Stone tablets, paper, and digital media are some of the more durable and useful forms of information we have learned to put into. In the 1980s, researchers began to discuss how to store information inside a quantum computer, where it is subject to all sorts of atomic-scale errors. They found a few methods, but they fell short of their rivals from classical computers, which provided an incredible combination of reliability and efficiency.
In a preprint posted on November 5th, Pavel Panteleev and Gleb Kalachev of Moscow State University show that quantum information can be protected from errors just as well as classical information can. They did it by combining two classical methods and inventing new ones.
Jens Eberhardt of the University of Wuppertal in Germany said that it was a huge achievement.
The quantum equivalent of classical bits are 100 qubits. They will need a lot more to become useful. As the number of qubits increases, the new method for quantum data will keep the size and complexity of future quantum computers to a minimum.
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The authors showed how their quantum method could be used to make classical information testable for errors, at the same time that another group discovered the same capability in a classical method. Alex Lubotzky of the Weizmann Institute of Science in Israel said it was amazing how a problem that had been open for 30 years was solved by two different groups.
We can't protect everything from errors. Classical information can be represented in a sequence of bits, 1s and 0s, as a mathematical representation. When we build these bits in the form of electrical circuits, we find that noise causes random bits to flip to the wrong value.
Claude Shannon and Richard Hamming discovered methods to detect and correct errors before computation began.
The method was practical. He added new bits to the sequence that acted like receipts to specify how some of the initial bits should sum up. The sum of all the other bits has an even value, if a digit is appended to it. Errors could be detected and corrected if the data bits were checked against the receipt bits.
The methods for correction are now called error-correcting codes. A code can be used to create a sequence of bits that can be used to repair an iron chain.
An iron chain can be repaired with the help of a code.
Creating a code was difficult for quantum computers. quantum computers use qubits that are all at once. These are vulnerable to two kinds of errors, which can either collapse them to a single value or throw off the balance between them. The protection of qubits is much more complicated because each error can interact with the other.
These qubits are not good. Panteleev said they are really noisy.
The problem was simpler than it seemed in 1995 when Peter Shor showed it. He used two classical codes to create a quantum code. He made the quantum ore of qubits into a strong chain. The first quantum code required many receipt qubits for an initial sequence.
Classical codes have three specific properties that are available, which is more advanced than the technology of classical codes. A code that had all three of them was called good. It should be able to correct many errors. The chain should be light and efficient if few receipt bits are added. The strength and efficiency of the chain should not be affected by how long a sequence of bits you started with. Shannon showed that you could always improve the ability to suppress errors by increasing the chain length. This finding was later reproduced in a quantum context.
Researchers wanted to create quantum codes with the same properties. For those three, they succeeded. There was an additional fourth property that they couldn't get in addition to the other three. The low-density parity check states that each receipt should only contain a small number of bits.
It is a nice thing to have for classical codes. It is indispensable for quantum codes.
When trying to combine classical codes with a good quantum code, the initial approach broke down. ClassicalLDPC codes were incompatible and could not be combined in an optimal way. For over 20 years, no one could figure out how to get a quantum code that simultaneously held the LDPC property with constant scaling.
In 2020, a group of researchers, including Panteleev and Kalachev, figured out new ways to combine classical codes to make a quantum code. The quantum chains that they forged became weaker with increasing length, but not as quickly as the codes that had come before. Breuckmann and Eberhardt created a quantum code that they thought would have constant scaling, but they were not able to prove it.
In 2021, Panteleev and Kalachev built on the surge of work to create a new quantum code, which they could prove possessed the elusive combination of all four properties. The classical codes have a symmetry that distinguishes them.
A common perspective in the mathematics of codes is that of a graph, a collection of edges connected by dots. The edges of the graph are represented by bits of information and the receipts are represented by bits of information. A code with a circular graph can be said to have rotational symmetry. The code of a graph can be identified with its geometric properties. The length of the shortest path around a torus can be identified with the strength of the code.
Panteleev and Kalachev have a quantum code that is similar to a combination of graphs. The quantum code is highly symmetric, like a torus. As the number of qubits in the graph increases, the lengths on the torus can be increased. Constant scaling is provided in addition to the other three properties.
The result shows that quantum codes match classical codes. It also provides a means to make quantum computers more efficient since they can correct errors as they are made larger.
Naomi Nickerson of the quantum computing company PsiQuantum said that the theoretical quality of the quantum codes has existed for a long time.
Panteleev and Kalachev became aware that their quantum code could be interpreted as a classical code with a special property. If the data is filled with a lot of errors, it means that checks of almost any receipt will reveal them. Local testability is a property that has constant scaling of all three properties, making for a new type of code that has been long evaded by researchers.
