Hybrid Quantum Algorithm Cuts Qubit Needs and Reduces Error Rates.

Quantum phase estimation, a cornerstone of many quantum algorithms, presents significant challenges in practical implementation due to the accumulation of errors in complex circuits. Lee, Choi, Min, Bae, and Bae address this issue by proposing two novel variations of the phase estimation algorithm, termed shifted and punctured phase estimation. These techniques aim to reduce circuit complexity and, consequently, error rates. The researchers demonstrate the efficacy of these methods within a hybrid quantum-classical implementation of the Harrow–Hassidim–Lloyd (HHL) algorithm, a quantum algorithm designed to solve linear systems of equations. By strategically identifying and removing unnecessary qubits and gates through a combined quantum-classical approach, the team achieves a reduction in both qubit and gate counts, ultimately leading to improved performance on existing superconducting quantum hardware.

Quantum phase estimation (QPE) serves as a cornerstone of many quantum algorithms, notably Shor’s factoring algorithm and the Harrow–Hassidim–Lloyd (HHL) algorithm for solving linear systems. QPE accurately determines the eigenvalues of a unitary operator, outputting an n-bit binary approximation of the phase. However, standard QPE can be inefficient when only a portion of the phase is required or when certain phase bits are already known, incurring unnecessary computational cost.

Researchers present two variations of the quantum phase estimation (QPE) algorithm – shifted phase estimation and punctured phase estimation – designed to reduce circuit complexity and, consequently, error rates in quantum computations. The shifted phase estimation method discards the most significant bit of the estimated phase via a bit-string left shift, focusing computation on lower-order components. The punctured phase estimation method streamlines the circuit by removing qubits corresponding to already known phase bits. Both approaches aim to improve efficiency by avoiding unnecessary computations on predetermined or irrelevant information.

The motivation for these developments stems from the practical challenges of building and operating quantum computers. Current quantum hardware is susceptible to gate, measurement, and decoherence errors, which accumulate throughout a circuit and degrade performance. Reducing the number of qubits and gates is therefore crucial for mitigating these errors.

To demonstrate the effectiveness of these variations, the researchers integrated them into a hybrid quantum–classical implementation of the HHL algorithm. This hybrid approach leverages both quantum and classical processors to identify and remove redundant qubits and gates. By reducing the number of quantum resources required, the resulting circuit exhibits lower error rates when executed on current superconducting hardware. Experimental results confirm the error-mitigation benefits of this hybrid method, suggesting a pathway towards more robust and scalable quantum computations.

This research integrates QSPE and QPPE into a hybrid quantum–classical implementation of the HHL algorithm. By leveraging classical processors to identify and remove unnecessary qubits and gates, the hybrid approach reduces circuit complexity and lowers the overall error rate. This strategy builds upon existing error-mitigation techniques that replace segments of quantum algorithms with classical computation, thereby optimising resource utilisation and enhancing algorithmic performance.

The hybrid HHL algorithm achieves this reduction in complexity through a systematic approach to phase information utilisation. The researchers establish theoretical foundations for this process, including the use of binary matrices, minimal distinguishing column sets, and a taxonomy of phase-estimation qubit types. This allows for a precise classification of qubits based on their role in the estimation process, enabling targeted removal of redundant components. The resulting algorithm demonstrates significantly reduced qubit and gate requirements compared to previous methods, paving the way for more efficient and reliable quantum computation.