Quantum Assisted Simulator (2011.06911v2)

Abstract: Quantum simulation can help us study poorly understood topics such as high-temperature superconductivity and drug design. However, existing quantum simulation algorithms for current quantum computers often have drawbacks that impede their application. Here, we provide a novel hybrid quantum-classical algorithm for simulating the dynamics of quantum systems. Our approach takes the Ansatz wavefunction as a linear combination of quantum states. The quantum states are fixed, and the combination parameters are variationally adjusted. Unlike existing variational quantum simulation algorithms, our algorithm does not require any classical-quantum feedback loop and by construction bypasses the barren plateau problem. Moreover, our algorithm does not require any complicated measurements such as the Hadamard test. The entire framework is compatible with existing experimental capabilities and thus can be implemented immediately.

Quantum Assisted Simulator: A Novel Hybrid Quantum-Classical Simulation Algorithm

In the field of quantum computing, novel approaches to the simulation of quantum dynamics are critical, particularly due to the limitations of noisy intermediate-scale quantum (NISQ) devices. This paper introduces a hybrid quantum-classical algorithm named the Quantum Assisted Simulator (QAS), designed to simulate the dynamics of quantum systems efficiently and immediately applicable to existing hardware capabilities. In contrast to existing variational quantum simulation algorithms, QAS presents substantial improvements by eliminating the classical-quantum feedback loop and bypassing the barren plateau problem.

The QAS algorithm builds upon a linear combination of quantum states to construct its Ansatz without the need for adjustable parameters within quantum circuits, which are typically found in variational quantum eigensolver (VQE) algorithms. This design choice contributes directly to evading the barren plateau problem, where gradient computation becomes exponentially hard as system size increases. Importantly, QAS circumvents challenges associated with classical optimizers in hybrid algorithms that could lead to inefficient training due to non-convex loss landscapes.

The QAS procedure comprises three steps: (1) Ansatz selection based on cumulative $K$-moment states, (2) efficient overlap matrix computation on a quantum computer, and (3) differential equation solving on a classical computer to update the parameters. The Ansatz selection, using $K$-moment states generated from the Hamiltonian's unitary components, systematically constructs the possible quantum states, leading to temporal evolution. The overlap matrix computation benefits from the simplification afforded by employing Pauli strings, thus ensuring feasible measurement procedures under current quantum computational conditions.

Remarkably, the QAS algorithm performs dynamical simulations with high fidelity, demonstrated through examples involving models like the Ising Hamiltonian and the LiH molecule Hamiltonian mapped onto a quantum computational basis. The implementation showcases not only full compatibility with NISQ devices but also adaptability to scenarios where circuit parameters could inherently suffer from barren plateaus, circumventing them with a distinct approach to parameter adjustment. Additionally, the paper provides insights into how QAS can be applied for real and imaginary time evolution, extending its utility to a broader range of quantum simulation tasks.

The implications for future development within quantum computing include exploring algorithm extensions for simulating open quantum systems, introducing generalizations to Gibbs state preparation, and aligning theoretical complexity aspects of quantum simulations with practical implementation. This paper's methodology also suggests the potential for quantum-inspired algorithms applicable to classical simulations, broadening the computational toolkit available for tackling exponentially complex dynamical systems.

As researchers continue to seek promising applications for NISQ devices, the Quantum Assisted Simulator algorithm offers an efficient, immediately implementable, and theoretically secure path for the evolution of quantum states, potentially paving the way for future innovations in quantum chemistry, combinatorial optimization, and beyond.