New method to systematically find qua optimal

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image: Quantum Operation Sequence (conceptual diagram) The six horizontal blue lines represent six qubits, with input on the left and output on the right. Operations are executed from left to right. Each red square represents a 1-qubit operation, and each green vertical line connecting two blue lines represents a 2-qubit operation. The optimal sequence of quantum operations is achieved with the fewest operations.
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Credit: National Institute of Information and Communication Technologies (NTIC); Keio University; Tokyo University of Science; School of Science, University of Tokyo

[Highlights]

– Development of a new method to find optimal quantum operation sequences for quantum computers
– Based on GRAPE, the new method systematically finds sequences of quantum operations and enables efficient execution of tasks
– Should help improve the performance of quantum computers and reduce environmental impact

[Abstract]

The National Institute of Information and Communication Technology (NTIC, President: TOKUDA ​​​​Hideyuki, Ph.D.), Keio University (President: ITOH Kohei, Ph.D.), University of Tokyo Science (Chair: Dr. ISHIKAWA Masatoshi), University of Tokyo (Chair: Dr. FUJII Teruo), succeeded for the first time in developing a method to systematically find the optimal quantum operation sequence for a quantum computer.

For a quantum computer to perform a task, we need to write a sequence of quantum operations. Until now, computer operators wrote their own sequences of quantum operations based on existing methods (recipes). What we have developed this time is a systematic method that applies Optimal Control Theory (GRAPE algorithm) to identify the theoretically optimal sequence among all imaginable quantum operation sequences.

This method is expected to become a useful tool for medium-scale quantum computers and is expected to help improve quantum computer performance and reduce environmental impact in the near future.

This result was published in the American scientific journal “Physical examination Aon August 23, 2022.

[Background]

Quantum computers, currently under development, are expected to have a major impact on society. Their benefits include reducing the environmental load by reducing energy consumption, researching new chemical substances for medical use, accelerating the research of 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). In order to obtain the best performance, it is necessary to complete the operations in time that the coherent quantum state is maintained. There was a need for a method to systematically identify optimal sequences.

[Achievements]

The research team developed a systematic method to identify the optimal quantum operation sequence.

When a computer stores and processes information, all information is converted into a string of bits with values ​​of 0 or 1. A sequence of quantum operations is a computer program written in a human-readable language that is converted so that it can be processed by a quantum computer (see Figure 1). The sequence of quantum operations consists of 1-qubit operations and 2-qubit operations. The best sequence is the one that has the fewest operations and shows the best performance (the number of red squares and green vertical lines is the smallest).

The new method analyzes all possible sequences of elementary quantum operations using a computational algorithm called GRAPE, a numerical algorithm from optimal control theory. Specifically, we create a table of quantum operation sequences and the performance index (fidelity F) for each sequence, ranging from thousands to millions, depending on the number of qubits and the number of operations studied. The optimal quantum operation sequence is systematically identified based on the accumulated data. Figure 2 shows the relationship between the length of the quantum operation sequence and its performance index, and it can be seen that if the number of qubits n is 4, five gates of 2 or more qubits are needed.

It is also possible for the new method to analyze the full list of all quantum operation sequences and evaluate conventional recipes. As such, it can provide a valuable tool to establish benchmarks for past and future research into the performance of few-qubit quantum algorithms.

[Future prospects]

The systematic method for finding the optimal quantum operation sequence for quantum computers should become a useful tool for medium-scale quantum computers. In the near future, it should improve the performance of quantum computers (see Figure 3) and help reduce the burden on the environment.

We have also found that there are many optimal sequences of quantum operations which are excellent. This means that a probabilistic approach could extend the applicability of this new method to larger tasks. Approaches based on the analysis of large datasets suggest the possibility of integrating machine learning into our new method to further improve predictive power. In the future, the research team will apply the results obtained this time to the optimization of tasks obtained from real quantum algorithms.


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