Efficient variational quantum simulator incorporating active error minimisation

Abstract: One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc, in order to accelerate the process of discovery. It is important to ask: Can this be achieved using near future quantum processors, of modest size and under imperfect control, or must it await the more distant era of large-scale fault-tolerant quantum computing? Here we propose a variational method involving closely integrated classical and quantum coprocessors. We presume that all operations in the quantum coprocessor are prone to error. The impact of such errors is minimised by boosting them artificially and then extrapolating to the zero-error case. In comparison to a more conventional optimised Trotterisation technique, we find that our protocol is efficient and appears to be fundamentally more robust against error accumulation.

• The paper introduces a variational simulation method that actively minimizes errors using extrapolation from accentuated noise conditions.
• It combines quantum and classical computation by iteratively optimizing variational parameters to simulate quantum dynamics on imperfect hardware.
• Numerical tests on the quantum Ising model demonstrate significantly reduced error rates, underscoring near-term quantum application potential.

Efficient Variational Quantum Simulator Incorporating Active Error Minimisation

The paper by Ying Li and Simon C. Benjamin addresses the significant challenge of simulating quantum systems with near-term quantum processors, which are constrained by their modest size and error-prone nature. Quantum simulation is projected to be a pivotal application of quantum computing, enabling advancements across various scientific disciplines, such as chemistry and materials science. This study explores whether meaningful quantum simulations can be achieved without the complete machinery of fault-tolerant quantum computers, leveraging a hybrid quantum-classical computational strategy.

Overview and Methods

The authors introduce a variational quantum simulation algorithm that combines classical and quantum computation, tailored to the constraints of current quantum hardware. Their method contrasts with the traditional Trotter-Suzuki decomposition, which decomposes the time evolution operator into a sequence of gate operations that fundamentally require fault-tolerant systems to manage the cumulative errors from numerous operations. They propose an alternative approach focusing on trial states parameterized by a tractable set of variational parameters, which are iteratively updated. The key here lies in balancing the quantum processor's ability to serve as a 'coprocessor', working on smaller, manageable quantum tasks that in turn, provide specific subroutine outputs to the classical processor. This fine-tunes the parameters simulating quantum system dynamics.

The most innovative aspect of this methodology is the active minimization of quantum errors—not by traditional error correction, which is resource-intensive, but by extrapolating from artificially accentuated error conditions toward a zero-error limit. This technique hinges on engineering the noise from quantum gate operations to controllable stochastic processes, achievable by surrounding imperfect operations with random Pauli gates. Consequently, the hybrid algorithm compensates for errors during the simulation of quantum dynamics through predominantly classical computational inference.

Results and Error Mitigation Strategy

The robustness of this algorithm is underscored by numerical simulations performed on small-scale models, specifically the quantum Ising model. These simulations demonstrate a substantially reduced error rate compared to Trotterisation methods, even in the presence of machine noise. The paper also describes shot noise mitigation via quantum circuits repeated numerous times to achieve statistical certainty, outlining an error structure where implementation errors don't necessarily degrade simulation fidelity if guided properly by inference techniques.

Furthermore, the authors detail the role of variational parameters, optimized for reducing computational overhead, consequently enhancing the feasibility of simulation on currently available quantum hardware.

Implications and Future Prospects

The implications of this research extend beyond immediate hardware constraints to influence near-term quantum computing applications. This approach potentially paves the way for performing meaningful computations on soon-to-be-realized quantum processors not intended for large-scale fault-tolerance. Moreover, integrating classical processing for quantum error mitigation might inspire more sophisticated algorithms investigating other quantum-specific tasks.

Looking ahead, further research can focus on expanding the variational parameter space and enhancing the sophistication of noise engineering techniques. Combining these elements could culminate in scalable strategies adaptable for larger quantum systems until such time that widespread fault tolerance becomes viable.

In summary, Li and Benjamin provide a foundational algorithm that achieves a pragmatic blend of quantum and classical computation, optimally leveraging available resources. This opens up new avenues for quantum simulation research with constrained quantum systems, promising a pathway for more immediate computational applications in the quantum domain.