Researchers have succeeded in developing a technique to quickly find the optimal quantum gate sequence for a quantum computer using a probabilistic method.

To make a quantum computer perform a task, it must use a compiler to convert instructions written in a programming language into a sequence of gate operations on quantum bits, or qubits for short. They previously applied optimal control theory (GRAPE algorithm) to an exhaustive search to develop a method to identify the theoretically optimal gate sequence, but as the number of qubits increases, the number of possible combinations increases.

As the number grows explosively, a thorough search becomes impossible. For example, if we were to perform an exhaustive search to find the optimal gate sequence for the task of generating an arbitrary 6-qubit quantum state, it would take longer than the age of the universe using the fastest classical computer available today.

Therefore, the researchers tried to develop a method to search for the optimal quantum gate sequence using a probabilistic approach and succeeded. Using the Fugaku supercomputer, it was confirmed and demonstrated that using a new probabilistic random search method, it is possible to search for the optimal quantum gate sequence for the above problem in a few hours.

This new method is expected to speed up quantum computer compilers, become a useful tool for practical quantum computers, and lead to better performance of quantum computing devices. It can also be applied to optimize quantum information processing in quantum relay nodes, thus it is expected to contribute to the realization of the quantum internet and the reduction of environmental impact.

This result was published in the journal *Physical review A* on May 6, 2024.

Quantum computers, which are currently under development, are expected to have a major impact on society. Among its benefits are the reduction of the environmental burden through the reduction of energy consumption, the search for new chemical substances for medical use, the acceleration of the search for materials for a cleaner environment, etc. One of the big problems with quantum computers is that the quantum state is very sensitive to noise. , so it is difficult to keep it stable for a long time (maintaining a coherent quantum state).

For best performance, operations must proceed in a time that allows the quantum state to remain consistent. However, apart from the special case where the number of qubits is very small, no good method for finding the optimal quantum gate sequence has been known.

A solution has been awaited that avoids the difficulty of the explosive increase in the number of possible gate sequences even in large-scale quantum computations and allows efficient searches within the time and computational resources that can be performed on classical computers.

The research team introduced a probabilistic method to develop a systematic method that can efficiently search for the optimal quantum gate sequence within runtime and computational resources.

When a computer stores and processes information, all information is converted into a string of bits with values of 0 or 1. A quantum gate sequence is a computer program written in a human-readable language after being converted by be able to process it. using a quantum computer. The quantum gate sequence consists of 1-qubit gates and 2-qubit gates. The best sequence is the one with the fewest gates and shows the best performance.

Their study shows the estimated computation time when performing a search to optimize fidelity F on the fastest classical computer for each gate arrangement using the optimal control theory algorithm GRAPE to prepare n qubit states. The solid blue line is the so-called age of the universe (13.7 billion years). As the number of qubits increases, the number of possible combinations increases explosively, so that an=6, the total computation time exceeds the age of the universe.

Analysis of all possible sequences for small qubit numbers reveals that there are many optimal quantum gate sequences. This suggests the possibility of expanding to large quantum tasks and finding the optimal quantum gate sequence using a probabilistic search method instead of an exhaustive search.

They also show the occurrence rate (p) of sequences with fidelity F=1 for the preparation of a state consisting of n=8 qubits, which was investigated using the Fugaku supercomputer. The speed p is expressed as a function of the number of 2-qubit CNOT gates (N) in the sequence. It is clear that the probabilistic method is very efficient because the F=1 occurrence rate increases rapidly when the lower limit of N (N=124) is exceeded.

For example, the occurrence rate of F=1 in N=129, which is slightly more than N=124, is greater than 50%, so if you search for a gate arrangement twice, you will find a quantum sequence that has F=1 at least once on average. Thus, it has been found that by using a probabilistic method, it is possible to search for optimal quantum gate sequences several orders of magnitude faster than when searching using an exhaustive search method.

The systematic and probabilistic method developed to provide optimal quantum gate sequences for quantum computers is expected to become a useful tool for practical quantum computers and speed up quantum computer compilers. It is expected to improve the performance of quantum computing devices and contribute to the development of quantum nodes in the quantum internet and the reduction of environmental burden.

In the future, the research team will integrate the results obtained in this study with machine learning approaches and apply them to optimize the performance of quantum computers, with the aim of further speeding up quantum compilers and creating a foundation of data of optimal quantum gate sequences.

The research team includes the National Institute of Information and Communications Technology, RIKEN, Tokyo University of Science and the University of Tokyo.

**More information:**

Sahel Ashhab et al, Quantum Circuit Synthesis Using Random Combinatorial Search, *Physical review A* (2024). DOI: 10.1103/PhysRevA.109.052605

Provided by the National Institute of Information and Communications Technology (NICT)

**Summons**: Researchers develop compiler-acceleration technology for quantum computers (2024, May 9) Retrieved May 10, 2024, from https://phys.org/news/2024-05-technology-quantum.html

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