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University of Basel

Computing in a chaotic world.

Text: Roland Wengenmayr

Quantum information is extremely fragile and can be disturbed by even the slightest interference. Error correction in a quantum computer will require highly sophisticated repair mechanisms. A glimpse into the mind of physicist James Wootton reveals what such mechanisms might look like.

Example of a surface code: Squares are arranged in a grid structure on an imaginary surface. On the corners of each square are physical qubits – e.g. ions. They are arranged in the states 1 and 0 in such a way that each square has an even number of ones. Deviations from this rule are errors. This pattern allows loops (in red) but no lines consisting of ones. If a line appears, the value of the qubits it is made up of (1 or 0) must be wrong. However, end points for these lines can be found, consisting of squares (orange, top), which each contain one error. By joining these into a loop (example in red, bottom), errors can be removed.
Example of a surface code: Squares are arranged in a grid structure on an imaginary surface. On the corners of each square are physical qubits – e.g. ions. They are arranged in the states 1 and 0 in such a way that each square has an even number of ones. Deviations from this rule are errors. This pattern allows loops (in red) but no lines consisting of ones. If a line appears, the value of the qubits it is made up of (1 or 0) must be wrong. However, end points for these lines can be found, consisting of squares (orange, top), which each contain one error. By joining these into a loop (example in red, bottom), errors can be removed.

Quantum information holds the key to algorithms capable of solving complex tasks that are beyond the scope of classical computers. The processing power of a quantum computer derives from an ingenious superposition of the quantum state of qubits. While the computer is performing its quantum logic operations, qubits become temporarily entangled with one another, in a special quantum state that is particularly susceptible to disturbances. The moment this state collapses, the value of the quantum information is lost.

Such a disturbance can be caused even by an attempt to read the quantum information in the course of a measurement. However, it can also be the result of external physical influences on the quantum system – something our world is full of. One example in the microworld is the ever-present effect of thermal energy, which even at low temperatures constantly jostles the physical carriers of quantum information, such as electron spins. Even the Earth’s magnetic field can disrupt quantum information – after all, spins are nothing more than tiny magnets, explains James Wootton, a theoretical physicist at the University of Basel. Wootton likens these disturbances to gremlins: little monsters that come out of nowhere to attack the highly sensitive world of quantum information from all sides.

Error correction procedure

James Wootton is researching new methods which allow quantum information to be safely packaged so as to protect it from disturbances. A quantum computer has to be able to detect errors in a kind of ongoing self-diagnosis. Depending on the procedure employed, errors are either repaired immediately, or tracked over the course of the operation and subsequently purged from the result. Diagnosis and correction must be performed with great care, however, as the quantum information itself must never be read while the computer is in action. Reading the information would constitute a measurement, destroying the quantum properties required in order to continue the processing operation.

The procedure can be compared to holding an unopened envelope against the light to find out whether or not it contains a letter, although the correspondence itself may not be read. This ingenious form of error correction goes even further still; the idea is that it will be able to spot individual missing letters and restore them – without actually reading the text itself.

Physical and logical qubits

This approach to error detection and correction is known as surface code. The surface code packages the quantum information so as to be largely protected from disturbances. Furthermore, it offers diagnostic possibilities allowing errors in the qubits to be detected and corrected without touching the quantum information itself. To this end, a distinction is made between two kinds of qubits: The basic building blocks are a large number of physical qubits. They are referred to as physical because each qubit relies on the quantum properties of an actual particle – e.g. the spin of an electron. These qubits can be thought of as the hardware, and are arranged on a surface – hence the name surface code – in a regular grid pattern, e.g. on the corners of the squares contained in a checkerboard pattern (see graphic). Other patterns are also possible.

Physical qubits can be used to verify the interactions between them without reading the quantum information itself. This information is contained in the logical qubits, which can be thought of as encoded software fragments distributed across the grid of physical qubits. By manipulating the physical qubits in a certain way, logical qubits can be moved and made to carry out operations. In correction cycles, they are not directly read by the surface code. Due to the broad distribution of the logical qubits across many different physical qubits, local errors do not have such a disruptive impact – in much the same way that a minor weaving fault is barely noticeable in the pattern of a carpet.

Keeping information stable

How can quantum information be packaged as stably as possible in logical qubits? In his theoretical considerations, Wootton sees the surface code as a two-dimensional world which he can populate with exotic particles. His favorites are called anyons. These are not true particles as such, but quasiparticles emerging from the totality of physical qubits. Anyons are also their own antiparticles. Accordingly, on his 2D playing field Wootton can conjure up anyon pairs from nothing and make them disappear again. And that is not all: If he pushes one of a pair of anyons over the edge of the playing field, on to the substitutes’ bench, as it were, its partner remaining on the field has no choice but to survive in a stable state, as dictated by the laws of quantum physics. This makes anyons stable transporters for logical qubits.

What is more, anyons can do things in the 2D world that are impossible in three dimensions. When one anyon moves in a loop around another, the anyon inside the loop changes. This enables them to perform quantum logic operations. Quantum physicists call this braiding. As the anyons are always carried by multiple physical qubits, the quantum information is much more stably packaged than would be the case in a single physical qubit. Equally, the rules have stabilizing implications for anyons. Quantum logic operations can be compared to different carpet patterns, in which weaving faults can be detected. Depending on the algorithm used, the quantum computer can either correct these faults immediately or record them in a log, without reading the quantum information itself.

Further experiments are needed to find out whether James Wootton’s theoretical concepts can be implemented in practice. For now, they remain a vision for the future. At present, the most highly controllable experiments with entangled qubits use ions – electrically charged atoms lined up like beads on an abacus, suspended in special “traps”. The next step for quantum computing research is to make the technological leap from one to two dimensions. Only then can surface code error correction be tested in the real world.


More articles in the current issue of UNI NOVA.

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