In the context of quantum computing, "magic states" refer to certain non-classical states of qubits that are used to enhance the performance of quantum algorithms, specifically quantum error-correcting codes and fault-tolerant quantum computation. Magic states play a crucial role in achieving fault tolerance and error correction in quantum systems.
The concept of magic states is closely related to the field of quantum error correction and fault-tolerant quantum computing, which aims to protect quantum information from errors and noise that naturally occur in quantum hardware. Magic states are used to implement certain quantum gates that are not intrinsically fault-tolerant. These gates are known as "non-Clifford gates," and they include operations like the T gate, which generates irrational phases and is not directly protected by typical error correction methods.
Here's why magic states are important and how they work:
Non-Clifford Gates and Fault Tolerance: Clifford gates are a specific set of quantum gates that can be implemented fault-tolerantly using stabilizer codes. However, non-Clifford gates, like the T gate, are not as easily protected by standard error correction methods. Magic states are used to perform these non-Clifford gates fault-tolerantly, enabling the construction of fault-tolerant quantum circuits.
Preparation of Magic States: Magic states are typically prepared using quantum processes that exploit specific quantum resources. For example, in the context of the T gate, a particular type of magic state called the "T state" is prepared. These states can be used to perform non-Clifford gates without compromising the fault tolerance of the quantum computation.
Error Resilience: Magic state distillation is a process used to enhance the quality of magic states and make them more resilient to errors. By iteratively applying quantum operations and measurements, it's possible to purify and improve the fidelity of magic states.
Threshold Theorems: Magic states are essential components for achieving quantum error correction thresholds, which are theoretical benchmarks for fault-tolerant quantum computation. Quantum error correction thresholds define the error rates that a quantum computer must achieve to perform computations reliably beyond a certain threshold.
In summary, magic states are specialized quantum states that play a crucial role in fault-tolerant quantum computation, enabling the implementation of non-Clifford gates in a way that is compatible with error correction techniques. Magic state distillation is an important process for improving the quality of these states and enhancing their fault tolerance. The study of magic states and their properties is an active area of research in the field of quantum computing.