Q U A N T U M C O M P U T E R S
Quantum computers can factorize large numbers in far fewer steps than classical computers. The best known classical algorithm requires
~ exp[1.9(log N)⅓ (log(log N))⅔ ]
steps, while a quantum computer can factorize the number in
~ (log N)3
steps. In this app, you can compare the performance of a classical computer with that of a quantum computer. To make the comparison fair, we assume that both computers run at a clock speed of 2 GHz, comparable to a modern laptop.
F A C T O R I Z I N G L A R G E N U M B E R S
Factorizing is the opposite of multiplying: given a number N you have to find the prime numbers that multiply to yield N. For example: 21 = 7 x 3. While multiplying can be done very efficiently (that is, in relatively few steps), factorizing numbers is computationally very demanding.
We care about factorizing a great deal in practice. The asymmetry in the level of difficulty can be exploited to create cryptographic codes in which encryption (via multiplication) is fast, but decryption without a key is slow (factorization). The cryptography used today is pretty much all based on this mathematical property.
5 x 10–8 seconds: hydrogen fusion reaction
50 ns is roughly the time it takes for the fusion of two deuterium nuclei to fuse into helium in a fusion reactor or hydrogen bomb.
4 x 10–7 seconds: nuclear fission
This is about the time between the emission of a neutron from one uranium nucleus and absorption by another nucleus.
5 x 10–2 seconds: woodpecker hammers
A woodpecker hits the tree trunk with its beak once every 50 ms as it hollows out the tree for its nest. They can be found almost everywhere on Earth, except Australasia, Antacrtica and Madagascar.
2 x 1012 seconds: humans leave Africa
Homo sapiens evolved in Africa and migrated to other continents between 100 and 50 thousand years ago. Some Polynesian islands were not colonised until a few thousand years ago.
3 x 10–6 seconds: shortening of the day
The 2004 earth quake that shook the Indian ocean, causing the Boxing Day tsunami, reduced the length of a day on Earth by about 3 μs by changing the Earth’s moment of inertia.
5 x 10–6 seconds: strobe light
Commercial high-speed strobe light produces flashes of a few microseconds, allowing for high-speed photography that freezes bullets in mid-air.
5 x 10–4 seconds: cracked glass
Cracks in glass propagate at a tremendous speed. A typical crack extends over a metre in just half a millisecond.
6 x 101 seconds: put the kettle on
It takes about a minute to bring half a litre of water from room temperature to boiling point in a modern kettle.
1 x 10–4 seconds: fastest shutter speed
A good modern digital camera can achieve shutter speeds of up to 1/8000, or about a thenth of a millisecond.
9 x 100 seconds: 100 m world record
It took Usain Bolt 9.58 seconds to run the 100 m, establishing the world record in Berlin in 2009.
3 x 10–1 seconds: the blink of an eye
We think the blink of an eye is a short time, but it still takes 0.3 seconds to complete. It takes a classical computer this long to factor a 20-digit number, but a quantum computer can factor a 300-digit number.
1 x 10–4 seconds: photon roundtrip time
The Large Hadron Collider accelerates protons to nearly the speed of light (or an energy of 7 TeV) around its 27 km ring. One roundtrip of a proton is 0.1 ms.
9 x 10–5 seconds: high-frequency trading
High-frequency traders buy and sell stock more than ten thousand times a second. This can sometimes cause a runaway effect, like the Flash Crash in 2010.
4 x 10–2 seconds: hummingbird
Hummingbirds hover over flowers by flapping their wings around 30 times per second. Some species flap their wings as fast as 80 times per second.
1 x 10–3 seconds: pulsars
Pulsars a very compact astronomical objects that emit a highliy focussed beam of radiation. They can rotate very fast, and produce a flash every few milliseconds as the beam sweeps across Earth.
2 x 10–5 seconds: tidal lengthening of the day
The moon causes tidal forces on the Earth, causing the tides. The energy for these tides is taken from the rotation energy of the Earth, lengthening each day by this amount.
3 x 108 seconds: building the Suez canal
The Suez canal was built from April 1859 to November 1869. It is 193 km long, and was the focal point of a political crisis between Egypt and the United Kingdom in 1956.
2 x 10–2 seconds: see an image
TVs have a refresh rate of 60Hz, which means that each image lasts about 17 ms before it is overwritten by a new one. Our brains are not fast enough to track this, and instead perceive a continuous motion.
1 x 10–2 seconds: see an image
The shortest time for the eye to see an image is 13 ms, and the brain retains the image for eight times longer in order to process its meaning.
2 x 108 seconds: light from nearby stars
The nearest stars are a few lightyears away. Alpha Centauri is 4.3 light years away, and Sirius is 8.6 light years away.
5 x 107 seconds: Oort cloud
The Oort cloud is a large cloud of comets surrounding the Solar system. It starts about 60 light days from the Sun and extends to about 2 light years out.
1 x 10–2 seconds: Phelps wins
The time between Michael Phelps and Milorad Cavic finishing the 100 m butterfly final in London 2012 was only 0.01 seconds.
9 x 10–3 seconds: hard drive seek time
On a computer hard disk that spins with 5 000 rpm, the time it takes to look up a sector is about 9 ms. By comparison, a Solid State Drive takes only 64 μs.
1 x 107 seconds: baboon gestation period
Baby baboons grow in the womb for six months, as opposed to nine months for humans.
4 x 106 seconds: a human foetus
At this age a human foetus is about the size of a chick pea, and has begun developing fingers and toes that are still slightly webbed at this stage.
7 x 10–3 seconds: spark plug
A spark plug creates the ignition in a combustion engine, and the spark itself lasts a couple of milliseconds. Efficient engines should have as short and hot a spark as possible.
1 x 106 seconds: lifetime of a mosquito
Adult mosquitos live can for up to anything between a week and a few months.
5 x 10–3 seconds: conversation
The time it takes to travel from your mouth to your conversaton partner’s ear is a couple of milliseconds.
3 x 105 seconds: survive without water
Water is essential for our survival. We can only go without it for about three days. Keep hydrated while your computer tries to factor this 90 digit number.
4 x 10–3 seconds: honey bee wing flap
A honey bee needs to flap its tiny wings very fast to maintain airborne: 250 times a second. They not only use them to fly, but they also use their wings to keep the hive warm at around 35 C.
3 x 10–3 seconds: neuron
It takes a neuron in the brain about 3 ms to fire. This means that shorter processes than this cannot possibly be perceived as anything other than instantaneous to the human brain.
6 x 104 seconds: ironman
It typically takes around 16 hours to complete the ironman, in which the contestant swims 2.4 miles, cycles 112 miles, and runs 26.2 miles.
2 x 10–3 seconds: breaking glass
If a loud tone is resonant with the vibration frequency of a glass, the sound can make the glass shatter. This occurs typically for kHz sounds, in which each vibration lasts about two milliseconds.
1 x 104 seconds: slow-roasted pork belly
The secret to a tender pork belly is to roast it slowly for a few hours at 120 C. Low temperatures allow the chewy collagen in the meat to melt into gelatine, which leads to moist and tender meat.
3 x 103 seconds: album of music
A typical music album last a little under an hour. This is historically determined by the fact that each side of a vinyl LP can only contain 20 to 25 minutes of music.
1 x 10–3 seconds: light travels 357 km
In just over 1 ms, light travels from London to Amsterdam if it would follow the curvature of the Earth. In an optical fibre, the speed of light is two thirds of that in air, so it would take a light pulse about 1.4 ms.
5 x 102 seconds: light from the Sun
It takes light about 8.5 minutes to travel from the Sun to the Earth. By comparison, it takes light about one million years to travel from the centre of the Sun to the surface.
9 x 10–4 seconds: Blackbird SR-17
The Blackbird SR-17 could fly at a top speed over Mach 3, which means that in 0.9 ms it would fly a distance of 1 m. When the Russians developed Mach 4.5 missiles, the Blackbird was retired.
1 x 1012 seconds: age of cave paintings
The first surviving human art comes in the form of cave paintings depicting hunting scenes in Chauvet cave.
5 x 10–2 seconds:
Snapping your fingers creates a loud sound by hitting the palm of your hand with your middle finger at high speed.
4 x 10–2 seconds: light from LA to Sydney
If light would follow the surface of the Earth, it would take 40 ms to travel from Los Angeles to Sydney.
4 x 1011 seconds: time between ice ages
During an ice age average temperatures are a few degrees lower than today. Ice ages recur roughly every ten thousand years.
2 x 1011 seconds: Stonehenge
The famous Wiltshire prehistoric monument is estimated to be between 4000 and 5000 years old.
4 x 10–2 seconds: a soap bubble pops
A soap bubble seems to pop instantaneously, but it still takes a large bubble tens of milliseconds.
3 x 10–2 seconds: washing machine
When a washing machine expells water from cloths, it does so via the centrifugal force by spinning up to 1800 rpm. Each revolution takes about 30 ms.
7 x 1010 seconds: Christianity founded
Two thousand years have past since the crucifiction of Jesus and the birth of Christianity. There are more than two billion christians on Earth, compared to 1.6 billion muslims.
3 x 1010 seconds: age of oldest universities
In the early twelfth century (and late tenth century), universities in Europe were founded. Bologna dates from 1088 and Oxford from 1096.
3 x 10–2 seconds: lightning
Lightning consists of a downward streamer and an upwards discharge that produces the bright flash. The total lightening strike lasts about 30 ms.
2 x 10–2 seconds: transatlantic fibre
Sending a message over a transatlantic fibre from London to New York takes about 20 ms. Real connection times are much longer due to the signal processing in various routers along the way.
1 x 1010 seconds: Newton’s Principia
In 1687, 328 years ago, Newton published his magnum opus, the Principia Mathematica, in which he explains the foundations of mechanics.
2 x 10–2 seconds: atomic fire ball
While the mushroom cloud is the well-known image of an atomic explosion, the interesting physics happens around 20 ms, when you can see the fire ball. The spikes are the metal support structure turning into plasma.
3 x 109 seconds: plastic bottle
When left to decompose, plastic bottles take about a century to fully degrade. Before that, the plastic will have made its way into the ecosystem.
2 x 10–2 seconds: tennis ball on racket
It takes time to reverse the direction of the ball on a racket. The shorter the turnaround time, the greater the force, which can be more than 200 N when returning a fast serve.
1 x 109 seconds: quantum information
In 1970—45 years ago—Stephen Wiesner proposed the first application of what we now know as quantum information: quantum money that cannot be falsified. This research ultimately led to quantum computers.
6 x 1012 seconds: supervolcanic eruption
By this time in the future, Earth will most likely have experienced a super-volcanic eruption that expels more than 400 cubic kilometres of magma. This will probably halt your calculation.
5 x 10–2 seconds: lowest audible tone
20 Hz is on average the lowest tone humans can hear, although lower tones can be felt in the body when they are sufficiently loud.
9 x 10–2 seconds: sneeze
During sneezing, you eject a large amount of mucus from your nasal cavity with force. The duration of the spray is about 90 ms.
1 x 1014 seconds: local galactic group
The radius of the volume in space containing the Local Galactic Group is 5 million light years. This is the group of galaxies around the Milky Way that are gravitationally bound to each other.
5 million years
7 x 1013 seconds: light from Andromeda
The Andromeda galaxy is two million light years away, which means it takes light two million years to get from Andromeda to us.
2 million years
8 x 10–2 seconds: airbag inflates
It takes a little under 2 ms for the triggering mechanism in an airbag to initiate the inflation of the bag, which takes place at a much slower rate of 60 to 80 ms.
1 million years
7 x 10–2 seconds: heartbeat of a pygmee shrew
This nervous little fellow has a heart that beats 14 times a second. Its body is about 5 cm long, and it lives in the undergrowth and eats insects and invertebrates.
3 x 1013 seconds: use of fire by hominids
One of the earliest technologies was the use of fire. Early hominids seem to have mastered this one million years ago.
1 x 1013 seconds: homo sapiens
As a species, we are about half a million years old. Our closest living relative is the bonobo, an endangered type of chimpanzee living in the Congo Basin.
5 x 10–2 seconds: Ferrari 458 gear change
It takes a Ferrari 458 60 ms to change gears. In normal cars with automatic transmission this takes about 200 ms, but in a Bugatti Veyron it takes only 8 ms.
2 x 1018 seconds: tidal lock
Provided the Earth and the moon are not engulfed by the Sun when it turns into a red giant, by this time they will be tidally locked, and permanently facing each other.
6 x 10–1 seconds: from thought to sound
The time it takes from forming a word in your mind to saying it out loud is about 600 ms.
1 x 1018 seconds: galactic pile-up
The Andromeda galaxy and the Milky Way are on a galactic collision course. In roughly 25 billion years they will collide. The collision itself will play out over several billion years.
5 x 10–1 seconds: GPS roundtrip time
GPS satellites are “parked” in geostationary orbits 36 thousand km above Earth, which means that they complete one orbit in 24 hours, hovering over the same spot on Earth. This leads to a long communication time.
5 x 10–1 seconds: a crickets’ chirp
Crickets make a characteristic chirping sound at 5 kHz. In addition, how many times a cricket chirps each second is closely related to the temperature, with 115 chirps a minute equal to 20 C and 150 chirps 25 C.
5 x 1017 seconds: age of the universe
The universe is 13.8 billion years old, and started with the Big Bang. The first galaxies formed as early as 200 million years after the Big Bang.
4 x 10–1 seconds: a drop of one metre
It takes a object 0.44 s to fall 1 m on Earth if we ignore air drag, no matter how heavy the object is.
3 x 1017 seconds: lifetime of the Sun
Stars the size of the Sun have a typical lifetime of about ten billion years before they go nova and become first a red giant, and then a white dwarf.
2 x 1017 seconds: formation of the Earth
Nearly five billion years ago the Earth formed from the debris orbiting the Sun. Early on, a Mars-sized object imacted the Earth, creating the moon.
4 x 10–1 seconds: multiple images
Modern digital SLR cameras cantypically take two and a half images per second at full resolution. However, the SD card usually cannot keep up with this for long.
4 x 10–1 seconds: Doherty threshold
A computer user interface feels responsive if the time between the user action and the computer response is less than 0.4 s. This is called the Doherty threshold.
8 x 1016 seconds: oxygen
The Earth’s atmosphere becomes oxygenated by single-cell organisms. This paves the way for multi-cellular organisms.
4 x 1016 seconds: multi-cellular life
A billion years after life develloped on Earth, multi-cellular life evolved into a few different ways: animals, fungi, land plants, and three different types of algae.
3 x 10–1 seconds: jumping spider
Jumping spiders creep up on their prey and jump the final distance. This takes about 0.3 s.
2 x 1016 seconds: sexual reproduction
Shortly after the first multi-cellular lifeforms appeared, sexual reproduction evolved as a means of procreation. So the metabolism (the chicken) came first.
3 x 10–1 seconds: turning on a light bulb
Switching on an incandescent light bulb is a relatively slow process. The bulb reaches maximum intensity 0.3 s after turning it on.
3 x 10–1 seconds: population growth
Every 0.3 s a baby is born somewhere on this planet. The death rate is one person every 0.5 s, which means that the global population is still growing fast.
1 x 1016 seconds: first land vertebrates
Around 350 million years ago the first tetrapods crawled from the water onto land, starting the colonisation of the continents by animals.
6 x 1015 seconds: flowers
150 million years ago the first flowers appear, along with pollenating insects.
2 x 10–1 seconds: acceptable gaming latency
One of the most important figures of merit in online gaming is the ping time, or the latency. Slow-paced games can deal with 0.2 s of latency, but fast online shooters require below 50 ms.
2 x 10–1 seconds: human reaction time
It takes about 0.2 seconds from the time you touch a hot stove to the involuntary retraction of your hand.
3 x 1015 seconds: dinosaurs
The T-rex and his friends roam the Earth, and birds begin to replace the pterosaurs. It’s still 24 million years until the meteor that hit Chicxulub and wiped out the dinosaurs.
1 x 1015 seconds: grass
The first grasses appear about 40 million years ago, well after the dinosaurs have gone extinct.
1 x 10–1 seconds: the black mamba
The black mamba is one of the fastest (and deadliest) snakes on the planet. It can move at a speed of 25 km/h, which means that it travels 1 m in only 0.14 seconds.
6 x 1014 seconds: glass
It takes glass about 20 million years to degrade, and this makes it one of the most durable materials known to man.
1 x 10–3 seconds: engine stroke
When idling, a car’s engine is still running. Each stroke of the engine last about a tenth of a second. When accelerating, the engine stroke can become ten times as fast.
3 x 1014 seconds: the first apes
Our ancestors—the apes—evolved about ten million years ago. Primates tend to live in trees in (sub-) tropical regions. Humans are the only apes that migrated to all continents.
1 x 10–1 seconds: false start
In the Olympics, if the athlete starts running within a tenth of a second after the starting shot, it is considered a false start.
4 x 1019 seconds: star formation stops
Due to the lack of available interstellar dust in nebulae, star formation will come to a halt. This means that the lights in the universe are going out. For the rest of time the universe will be dark.
1 x 100 seconds: the second
The second is our unit of time, defined in the Système International as the duration of 9 192 631 770 periods of the radiation of two hyperfine levels of a caesium atom.
2 x 1019 seconds: black hole evaporation
Primordial black holes of 1011 kg (the size of a small asteroid) take this long to evaporate via Hawking radiation. Stellar black holes take much, much longer.
9 x 10–1 seconds: heart beat
The average heart beat rate of an adult human at rest is about 70 beats per minute, which translates to one beat every 0.9 seconds.
1 x 1019 seconds: Local Group merger
Around this time the 47 galaxies of the Local Group will have merged into one large supergalaxy.
8 x 10–1 seconds: sound travels 280 m
If you shout from the top of the Shard in London it takes the sound 0.8 seconds to reach street level, still well in time to warn passers by about the falling flower pot.
7 x 1018 seconds: big bang echo fades away
The cosmic microwave background radiation—currently at 2.7 K—cools further to 0.3 K. This is undetectable with current technology.
8 x 10–1 seconds: burning a match head
The head of a match will keep going in strong winds (or even under water) because the head has its own oxygen supply. It burns out in roughly 0.8 s.
7 x 10–1 seconds: halflife of C16
Carbon comes in a variety of isotopes. A nucleas with 6 protons and 10 neutrons is unstable, however, and such a nucleaus has a 50:50 chance of decaying after 0.7 s.
4 x 1018 seconds: cosmic isolation
The universe’s expansion causes all galaxies beyond the Milky Way’s Local Group to disappear beyond the cosmic horizon, removing them from the observable universe.