#PETER SHOR QUANTUM ERROR CORRECTION HOW TO#
#PETER SHOR QUANTUM ERROR CORRECTION CODE#

The two identical triplets, however, retain an accurate record of the original qubit state. If one qubit out of the nine is disturbed, then the triplet it belongs to will become different from the other two. The nine-qubit state is a set of three groups containing three qubits each, all of which are identical at the start.

#PETER SHOR QUANTUM ERROR CORRECTION HOW TO#

Shor explained how to create, from a single qubit, a state of nine qubits that are connected through quantum entanglement and that encode the original superposition. The problem is that any direct test of a qubit amounts to a measurement that destroys its superposed state. Shor addressed this concern in 1995 by coming up with a way to test whether a qubit has been disturbed and, if so, correct it. Some researchers argued that it would be impossible to preserve qubits long enough to perform a calculation. A qubit can maintain its identity only as long as it is kept strictly isolated from disturbances that would knock it out of its quantum superposition and force it to become either a one or a zero. īut doubts also arose about the feasibility of quantum computing. In 1994, Peter Shor of AT&T Bell Labs in Murray Hill, New Jersey, showed that such a device could rapidly find the factors of large numbers, a task that is prohibitively time-consuming using conventional computers. Instead of ones and zeros, the quantum bits (“qubits”) could be in states that were partially one and partially zero-a more versatile system.

The idea of quantum computing is often credited to Richard Feynman, who gave a talk in 1981 arguing that quantum combinations, or “superpositions,” of two distinct states could form the elements of a computer. The discovery inspired fault-tolerant designs that could make large-scale quantum computers feasible, as well as methods to preserve information transmitted by quantum-mechanical means. They devised error-correction methods that would protect the fragile quantum states essential to the inner workings of a quantum computer. In the mid 1990s, two researchers working independently showed theoretically how to get around one major difficulty that some thought insurmountable. Quantum computers were dreamed up long before any practical demonstration became possible. Landmarks articles feature important papers from the archives of the Physical Review journals. Error-correction techniques allowing qubits to recover from unwanted disturbances will be a crucial part of any large-scale quantum computer. This arrangement of gold electrodes on a chip can hold up to twelve magnesium ions 40 micrometers above its surface while laser light cools them, enabling the ions to functions as qubits.

#PETER SHOR QUANTUM ERROR CORRECTION CODE#

In the first picture, the encoding for correcting phase-flips is concatenated with an equivalent code for handling bit-flips, so that the same type of process can be used to correct both types of errors.S. The classical information from this measurement is then used to determine whether any corrective single-qubit operations (phase-flips in this specific case) are needed to repair the encoded state. The process is performed by entangling the state with one or more ancillary qubits in such a way that a measurement on the ancillary qubits is equivalent to a measurement in the required joint basis. This involves a joint measurement across the state in a basis that will identify which qubit (if any) has an error, without gathering any information about the encoded logcial state.

The next step of the process is syndrome extraction. This lets you know the original state is still recoverable. If you imagine that happening to the states shown in that picture, you should be able to see that you could tell what the original state was just by looking at the phase held by the majority of the physical qubits.

Start with the second picture: a phase-flip error on one physical qubit would take a qubit in the |0> + |1> state to |0> - |1>, and vice versa. These codes are fairly simple, so you should be able to understand a fair bit just by looking at the equations. I assume you have realised, but there's a typo in the first image, where the denominator should be root(8) rather than root(1).

Peter shor quantum error correction