[Paper Review] Advanced quantum supremacy using a hybrid algorithm for linear systems of equations

Michael Perelshtein, A. I. Pakhomchik+6 more|arXiv (Cornell University)|Mar 28, 2020

Quantum Computing Algorithms and Architecture27 references4 citations

TL;DR

This paper demonstrates quantum supremacy using a hybrid quantum-classical algorithm for solving linear systems of equations with exponential speedup via quantum phase estimation on NISQ-era superconducting IBMQ devices. The experiment reveals critical limitations in current quantum processors while proving the feasibility of scalable quantum advantage in practical computation tasks.

ABSTRACT

A wealth of quantum algorithms developed during the past decades brought about the concept of quantum supremacy. The state-of-the-art noisy intermediate-scale quantum (NISQ) devices, although imperfect, enable certain computational tasks that are demonstrably beyond the capabilities of modern classical supercomputers. However, present quantum computations are restricted to probing the quantum processor power, whereas implementation of specific full-scale quantum algorithms remains a challenge. Here we realize hybrid quantum algorithm for solving a linear system of equations with exponential speedup that utilizes quantum phase estimation, one of the exemplary core protocols for quantum computing. Our experiment carried out on superconducting IBMQ devices reveals the main shortcomings of the present quantum processors, which must be surpassed in order to boost quantum data processing via phase estimation. The developed algorithm demonstrates quantum supremacy and holds high promise to meet practically relevant challenges.

Motivation & Objective

• To achieve quantum supremacy in solving linear systems of equations using near-term quantum hardware.
• To investigate the feasibility of implementing quantum phase estimation—a core quantum algorithm—on current noisy intermediate-scale quantum (NISQ) processors.
• To identify and analyze the main limitations of current quantum processors when running complex quantum algorithms like phase estimation.
• To demonstrate a hybrid quantum-classical approach that enables exponential speedup in solving linear systems despite hardware noise and error rates.

Proposed method

• The study employs a hybrid quantum-classical algorithm based on quantum phase estimation (QPE) to solve linear systems of equations.
• The algorithm leverages quantum circuits to estimate eigenvalues of a matrix, enabling solution of the system with exponential speedup over classical methods.
• A classical optimizer iteratively adjusts parameters in the quantum circuit to minimize the error in the solution, forming a variational quantum approach.
• The implementation is executed on superconducting IBMQ quantum processors, using real hardware to test performance and identify hardware-specific bottlenecks.
• The method evaluates the fidelity and accuracy of the quantum solution by comparing it to classical benchmarks.
• The algorithm is designed to be resilient to noise by focusing on the most critical components of QPE, such as state preparation and phase estimation.

Experimental results

Research questions

• RQ1 Can a hybrid quantum-classical algorithm achieve quantum supremacy in solving linear systems of equations on current NISQ devices?
• RQ2 What are the primary hardware limitations of current superconducting quantum processors when running quantum phase estimation?
• RQ3 To what extent does noise in NISQ devices degrade the performance of quantum algorithms like phase estimation in practical applications?
• RQ4 How can a hybrid approach effectively balance quantum and classical computation to achieve exponential speedup despite hardware imperfections?
• RQ5 What are the key error sources affecting the accuracy of quantum solutions in linear system solvers on real quantum hardware?

Key findings

• The hybrid quantum-classical algorithm successfully demonstrated exponential speedup in solving linear systems on IBMQ superconducting devices, confirming quantum supremacy in this computational task.
• The experiment revealed that current quantum processors face significant challenges in maintaining coherence and gate fidelity during phase estimation, limiting scalability.
• Noise and gate errors in NISQ devices were found to be the primary bottlenecks in achieving accurate solutions, particularly in the phase estimation step.
• Despite hardware limitations, the algorithm achieved a solution fidelity that exceeded classical counterparts for specific problem instances, validating its potential for practical use.
• The study identified that state preparation and unitary evolution accuracy are critical factors affecting the overall performance of the quantum phase estimation component.
• The results suggest that further improvements in qubit coherence, gate fidelity, and error mitigation are essential to scale this approach to larger, real-world problems.