Quantum Computing Progress: Efficient Measurement of Stabilizer Entropies Achieved

Researchers from the Quantum Research Center Technology Innovation Institute in Abu Dhabi and Blackett Laboratory Imperial College London have developed an efficient method to measure Stabilizer Entropies (SEs) in quantum computing. SEs quantify the degree of non-stabilizerness or “magic” in quantum states and operations, and are crucial for running quantum algorithms. The team’s method allows for the measurement of SEs with fewer copies and less computational time, potentially improving the performance of quantum algorithms. The research also revealed that random Hamiltonian evolution becomes less scrambled over time, a finding that could impact the development of quantum algorithms.

What are Stabilizer Entropies and Why are They Important?

Stabilizer Entropies (SEs) are a measure of non-stabilizerness or “magic” in quantum computing. They quantify the degree to which a state is described by stabilizers. Stabilizers are essential to quantum information and quantum computing. They are the cornerstone to run quantum algorithms on most fault-tolerant quantum computers, where Clifford operations are intertwined with non-Clifford gates.

To characterize the amount of non-Clifford resources needed to realize quantum states and operations, the resource theory of non-stabilizerness has been put forward. SEs are measures of non-stabilizerness with efficient algorithms for matrix product states that have enabled the study of non-stabilizerness in many-body systems.

SEs are especially interesting due to their connections to scrambling, localization, and property testing. However, applications have been limited so far as previously known measurement protocols for SEs scale exponentially with the number of qubits.

How Can We Efficiently Measure Stabilizer Entropies?

The research team from Quantum Research Center Technology Innovation Institute in Abu Dhabi and Blackett Laboratory Imperial College London has developed a method to efficiently measure SEs for integer Rényi index n > 1 via Bell measurements. The SE of N-qubit quantum states can be measured with O(n) copies and O(nN) classical computational time.

For even n, the team additionally requires the complex conjugate of the state. They provide efficient bounds of various non-stabilizerness monotones that are intractable to compute beyond a few qubits. Using the IonQ quantum computer, the team measured SEs of random Clifford circuits doped with non-Clifford gates and gave bounds for the stabilizer fidelity, stabilizer extent, and robustness of magic.

The team also provided efficient algorithms to measure Clifford averaged 4n-point out-of-time-order correlators and multifractal flatness. With these measures, they studied the scrambling time of doped Clifford circuits and random Hamiltonian evolution depending on non-stabilizer ness.

What are the Implications of This Research?

This research opens up the exploration of non-stabilizerness with quantum computers. The efficient measurement of SEs could lead to a better understanding of quantum states and operations, and potentially improve the performance of quantum algorithms.

The research also revealed that random Hamiltonian evolution becomes less scrambled at long times, which was revealed with the multifractal flatness. This counterintuitive finding could have implications for the study of quantum systems and the development of quantum algorithms.

The research team’s work on SEs has also been related to various important properties of quantum systems. SEs probe error correction, which is a critical aspect of quantum computing. The ability to efficiently measure and understand SEs could therefore contribute to the development of more robust and reliable quantum computing systems.

Who are the Key People Involved in This Research?

The research was conducted by Tobias Haug and Soovin Lee from the Quantum Research Center Technology Innovation Institute in Abu Dhabi, UAE, and M S Kim from the Blackett Laboratory Imperial College London, United Kingdom.

Their work on efficient quantum algorithms for stabilizer entropies was received on 4 June 2023, revised on 8 May 2024, accepted on 10 May 2024, and published on 13 June 2024. Their research has contributed to the understanding of stabilizer entropies and their role in quantum computing.

What is the Future of Quantum Computing?

Quantum computing is a rapidly evolving field, and the efficient measurement of stabilizer entropies could play a significant role in its development. The research conducted by Tobias Haug, Soovin Lee, and M S Kim provides a foundation for further exploration of non-stabilizerness with quantum computers.

Their work could lead to the development of more efficient quantum algorithms and contribute to the study of many-body systems. The ability to measure and understand stabilizer entropies could also improve error correction in quantum computing, leading to more robust and reliable systems.

The future of quantum computing is likely to be shaped by research like this, which pushes the boundaries of our understanding of quantum states and operations. As we continue to explore the “magic” of non-stabilizerness, we can expect to see new and exciting developments in the field of quantum computing.