Causes and ways to eliminate quantum errors
A quantum computer is a very strange device, based on the abstract idea of superposition, which is completely incomprehensible to many people. And this is what makes such devices many times more sensitive to quantum errors that arise for various reasons. Correcting them is very important for creating practical quantum computers that can perform useful calculations. Otherwise, errors will quickly destroy fragile quantum information. How does science today propose to solve this problem?
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As technology develops, the number of qubits in quantum computers is gradually increasing. However, the current level is still completely insufficient to ensure completely fault-tolerant computations. At the same time, it is necessary to strive to use as few qubits as possible to execute programs. One way to achieve this is reuse, when each qubit is used not just once, but as many times as possible when executing a program. They calculate some operation, reset the state of the qubits used for this and put them back into operation. There are three “main” approaches to implementing reuse: quantum teleportation, quantum error correction, and quantum computation based on measurements.
Errors in regular computers
When solving any problem on modern computers, there is usually less than one error in a million billion (1015) operations. That is, we can assume that for most tasks in the components of such a device there is no “noise” at all – errors in calculations that can occur due to imperfections in the physical implementation of the computer. At the same time, components such as modems and CD drives are significantly susceptible to noise. To level out its impact, correcting codes (error correction codes) are used: structured redundant information is added to the data, and if part of the data is damaged for some reason, the redundancy will allow us to restore all the original information.
Quantum errors
Errors in quantum computing can arise due to:
decoherence — disruption of the predictable and interconnected state of particles when a quantum-mechanical system interacts with the environment through a process that is irreversible from the point of view of thermodynamics;
management errors;
“noise” of the environment.
Correction of quantum errors is becoming increasingly popular. The main difficulty is to accurately determine their sources and causes. And since everything happens at the level of elementary particles, developers must have a very deep understanding of the physical principles and structure of quantum computers. And specialized detection tools are also required.
Reasons for quantum error correction:
Quantum states are incredibly fragile and error-prone. Even the slightest change can be fatal. For example, a single photon that is absorbed or scattered by the environment can flip a qubit, causing a computational error.
As the size of a quantum computer grows, so does the probability of errors in it. The more imperfect computing elements in the design, the more “noise” they introduce. There is exponential growth in the number of errors.
Quantum error correction depends on principles quantum entanglementThe idea is to create a code that is distributed across multiple qubits, so that any error can be detected and corrected without disrupting the computation itself. This is done by using entangled states between qubits.
To correct quantum errors, we need redundancy in quantum states. This means that multiple copies of the same quantum state are stored in different qubits.
Quantum Error Correction Methods
For better protection against quantum errors and noise, it is proposed to use logical qubitseach of which is “assembled” from several physical qubits. But this leads to a decrease in the computing power of the computer, so the more physical qubits are available, the higher the reliability of the calculations.
Also, to correct errors, the number of measurements is increased, algorithms with fewer operations are developed, and quantum gates are adjusted.
As in conventional computers, quantum errors are corrected by adding redundant information. However, this is where the similarity ends, because quantum computers cannot use correction algorithms created for silicon processors; this limitation is imposed on us by the very nature of quantum computing. Today, the most commonly used stabilizer codesdeveloped on the basis of Quantum Error Correction Theories by Peter Shor and Andrew Stan. But this is not the only component, they also use error detection codes, error correction codes And fault-tolerant codes. Each type has its own advantages and disadvantages, and researchers are looking for more efficient and reliable methods. One of the most promising approaches is quantum codes, which allow multiple errors to be corrected simultaneously. They are also called topological codes, because they are based on the principle of topological protection, which is a property of certain materials.
Error-correcting codes are used to detect and correct errors that may occur in qubits. For example, the three-qubit bit code uses three qubits to encode a single logical qubit in such a way that any of the three can be measured to detect an error. If an error is detected, the code can correct it by flipping the value of the affected qubit.
Another aspect of quantum error correction is error tolerance: the ability of a system to continue to operate even when one or more of its components are “noisy”. This is partly implemented in the NISQ generation of quantum computers, so with a certain stretch they can already be considered from a practical point of view. Resistance to “noise” is necessary for the creation of reliable quantum computers that can perform complex calculations.
Surface code — a correcting code that itself must be error-resistant. It is a two-dimensional array of qubits that uses a combination of measurement and error correction operations to protect qubits from noise. It is considered one of the most promising error-correcting codes.
Conclusion
Error-correcting codes are an important part of efforts to protect qubits from noise and other errors in quantum computing. These codes are essential for developing reliable quantum computers that can perform complex calculations. And while there are challenges to implementation, this is a promising technology for the future of computing.
Excess noise in quantum computers does not allow going beyond the experimental devices. The solution will probably be found in the integration of quantum systems with classical (non-quantum). In order to assemble a sufficiently balanced system with a minimum noise level, it is proposed to use Rydberg qubits as its basis. Currently, a program of “optimization with quantum devices of intermediate results with noise” (ONISQ) is being developed on their basis. Rydberg qubits are valuable for their homogeneity of properties: each qubit is indistinguishable from another in behavior. This cannot be said about other platforms, such as superconducting qubits, each of which is unique and not interchangeable, like neurons in the human brain. Therefore, maintaining high performance in our case is associated not with increasing the number of neurons, but with the development and ordering of connections between them. So far, scientists from DARPA have managed to connect 48 logical qubits, but much more will be needed to achieve the level of complexity necessary for practical quantum computers. It is believed that with the new methodology, development will require much less time and resources than originally expected.
