Quantum Simulations Become Twice As Efficient with New Error-Correction Technique

Researchers are continually seeking methods to improve the accuracy of quantum simulations on existing, limited quantum computers. Seung Park, Sangjin Lee, and Kyunghyun Baek, from the Institute for Convergence Research and Education in Advanced Technology at Yonsei University and the Quantum Universe Center at the Korea Institute for Advanced Study, present a novel approach to reduce the computational demands of product-formula based quantum simulation. Their work introduces a dual-channel multi-product formula that demonstrably improves the scaling of Trotter errors, effectively halving the required circuit depth to achieve a given simulation precision. This reduction in circuit complexity is significant because it directly lowers the burden of physical error mitigation, paving the way for more reliable quantum simulations with current and near-future quantum hardware.

Dual channel multi-product formula reduces Trotter error scaling in quantum simulation significantly

Researchers have developed a new quantum simulation technique that significantly reduces the computational resources needed to achieve precise results. This breakthrough centres on an improved multi-product formula (MPF) designed to mitigate algorithmic errors in near-term quantum computers. The work addresses a critical challenge in quantum simulation: the need for an increasing number of computational steps, known as Trotter steps, to enhance accuracy.
By introducing a dual-channel MPF, scientists have achieved a two-fold improvement in Trotter error scaling, effectively halving the circuit depth required for a given level of simulation precision. This novel approach directly tackles the limitations imposed by current quantum hardware, where performance is often constrained by the length and complexity of quantum circuits.

The dual-channel MPF leverages a combination of MPF circuits to enhance simulation accuracy while simultaneously minimising circuit depth. Numerical simulations demonstrate that this method yields substantially smaller algorithmic errors compared to conventional MPF schemes, all while maintaining consistent sampling error.

The reduction in circuit depth is particularly significant, as it translates to a lower overhead for physical error mitigation when the simulation is implemented on actual quantum hardware. The core innovation lies in the method’s ability to achieve enhanced algorithmic performance with fewer quantum gates.

For a fixed count of CNOT gates, a standard measure of quantum circuit complexity, the proposed dual-channel MPF demonstrably outperforms existing techniques. This advancement is crucial for progressing quantum simulation on noisy intermediate-scale quantum (NISQ) devices, where minimising circuit length is paramount to reducing the accumulation of physical errors. The research paves the way for more efficient and accurate simulations of complex quantum systems, potentially accelerating discoveries in materials science, drug discovery, and fundamental physics.

Construction and implementation of a dual-channel multi-product formula for improved Trotterisation offers significant performance gains

A dual-channel multi-product formula underpinned the methodological approach to enhance quantum simulation accuracy and reduce circuit depth. The research began by decomposing a target Hamiltonian into k-local Hamiltonians, enabling the construction of an α-th order product formula, Tα(t), representing the time evolution operator.

This formula was built from a product of terms, each implementing a component of the Hamiltonian using native quantum gates, with the first and second-order Trotter product formulas serving as foundational examples. To mitigate the accumulation of Trotter errors, the study introduced a dual-channel multi-product formula, a refinement of conventional MPF schemes.

This involved implementing multiple quantum circuits and then employing classical post-processing of the measurement outcomes. The dual-channel approach leverages two distinct types of product formulas, strategically combining their strengths to achieve a two-fold improvement in Trotter error scaling compared to standard MPF methods.

Numerical simulations were then performed to validate the proposed method’s performance under both ideal and noisy conditions. These simulations assessed algorithmic errors for a fixed CNOT count, a measure of quantum circuit complexity, demonstrating a significant reduction in error with the dual-channel MPF while maintaining consistent sampling error.

The work specifically targeted a reduction in circuit depth, anticipating that this would lower the overhead associated with physical error mitigation when implemented on actual quantum hardware. This reduction in circuit depth allows for achieving target simulation precision with approximately half the circuit depth of conventional MPF schemes.

Accuracy of time-dependent simulations scales with folding number and product formula order, but plateaus with increasing computational cost

For the transverse-field Ising chain with eight spins, calculations of the expectation value of the global z-magnetization at time 0.8, using a random product state as the initial state, revealed absolute errors dependent on the folding number K. The method achieved absolute errors of 10⁻¹³ for K = 1, diminishing to 10⁻¹¹ for K = 3, 10⁻⁹ for K = 5, and finally reaching 10⁻⁷ for K = 7.

Fitting data to the function c₁(t/nmid)²K demonstrated exponents of approximately 1.129, 2.027, and 2.098 for the multi-product formula method using regular first-order product formulas, and for the dual-channel multi-product formula based on first- and third-order product formulas, respectively. Simulations of the XXZ spin chain with an external magnetic field, utilising a Néel state as the initial condition, measured the magnetization on even sites at time 0.3.

With depolarizing noise applied to CNOT gates ranging from 10⁻⁸ to 10⁻⁶, the dual-channel multi-product formula consistently outperformed the multi-product formula based on symmetric product formulas and second-order product formulas across all tested noise levels. Relative error, plotted against the number of CNOT gates, showed that the proposed method maintained better performance with respect to circuit depth.

Conditioning problems were addressed by setting a criterion of ||c||₁ This allowed for a larger set of folding-number choices that yielded well-conditioned results, leading to higher accuracy with the proposed protocol. The research demonstrates a halving of quantum circuit depth compared to the multi-product formula method with symmetric product formulas, potentially reducing overhead for physical error mitigation.

Dual channel decomposition halves Trotter error scaling for quantum simulations, improving their accuracy and efficiency

Researchers have developed a new quantum simulation technique based on the multi-product formula that improves the scaling of Trotter error, a significant source of inaccuracy in near-term quantum computations. This dual-channel multi-product formula achieves a two-fold improvement in error scaling compared to conventional methods, effectively halving the required circuit depth to reach a target simulation precision.

Reduced circuit depth is crucial because it lowers the overhead associated with mitigating physical errors on current quantum hardware. The approach builds upon existing product formula techniques for approximating quantum dynamics by decomposing the Hamiltonian into local components. By employing a linear combination of different folded product formulas, the method achieves enhanced accuracy without the exponential increase in circuit complexity often associated with higher-order formulas.

Numerical simulations confirm the improved performance of the dual-channel multi-product formula, demonstrating smaller algorithmic errors for a given circuit count while maintaining consistent sampling error. The authors acknowledge that the method’s performance relies on accurate classical post-processing of measurement outcomes, a standard requirement for multi-product formula approaches.

Future research may focus on extending this technique to more complex quantum systems and exploring its integration with advanced error mitigation strategies. This work establishes a pathway towards more efficient and precise quantum simulations on near-term devices, potentially accelerating progress in fields such as materials science and drug discovery.