× close

Estimated computation time for using GRAPE to perform a search to optimize fidelity F for each gate placement and prepare states for n qubits. The solid blue line is the time from the beginning of the universe to the present (13.7 billion years).Credit: National Institute of Information and Communications Technology (NICT), RIKEN; Tokyo University of Science; Faculty of Science, University of Tokyo

Researchers have successfully developed a technology that uses probabilistic methods to rapidly search for optimal quantum gate arrays for quantum computers.

To make a quantum computer perform a task, a compiler must be used to convert instructions written in a programming language into a series of gate operations on quantum bits (qubits for short). They had previously developed a method to identify the theoretically optimal gate sequence by applying optimal control theory (GRAPE algorithm) to an exhaustive search, but as the number of qubits increases, the possible The number of combinations increases.

If the number increases explosively, a comprehensive search will become impossible. For example, if we perform an exhaustive search to find the optimal gate sequence for the task of generating an arbitrary quantum state of 6 qubits, using the fastest classical computer currently available, It will take time.

The researchers therefore attempted to develop a method to search for the optimal quantum gate arrangement using a probabilistic approach, and were successful. Using the supercomputer “Fugaku”, we confirmed and demonstrated that it is possible to search for the optimal quantum gate array for the above problem in a few hours using a new stochastic random search method.

This new method is expected to speed up quantum computer compilers, making them a useful tool for practical quantum computers and leading to improved performance of quantum computing devices. It can also be applied to optimize quantum information processing at quantum relay nodes, so it is expected to contribute to the realization of the quantum internet and the reduction of environmental impact.

This result was published in a magazine *Physical review A* May 6, 2024.

Quantum computers, which are currently under development, are expected to have a major impact on society. Benefits include reducing environmental impact through reduced energy consumption, discovering new chemicals for medical use, and accelerating the search for materials for a cleaner environment. One of the big problems with quantum computers is that quantum states are very sensitive to noise. , Therefore, it is difficult to maintain stability for a long time (maintain a coherent quantum state).

For best performance, operations should continue long enough for the quantum state to remain coherent. However, there is no known good method for finding the optimal quantum gate array, except in special cases where the number of qubits is very small.

A solution that avoids the difficulty of explosively increasing the number of possible gate sequences even in large-scale quantum computations and allows efficient exploration within the time and computational resources that can be performed on classical computers. A plan was awaited.

The research team introduced a stochastic method to develop a systematic method that can efficiently search for optimal quantum gate sequences within the limits of execution time and computational resources.

When computers store and process information, all information is converted into strings of bits with values of 0 or 1. A quantum gate sequence is a computer program written in a human-readable language that has been transformed so that it can be processed. by quantum computers. A quantum gate sequence consists of a 1-qubit gate and a 2-qubit gate. The best sequence is the one with the least number of gates and the best performance.

Their work uses the optimal control theory algorithm GRAPE to prepare n-qubit states to estimate the computational time of performing a search to optimize the fidelity F on the fastest classical computer for each gate placement. is shown. 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 exponentially, so for n=6 the total computational time exceeds the age of the universe.

Analyzing all possible sequences for a small number of qubits reveals that there are many optimal quantum gate sequences. This suggests the possibility of extending to large-scale quantum tasks and finding optimal quantum gate sequences using probabilistic rather than exhaustive search methods.

It also shows the occurrence rate (p) of sequences with fidelity F=1 when preparing a state consisting of n=8 qubits, which was investigated using the supercomputer “Fugaku.” The rate p is expressed as a function of the number (N) of two-qubit CNOT gates in the sequence. We see that the probabilistic method is very efficient, as the probability of F=1 increases rapidly above the lower bound of N (N=124).

For example, the occurrence rate of F=1 at N=129, which is slightly larger than N=124, is more than 50%, so if you search the gate arrangement twice, you will find a quantum string with F=1. On average at least once. In this way, it was found that by using the stochastic method, it is possible to search for an optimal quantum gate array several orders of magnitude faster than when using the exhaustive search method.

The development of a systematic and probabilistic method to provide optimal quantum gate sequences for quantum computers will be a useful tool for practical quantum computers, and is expected to 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, thereby further speeding up quantum compilers and building a database of optimal quantum gate arrays. The company aims to do so.

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

**For more information:**

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

**Magazine information:**

Physical review A

*
*

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