal superpositions with opposite phase. The sequence H, Z, H turns |0⟩ into |1⟩, although H and Z alone never change the chance of measuring 1 from 50%. The engine applies each gate as a 2 × 2 complex matrix to the state, then animates the matching rotation.

Use the gate buttons in the panel on the scene. “Measure” makes the arrow jump to a pole.

Sources: [Wikipedia: Bloch sphere](https://en.wikipedia.org/wiki/Bloch_sphere); [Wikipedia: Qubit](https://en.wikipedia.org/wiki/Qubit)

### Look, and it is gone
*Measurement*

A measurement always returns a plain 0 or 1. The superposition does not survive.

Here is the catch. You can never read the arrow directly. Measuring a qubit always gives a plain 0 or 1. This qubit leans a little away from the top. Measured, it gives 0 about three times in four, and 1 about once in four. Each measurement destroys the superposition: the arrow jumps to the pole it landed on. To try again, you must prepare a fresh qubit. So a quantum computer cannot simply read out all its amplitudes. A good quantum algorithm makes the right answer very likely before anyone looks.

Chapter I · Step 3 · The Born rule

#### Look, and it is gone

Measuring α|0⟩ + β|1⟩ gives 0 with probability |α|² and 1 with probability |β|². Afterwards the qubit *is* in the state it reported; the original amplitudes cannot be recovered. You only learn them statistically, by preparing and measuring many identical copies.

- **Prepared here**: tilted 60° cos²(30°) = 75% for 0, 25% for 1

- **One measurement**: 1 bit whatever the amplitudes were

Watch the tally in the panel on the scene: single results are random, but the counts settle near 75 : 25. Try other preparations, or measure 100 copies at once.

Source: [Wikipedia: Qubit](https://en.wikipedia.org/wiki/Qubit)

## Chapter II · Entanglement

### Two coins that always agree
*Entanglement*

Two qubits can share one state that neither of them has alone.

Now take two qubits, both starting at 0. A Hadamard gate puts the first one into superposition. Then a controlled-NOT gate flips the second qubit only where the first is 1. The two are now entangled. Look at the arrows: both shrink to nothing. Neither qubit has a state of its own any more; only the pair does. Measure them. Each result is random, 0 or 1, yet the two always agree. Run it again and again: never 01, never 10.

Chapter II · Step 4

#### Two coins that always agree

Applying H to qubit A and then a controlled-NOT (CNOT) from A to B turns |00⟩ into the **Bell state** (|00⟩ + |11⟩)/√2. It cannot be written as “a state of A” times “a state of B”. Measured, the pair gives 00 or 11, each half the time, and never 01 or 10.

- Start: |00⟩. Both arrows point up.

- H on A: (|00⟩ + |10⟩)/√2. A is in superposition, B is still 0.

- CNOT: (|00⟩ + |11⟩)/√2. Each arrow shrinks to the centre: alone, each qubit is a perfect coin toss.

The arrows show each qubit’s own (reduced) state, computed from the four amplitudes. An arrow of zero length means the qubit is maximally entangled with its partner. Entanglement cannot be used to send a message: each side alone sees only random results.

Source: [Wikipedia: Quantum entanglement](https://en.wikipedia.org/wiki/Quantum_entanglement)

### “Spooky action at a distance”
*1935 → 2022*

Einstein doubted it. Experiments proved him wrong, and earned a Nobel Prize.

In 1935 Einstein, Podolsky and Rosen argued that such correlations showed quantum mechanics must be incomplete. Einstein later called it spooky action at a distance. In 1964 John Bell showed that the question could be settled by experiment. John Clauser in 1972, Alain Aspect in 1982, and later teams led by Anton Zeilinger found that nature breaks Bell’s limit, just as quantum mechanics predicts. The three shared the 2022 Nobel Prize in Physics. Entanglement is now a working resource, and quantum computers make it on purpose.

Chapter II · Step 5 · 1935 → 2022

#### “Spooky action at a distance”

Could the two results be fixed in advance, like a pair of gloves packed in separate boxes? Bell proved that any such “local hidden variable” theory must obey a limit on how strongly results can be correlated. Quantum mechanics predicts that the limit can be broken, and experiments agree.

- 1935 Einstein, Podolsky and Rosen: the EPR paradox

- 1947 Einstein, in a letter to Max Born: “spukhafte Fernwirkung”

- 1964 John Bell’s theorem

- 1972 Clauser and Freedman: first violation of a Bell inequality

- 1982 Aspect: settings switched while the photons are in flight

- 1998 Zeilinger’s Innsbruck team closes the locality loophole

- 2015 Loophole-free tests in Delft, Vienna and Boulder

- 2022 Nobel Prize to Aspect, Clauser and Zeilinger

Nobel citation: “for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science.” In the scene the qubits drift apart; the agreement does not depend on distance, but it still cannot carry a message faster than light.

Sources: [Wikipedia: Bell test](https://en.wikipedia.org/wiki/Bell_test); [Wikipedia: Quantum entanglement](https://en.wikipedia.org/wiki/Quantum_entanglement); [NobelPrize.org: Physics 2022](https://www.nobelprize.org/prizes/physics/2022/summary/)

## Chapter III · Interference

### Answers that cancel
*Interference*

Amplitudes behave like waves. Wrong answers can wipe each other out.

Amplitudes are not ordinary probabilities. They can be positive or negative, so they can cancel each other, like waves. Three qubits after Hadamard gates: all eight possible inputs, with equal amplitude. A hidden function, the oracle, flips the sign of some of them. This one flips exactly half: it is balanced. More Hadamard gates make the amplitudes interfere. For a balanced function, everything flowing into 000 cancels exactly. For a constant function, everything piles up on 000 instead. One query tells the two apart. A classical computer may need five of the eight inputs.

Chapter III · Step 6 · 1992

#### Answers that cancel

A quantum computer does not simply “try every answer at once”. If it did, measuring would just hand back one random answer. Its power comes from **interference**: arranging the amplitudes so that paths to wrong answers cancel and paths to right answers reinforce.

The Deutsch–Jozsa problem (David Deutsch and Richard Jozsa, 1992) is the textbook example. A function on n-bit inputs is promised to be either *constant* or *balanced* (1 for exactly half the inputs). A classical computer may have to check just over half the inputs, 2ⁿ⁻¹ + 1. The quantum algorithm needs one call.

- H on every qubit: equal amplitude 1/√8 on all eight inputs.

- Oracle: multiplies each amplitude by −1 wherever the function is 1.

- H on every qubit again, then measure. Constant: always 000. Balanced: never 000.

Bars above the line are positive amplitudes, bars below are negative. It is a toy problem, but it shows the key idea behind real algorithms.

Sources: [Wikipedia: Deutsch–Jozsa algorithm](https://en.wikipedia.org/wiki/Deutsch%E2%80%93Jozsa_algorithm); [Wikipedia: Quantum computing](https://en.wikipedia.org/wiki/Quantum_computing)

### Finding a needle faster
*1996 · Lov Grover*

Flip the sign of the answer, reflect about the average, repeat.

In 1996 Lov Grover found a quantum way to search an unsorted list faster. Start with every item equally likely. The oracle marks the right one by flipping its sign. Then every amplitude is reflected about the average. The marked one grows; all the others shrink. Repeat. With eight items, two rounds lift the chance of finding the answer from one in eight to about ninety-five percent. For a million items about 785 rounds are enough, instead of up to a million guesses. A big gain, but a square-root one, not an exponential one.

Chapter III · Step 7 · 1996

#### Finding a needle faster

Grover’s algorithm searches N unsorted items with about (π/4)√N calls to the oracle, where a classical search needs on the order of N. Bennett, Bernstein, Brassard and Vazirani proved that no quantum algorithm can do better than about √N, so the speed-up is quadratic, not exponential.

- **8 items, 1 round**: 78% chance of the marked item

- **8 items, 2 rounds**: 95% the best stopping point

- **1,000,000 items**: ~785 rounds (π/4)·√1,000,000

- **Keys for ciphers like AES**: Double the length a 256-bit key keeps ~128-bit security

The gold line is the average amplitude. Each “diffuse” replaces every amplitude a with 2 × average − a. Too many rounds overshoot and the chance falls again: try it with the buttons.

Sources: [Wikipedia: Grover’s algorithm](https://en.wikipedia.org/wiki/Grover%27s_algorithm); [Wikipedia: Post-quantum cryptography](https://en.wikipedia.org/wiki/Post-quantum_cryptography)

## Chapter IV · Breaking codes

### Factoring by rhythm
*1994 · Peter Shor*

A quantum computer could find the hidden period that unlocks a number’s factors.

In 1994 Peter Shor found a quantum algorithm that factors whole numbers dramatically faster than any known classical method. Its trick is to turn factoring into finding a rhythm. Take 15 and pick 7. Powers of 7 divided by 15 leave remainders 1, 7, 4, 13, and then repeat. The pattern repeats every four steps. Finding that period is the hard part, and it is where a quantum computer uses interference. Then ordinary arithmetic finishes the job: 7 squared is 49, and the numbers either side, 48 and 50, share the factors 3 and 5 with 15. In 2001 a team at IBM and Stanford ran Shor’s algorithm on seven qubits and factored exactly this number.

Chapter IV · Step 8 · 1994

#### Factoring by rhythm

Shor’s algorithm factors an integer N in a time that grows only polynomially with its number of digits. The best known classical method, the general number field sieve, is sub-exponential, so for large numbers the gap is enormous.

- Pick a number a that shares no factor with N.

- **Quantum part:** find the period r after which aˣ mod N repeats. A quantum Fourier transform makes the amplitudes interfere so that measuring reveals r.

- **Classical part:** if r is even, gcd(a^r/2 − 1, N) and gcd(a^r/2 + 1, N) are usually factors.

- **First run on hardware**: 2001 15 = 3 × 5, with 7 nuclear spins (NMR)

- **Published by**: Vandersypen et al., *Nature* IBM Almaden and Stanford

The bars show aˣ mod 15 for x = 0 … 15; equal colours mean equal values, so the period is the length of the repeating pattern. In the real algorithm the quantum computer never lists these values; interference reveals only the period. Pick a different a with the buttons. Some choices fail, and the algorithm simply tries again.

Sources: [Wikipedia: Shor’s algorithm](https://en.wikipedia.org/wiki/Shor%27s_algorithm); [Vandersypen et al., factoring 15 with NMR (Nature 2001; arXiv)](https://arxiv.org/abs/quant-ph/0112176); [Physics Today (2002) on the first Shor demonstration](https://physicstoday.aip.org/news/a-quantum-computer-has-now-factored)

### The race to replace the locks
*1977 → 2024*

Today’s public-key encryption would fall to a large quantum computer. New locks are already being fitted.

Much of the internet’s security, including RSA encryption from 1977, rests on the fact that factoring huge numbers is practically impossible. A large, error-corrected quantum computer running Shor’s algorithm would break that. A 2025 estimate put a 2048-bit RSA key within reach of under a million noisy qubits, running for under a week. No machine is anywhere near that size. But secrets recorded today could be decrypted later, so the switch has already begun. In August 2024 the US standards agency NIST published its first post-quantum standards. The main ones rest on lattices: finding the nearest point in a vast, many-dimensional grid.

Chapter IV · Step 9 · 1977 → 2025

#### The race to replace the locks

RSA (Rivest, Shamir and Adleman, 1977) is safe because multiplying two large primes is easy but undoing it is not. Shor’s algorithm would also break the other widely used public-key systems based on discrete logarithms. Ciphers such as AES are much less affected: longer keys are enough (step 7).

- **2019 estimate (RSA-2048)**: 20 million noisy qubits, about 8 hours

- **2025 estimate (Gidney)**: noisy qubits, under a week; assumes 0.1% gate error

- **NIST standards, 13 August 2024**: FIPS 203 ML-KEM · FIPS 204 ML-DSA · FIPS 205 SLH-DSA derived from CRYSTALS-Kyber, CRYSTALS-Dilithium and SPHINCS+. HQC chosen as a backup on 11 March 2025; FALCON to follow as FIPS 206

“Harvest now, decrypt later”: data that must stay secret for many years can be recorded today and broken once a large enough machine exists. In the scene, two very different sets of arrows (a short “good” basis and a long, skewed “bad” one) build exactly the same grid of points. With the good basis, finding the grid point nearest to the glowing target is easy; with only the bad one, and in very many dimensions instead of two, it is believed to be hard even for quantum computers.

Sources: [Wikipedia: RSA](https://en.wikipedia.org/wiki/RSA_(cryptosystem)); [Wikipedia: Shor’s algorithm](https://en.wikipedia.org/wiki/Shor%27s_algorithm); [Gidney, How to factor 2048-bit RSA with less than a million noisy qubits (arXiv 2025)](https://arxiv.org/abs/2505.15917); [NIST CSRC: Post-Quantum Cryptography Standardization](https://csrc.nist.gov/projects/post-quantum-cryptography/post-quantum-cryptography-standardization); [Wikipedia: NIST PQC Standardization](https://en.wikipedia.org/wiki/NIST_Post-Quantum_Cryptography_Standardization); [Wikipedia: Post-quantum cryptography](https://en.wikipedia.org/wiki/Post-quantum_cryptography)

## Chapter V · Building qubits

### Colder than space
*1985 → 2025 · Nobel Prize in Physics*

Superconducting qubits are circuits you could hold in your hand that behave like single atoms.

So how do you build a qubit? The most common approach uses tiny superconducting circuits, cooled in a dilution refrigerator. Each stage is colder than the one above. The bottom plate sits less than fifteen thousandths of a degree above absolute zero, far colder than deep space. The heart of each qubit is a Josephson junction: two superconductors separated by an insulating layer only a few atoms thick. In 1985 John Clarke, Michel Devoret and John Martinis showed that a whole circuit like this can act as one quantum object: it tunnels, and it takes only certain energies. That work won the 2025 Nobel Prize in Physics. Today such circuits are driven by microwave pulses at a few gigahertz.

Chapter V · Step 10 · 1985 → 2025

#### Colder than space

A superconducting qubit is an electrical circuit whose current flows without resistance. A **Josephson junction** (predicted by Brian Josephson in 1962) makes its energy levels unevenly spaced, so the lowest two can serve as |0⟩ and |1⟩. Microwave pulses rotate the qubit; the length of the pulse sets the angle. The transmon design, introduced in 2007, is used in IBM’s and Google’s processors.

- **Chip temperature**: in a dilution refrigerator (helium-3 / helium-4 mixture)

- **Deep space**: 2.7 K the cosmic microwave background, ~200 times warmer

- **Qubit frequency**: ~5 GHz a typical value

- **Coherence (2025)**: ~1 ms best transmons reached milliseconds

- **Nobel Prize in Physics 2025 (announced 7 October 2025)**: John Clarke (UC Berkeley), Michel H. Devoret (Yale, UC Santa Barbara), John M. Martinis (UC Santa Barbara) “for the discovery of macroscopic quantum mechanical tunnelling and energy quantisation in an electric circuit”

Plate temperatures in the scene are indicative; the stages are simplified. The chip at the bottom shows a 4 × 4 grid of qubits for illustration.

Sources: [Wikipedia: Superconducting quantum computing](https://en.wikipedia.org/wiki/Superconducting_quantum_computing); [Wikipedia: Dilution refrigerator](https://en.wikipedia.org/wiki/Dilution_refrigerator); [Wikipedia: Josephson effect](https://en.wikipedia.org/wiki/Josephson_effect); [Wikipedia: Cosmic microwave background](https://en.wikipedia.org/wiki/Cosmic_microwave_background); [NobelPrize.org: Physics 2025](https://www.nobelprize.org/prizes/physics/2025/summary/); [UC Santa Barbara: two quantum pioneers win the Nobel Prize](https://engineering.ucsb.edu/news/two-ucsb-quantum-pioneers-win-nobel-prize-physics); [Wikipedia: John Clarke (physicist)](https://en.wikipedia.org/wiki/John_Clarke_(physicist))

### Ions, atoms, light and spin
*Many ways to build a qubit*

Different labs trap single atoms, single electrons or single photons. Each has its own trade-offs.

Superconducting circuits are not the only way. Trapped ions are single charged atoms, held in a vacuum by electric fields and controlled with lasers. Their qubits are very stable and very accurate: Quantinuum’s 98-qubit Helios reports two-qubit gates that succeed 99.92 percent of the time. Neutral atoms are held by tightly focused laser beams called optical tweezers. In 2025 a Caltech team trapped a record 6,100 of them. Others store qubits in particles of light, or in the spins of single electrons in silicon chips. No approach has clearly won yet.

Chapter V · Step 11

#### Ions, atoms, light and spin

- **Trapped ions**: Paul trap + lasers Oscillating electric fields hold the ions; laser pulses perform gates in microseconds

- **Helios (Quantinuum, Nov 2025)**: 98 qubits barium ions; 99.921% two-qubit, 99.9975% one-qubit gate fidelity

- **Neutral atoms**: Optical tweezers Atoms excited to large “Rydberg” states interact strongly enough to make two-qubit gates

- **Caltech (Sep 2025)**: 6,100 atoms caesium; ~13 s coherence; 99.98% single-qubit accuracy; not yet entangled

- **Photons**: Particles of light China’s Jiuzhang (2020) sent 76 photons through an optical network

- **Spins in silicon**: Single electrons built with chip-making methods; Diraq is one of DARPA’s Stage C companies

Trade-offs: superconducting gates are very fast but the chips need extreme cold; ions and atoms are identical by nature and hold their state for a long time, but gates are slower. The miniature models are not to scale.

Sources: [Wikipedia: Trapped-ion quantum computer](https://en.wikipedia.org/wiki/Trapped-ion_quantum_computer); [Quantum Computing Report: Quantinuum Helios (Nov 2025)](https://quantumcomputingreport.com/quantinuum-launches-helios-quantum-computer-with-industry-leading-fidelity-and-singapore-partnership/); [Wikipedia: Neutral atom quantum computer](https://en.wikipedia.org/wiki/Neutral_atom_quantum_computer); [Caltech: record 6,100-qubit array (Sep 2025)](https://www.pma.caltech.edu/news/caltech-team-sets-record-with-6100-qubit-array); [Wikipedia: Quantum computing](https://en.wikipedia.org/wiki/Quantum_computing); [Quantum Computing Report: DARPA selects four companies for Stage C](https://quantumcomputingreport.com/darpa-selects-atom-computing-diraq-ibm-and-ionq-for-final-stage-c-verification-under-quantum-benchmarking-initiative/)

## Chapter VI · Taming errors

### Fragile by nature
*Noise*

The same sensitivity that makes qubits powerful makes them easy to disturb.

Qubits are fragile. Heat, stray fields, even cosmic rays nudge them, and the superposition leaks away into the environment. This is decoherence. Ordinary computers fight errors by keeping copies. Quantum mechanics forbids copying an unknown qubit, so that trick fails. Instead, one logical qubit is spread across many physical qubits. Helper qubits keep checking the parity of their neighbours, without ever reading the data itself. When an error strikes, nearby checks light up. A decoder reads the pattern and works out the fix. Try injecting errors yourself.

Chapter VI · Step 12 · 1995 →

#### Fragile by nature

Decoherence is the loss of a qubit’s phase relationship as it interacts with its surroundings. It limits how many gates can run before the answer is lost. Quantum error correction gets round the no-cloning rule by encoding one **logical qubit** in an entangled state of many **physical qubits**, and measuring only “syndromes”: parities that reveal errors but not the stored information.

- 1995 Peter Shor’s 9-qubit code

- 1996 Andrew Steane’s 7-qubit code; the 5-qubit code (Laflamme and others), the smallest possible

- today The **surface code**: only checks between neighbours on a flat grid, which suits chips

- **Threshold theorem**: Below a critical error rate, errors can be suppressed as much as needed a commonly quoted per-gate target is about 10⁻³

- **Surface code, distance d**: 2d² − 1 physical qubits per logical qubit in this layout (49 for d = 5)

In the scene, white spheres are data qubits and each tile is a check. Teal tiles detect bit flips (X errors); amber tiles detect phase flips (Z errors). The decoder shown here is ideal; real decoders must guess the most likely error from the lit tiles, fast.

Sources: [Wikipedia: Quantum decoherence](https://en.wikipedia.org/wiki/Quantum_decoherence); [Wikipedia: Quantum error correction](https://en.wikipedia.org/wiki/Quantum_error_correction); [Wikipedia: Quantum computing](https://en.wikipedia.org/wiki/Quantum_computing)

### Crossing the threshold
*December 2024*

For the first time, a bigger code made a better qubit.

Error correction only helps if the physical qubits are good enough. Below a threshold, adding qubits makes the logical qubit better; above it, worse. In December 2024 Google reported crossing that line with its 105-qubit Willow chip. Each time the code grew, from distance 3 to 5 to 7, the logical error rate fell by a factor of about 2.1. The distance-7 logical qubit outlived the chip’s best physical qubit by about 2.4 times. Still, useful algorithms need far lower error rates, and many more qubits.

Chapter VI · Step 13 · 2024

#### Crossing the threshold

Google Quantum AI’s Willow results, published in *Nature* on 9 December 2024, showed surface-code memories whose logical error rate fell as the code grew: the first clear demonstration of operating “below threshold” at growing code size.

- **Willow**: 105 qubits superconducting transmons

- **Distance-7 code**: 101 qubits 0.143% error per cycle of correction

- **Suppression per step (Λ)**: 2.14 going from d to d + 2

- **vs best physical qubit**: 2.4× longer-lived

- Dec 2023 A neutral-atom team (Bluvstein, Lukin et al.) runs a 48-logical-qubit processor

- Apr 2024 Microsoft and Quantinuum: 4 logical qubits from 30 trapped ions, error rates up to 800 times lower than physical

- Nov 2025 Quantinuum Helios: 48 error-corrected logical qubits reported

Caveats: these are mostly memories and small demonstrations, not long fault-tolerant algorithms, which are thought to need logical error rates near 10⁻⁶ or lower. In the panel on the scene, the d = 3 and d = 5 values are derived from Λ and the measured d = 7 value.

Sources: [Google Quantum AI, Quantum error correction below the surface code threshold (Nature, Dec 2024)](https://www.nature.com/articles/s41586-024-08449-y); [Wikipedia: Willow processor](https://en.wikipedia.org/wiki/Willow_processor); [Wikipedia: Quantum error correction](https://en.wikipedia.org/wiki/Quantum_error_correction); [Wikipedia: Neutral atom quantum computer](https://en.wikipedia.org/wiki/Neutral_atom_quantum_computer); [Quantum Computing Report: Quantinuum Helios (Nov 2025)](https://quantumcomputingreport.com/quantinuum-launches-helios-quantum-computer-with-industry-leading-fidelity-and-singapore-partnership/)

## Chapter VII · Real or hype?

### Quantum advantage?
*2019 → 2025*

Claims of beating supercomputers keep coming, and so do the rebuttals.

In 2019 Google’s 53-qubit Sycamore chip finished a random sampling task in 200 seconds, and estimated a supercomputer would need ten thousand years. IBM replied that a better classical method could do it in about two and a half days. Later estimates fell to seconds. This back-and-forth is normal. Claims of quantum advantage are often answered by cleverer classical algorithms. In 2024 Willow ran a harder sampling task in five minutes. In 2025 Google reported a verifiable speed-up of about 13,000 times for a physics calculation it calls Quantum Echoes. These tasks were chosen because they are hard for classical computers, not because they are useful. A clear, practical advantage is still being tested and debated.

Chapter VII · Step 14 · 2019 → 2025

#### Quantum advantage?

“Quantum supremacy” or “advantage” means a quantum computer doing some task faster than any classical computer could. The chosen tasks, like sampling the output of random circuits, are built to be hard to simulate, not to be useful, and classical methods keep improving.

- **Sycamore (2019)**: 200 s vs a claimed 10,000 years classically

- **IBM’s reply (2019)**: ~2.5 days on the Summit supercomputer

- **Later estimate (2024)**: ~6 s on the Frontier supercomputer, with better tensor-network methods

- **Willow (Dec 2024)**: 5 min vs an estimated 10²⁵ years

- **Quantum Echoes (Willow, Oct 2025, *Nature*)**: ~13,000 × faster on one task an out-of-time-order correlator; “verifiable” because another quantum computer can check it

Other claims include China’s photonic Jiuzhang (2020) and D-Wave’s annealer (2024), which a later study argued could be matched classically. The chart uses a logarithmic scale: each step up is ten thousand times longer. Bars for classical estimates are only as good as the best algorithm known at the time.

Sources: [Wikipedia: Sycamore processor](https://en.wikipedia.org/wiki/Sycamore_processor); [Wikipedia: Quantum supremacy](https://en.wikipedia.org/wiki/Quantum_supremacy); [Wikipedia: Willow processor](https://en.wikipedia.org/wiki/Willow_processor); [Quantum Computing Report: Google’s Quantum Echoes (Oct 2025)](https://quantumcomputingreport.com/google-quantum-ai-achieves-verifiable-quantum-advantage-on-willow-chip-with-quantum-echoes-algorithm/); [Wikipedia: Quantum computing](https://en.wikipedia.org/wiki/Quantum_computing)

## Epilogue

### From strange physics to a new kind of computer
*2026 and beyond*

Superposition, entanglement and interference are real. The question is how soon they become useful.

Where does that leave us? Companies publish roadmaps. IBM, for example, aims to deliver a machine with 200 error-corrected logical qubits by 2029. DARPA’s test will judge whether any approach can be worth its cost by 2033. The original motivation still stands. In the early 1980s Richard Feynman and Yuri Manin suggested that quantum hardware could simulate nature far better than ordinary computers, and in 1996 Seth Lloyd proved it. However long it takes, the ingredients are real: superposition, entanglement and interference have all been shown in the lab, and engineers are learning to compute with them.

Epilogue · 2026 →

#### A new kind of computer

- 1935 EPR paradox: entanglement questioned

- 1964 Bell’s theorem makes it testable

- 1982 Feynman: quantum hardware to simulate physics

- 1985 Macroscopic quantum tunnelling in a circuit

- 1994 Shor’s factoring algorithm

- 1995 First quantum error-correcting code

- 1996 Grover’s search algorithm

- 2001 15 = 3 × 5 on seven qubits

- 2019 Sycamore’s supremacy claim

- 2022 Nobel Prize for Bell tests

- 2024 Error correction below threshold; NIST post-quantum standards

- 2025 Nobel Prize for quantum circuits

- 2026 DARPA’s final-stage tests begin

- **IBM Starling (company target)**: 2029 200 logical qubits, 100 million operations

- **DARPA QBI**: 2033 is utility scale reachable?

Roadmap dates are companies’ own goals, not guarantees. All full-screen stills are AI-generated illustrations, not photographs. The 3D scenes are simplified models; the qubit maths in the interactive steps (state vectors and gates) is computed exactly.

#### Sources

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[Quantum Computing Report: DARPA selects four companies for Stage C](https://quantumcomputingreport.com/darpa-selects-atom-computing-diraq-ibm-and-ionq-for-final-stage-c-verification-under-quantum-benchmarking-initiative/)
[Wikipedia: Quantum computing](https://en.wikipedia.org/wiki/Quantum_computing)
[Wikipedia: Qubit](https://en.wikipedia.org/wiki/Qubit)
[Wikipedia: Bloch sphere](https://en.wikipedia.org/wiki/Bloch_sphere)
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[NobelPrize.org: Physics 2022](https://www.nobelprize.org/prizes/physics/2022/summary/)
[Wikipedia: Deutsch–Jozsa algorithm](https://en.wikipedia.org/wiki/Deutsch%E2%80%93Jozsa_algorithm)
[Wikipedia: Grover’s algorithm](https://en.wikipedia.org/wiki/Grover%27s_algorithm)
[Wikipedia: Shor’s algorithm](https://en.wikipedia.org/wiki/Shor%27s_algorithm)
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[Wikipedia: RSA](https://en.wikipedia.org/wiki/RSA_(cryptosystem))
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[Wikipedia: NIST PQC Standardization](https://en.wikipedia.org/wiki/NIST_Post-Quantum_Cryptography_Standardization)
[Wikipedia: Post-quantum cryptography](https://en.wikipedia.org/wiki/Post-quantum_cryptography)
[Wikipedia: Superconducting quantum computing](https://en.wikipedia.org/wiki/Superconducting_quantum_computing)
[Wikipedia: Dilution refrigerator](https://en.wikipedia.org/wiki/Dilution_refrigerator)
[Wikipedia: Josephson effect](https://en.wikipedia.org/wiki/Josephson_effect)
[Wikipedia: Cosmic microwave background](https://en.wikipedia.org/wiki/Cosmic_microwave_background)
[NobelPrize.org: Physics 2025](https://www.nobelprize.org/prizes/physics/2025/summary/)
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[Wikipedia: John Clarke (physicist)](https://en.wikipedia.org/wiki/John_Clarke_(physicist))
[Wikipedia: Trapped-ion quantum computer](https://en.wikipedia.org/wiki/Trapped-ion_quantum_computer)
[Quantum Computing Report: Quantinuum Helios (Nov 2025)](https://quantumcomputingreport.com/quantinuum-launches-helios-quantum-computer-with-industry-leading-fidelity-and-singapore-partnership/)
[Wikipedia: Neutral atom quantum computer](https://en.wikipedia.org/wiki/Neutral_atom_quantum_computer)
[Caltech: record 6,100-qubit array (Sep 2025)](https://www.pma.caltech.edu/news/caltech-team-sets-record-with-6100-qubit-array)
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[Wikipedia: Quantum error correction](https://en.wikipedia.org/wiki/Quantum_error_correction)
[Google Quantum AI, Quantum error correction below the surface code threshold (Nature, Dec 2024)](https://www.nature.com/articles/s41586-024-08449-y)
[Wikipedia: Willow processor](https://en.wikipedia.org/wiki/Willow_processor)
[Wikipedia: Quantum supremacy](https://en.wikipedia.org/wiki/Quantum_supremacy)
[Wikipedia: Sycamore processor](https://en.wikipedia.org/wiki/Sycamore_processor)
[Quantum Computing Report: Google’s Quantum Echoes (Oct 2025)](https://quantumcomputingreport.com/google-quantum-ai-achieves-verifiable-quantum-advantage-on-willow-chip-with-quantum-echoes-algorithm/)
[The Quantum Insider: IBM roadmap to Starling (Jun 2025)](https://thequantuminsider.com/2025/06/10/ibm-offers-roadmap-toward-large-scale-fault-tolerant-quantum-computer/)