Read more: “Instant Expert 33: Quantum information“
The theory is in place, and we have no shortage of ideas as to how we can physically implement a quantum computer. But what might we use them for if we did? There are many suggestions – some practical, some highly fanciful
Ultrasecure encoding
One quantum information technology is already up and running. Various small-scale quantum cryptographic systems for secure information transfer, typically using polarised photons as their qubits, have been implemented by labs and companies such as Toshiba, Hewlett Packard, IBM and Mitsubishi. In October 2007, a quantum cryptography system developed by and his colleagues at the University of Geneva in Switzerland was used to transmit votes securely between the city’s central polling station and the counting office during the Swiss national elections. A similar trial system developed by the researchers’ company, ID Quantique, was used to transmit data securely .
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The distance through which quantum states can be transmitted through fibre-optic cables is limited to tens of kilometres owing to random diffusion. One promising way to get around this is akin to error correction protocols devised for quantum computers: to spread information over more than one qubit (see “Quantum information: The promise“). But this might pose a security risk by giving more information for an eavesdropper to hack.
Transmission via air is an alternative. The world record in faithfully teleporting a qubit of information, held by Anton Zeilinger of the University of Vienna, Austria, and his colleagues, is over a distance of . This indicates that delicate quantum states can be transmitted significant distances through air without being disturbed – and suggests that a worldwide secure quantum network using satellites is a distinct possibility.
Quantum simulation
Richard Feynman’s original motivation for thinking about quantum computers in 1981 was that they should be more effective than classical computers at simulating quantum systems – including themselves.
This sounds a little underwhelming, but many of science’s thorniest practical problems, such as what makes superconductors superconduct or magnets magnetic, are difficult or impossible to solve with classical computers.
Quantum information theorists have already developed intricate algorithms for approximating complex, many-bodied quantum systems, anticipating the arrival of quantum computers powerful enough to deal with them.
The beauty is that such simulators would not be limited to existing physics: we could also use them to glean insights into phenomena not yet seen. Quantum simulations might tell us, say, where best to look in nature for Majorana particles, for example in complex many-bodied superconductor states. Since these particles, thought to be their own antiparticles, have properties that could make them ideally suited to making robust quantum memories (see “Quantum information: Building a quantum computer“), this raises the intriguing possibility of using quantum computers to suggest more powerful quantum computers.
Metrology
Making precise measurements is a potentially highly significant application of quantum computers. When we record sensitive measurements of physical quantities, such intervals in time or distances in space, the effects of classical noise mean that the best statistical accuracy we can achieve increases with the square-root of the number of bits used to make the recording.
Quantum uncertainty, meanwhile, is determined by the Heisenberg uncertainty principle and improves much more rapidly, simply with the number of measurements made. By encoding distances and time intervals using quantum information – probing them using polarised laser photons, for example – much greater accuracies can be achieved.
This principle is already being applied in giant “interferometers” that use long laser beams in a bid to detect the elusive gravitational waves predicted by Einstein’s relativity, such as the LIGO detector in Livingston, Louisiana. In these cases we can think of gravity as noise that disturbs qubits – the qubits being the position and momentum of laser photons. By measuring this disturbance, we can estimate the waves’ strength.
Number crunching
The promise of quantum computers rests largely on two algorithms. One, developed in 1994 by , then of Bell Laboratories, provides a way for a quantum computer to speedily find the prime factors of large numbers. Classical computers effectively have to try to divide the given number by all possible prime factors (2, 3, 5, 7, 11 and so on) in turn, whereas quantum computers can do these divisions simultaneously.
Conventional encryption methods rely on the fact that classical computers cannot factorise efficiently. If Shor’s algorithm were ever implemented on a large scale, encrypted information such as the PIN for your bank card would be vulnerable to hacking – and quantum cryptography would be the only viable defence (see below). There is no need to worry just yet: demonstrations so far, for example using a 7-qubit nuclear-spin quantum computer, .
In the longer term, an algorithm devised by physicist in 1996, also at Bell Labs, may become a quantum computer’s greatest selling point. This provides a recipe by which a quantum computer can radically speed up how we access and search large bodies of data. Take the example of a database listing the contents of a library. Searching this database for a particular book with a classical computer takes a time that scales with the number of books, n; Grover’s algorithm shows that for a quantum computer it scales with √n. For a library of a million books, this amounts to 1000 times faster.
“A quantum computer could search the database of a million-book library 1000 times faster than a classical computer”
Implementing such an algorithm has ubiquitous appeal: almost all computationally hard problems – for instance that of the travelling salesman who has to find the shortest route between a number of different cities – ultimately reduce to a search for the optimal solution.There’s a way to go yet. The biggest Grover search yet performed, with 3 qubits, allows for a search of just 8 database elements.
This article appeared in print under the headline “Killer quantum apps”
