Quantum computers as universal quantum simulators: state-of-art and perspectives (1907.03505v2)

Abstract: The past few years have witnessed the concrete and fast spreading of quantum technologies for practical computation and simulation. In particular, quantum computing platforms based on either trapped ions or superconducting qubits have become available for simulations and benchmarking, with up to few tens of qubits that can be reliably initialized, controlled, and measured. The present review aims at giving a comprehensive outlook on the state of art capabilities offered from these near-term noisy devices as universal quantum simulators, i.e. programmable quantum computers potentially able to calculate the time evolution of many physical models. First, we give a pedagogic overview on the basic theoretical background pertaining digital quantum simulations, with a focus on hardware-dependent mapping of spin-type Hamiltonians into the corresponding quantum circuit model as a key initial step towards simulating more complex models. Then, we review the main experimental achievements obtained in the last decade regarding the digital quantum simulation of such spin models, mostly employing the two leading quantum architectures. We compare their performances and outline future challenges, also in view of prospective hybrid technologies, towards the ultimate goal of reaching the long sought quantum advantage for the simulation of complex many body models in the physical sciences.

Quantum Computers as Universal Quantum Simulators: State-of-the-Art and Perspectives

This paper presents a comprehensive review of the current state and future outlook for quantum computers operating as universal quantum simulators (UQS). The document delineates the potential of quantum computing platforms, primarily those based on trapped ions and superconducting qubits, for simulating complex physical systems by calculating their time evolution. The discussion spans theoretical frameworks, experimental achievements in the last decade, and future challenges with a focus on achieving quantum advantage.

Theoretical Background

Quantum computers hold the promise of efficiently simulating the time evolution of quantum systems, a task that classical computers struggle with due to exponential resource scaling. The paper discusses the foundational principles of digital quantum simulations, highlighting the importance of mapping spin-type Hamiltonians onto quantum circuits. The discussed techniques emphasize the use of the Suzuki-Trotter decomposition for breaking down complex Hamiltonians into realizable quantum gates. This decomposition is fundamental for simulating non-commuting Hamiltonians through a sequence of controllable quantum operations.

Experimental Achievements

Recent advances in quantum computing have seen the implementation of quantum simulations through platforms like trapped ions and superconducting circuits. Trapped ion systems, with their ability to maintain coherence over long periods, have showcased simulations of spin models with high fidelity. On the other hand, superconducting qubits offer faster gate operations, albeit with shorter coherence times, establishing a different niche in quantum simulation tasks.

The paper reviews notable experimental advancements such as the simulation of two-spin models on trapped ion systems by Lanyon et al., demonstrating the flexibility and reprogrammability of these platforms. For superconducting circuits, digital quantum simulation experiments have achieved remarkable fidelity levels for simulations extended up to five Trotter steps, marking significant progress towards realistic quantum computations.

Bold Claims and Implications

A prominent assertion from this review is that current noisy intermediate-scale quantum (NISQ) devices, despite their limitations, are on the brink of reaching quantum advantage for specific computational tasks. The integration of hybrid technologies, combining classical and quantum methods, could enhance the capabilities of existing quantum simulators.

The exploration of quantum algorithms for simulating quantum field theories, as noted in the recent experiments on superconducting circuits, signals a transformative potential for quantum computers beyond traditional classical computations. This is coupled with the paper of machine learning applications, which could leverage quantum parallelism for tackling complex data sets.

Future Developments

The paper speculates on prospective developments, emphasizing error mitigation techniques to enhance the fidelity of quantum simulations on NISQ devices. There is a clear trajectory towards extending quantum volume, a metric integrating gate fidelity and qubit count, to larger quantum systems, thus crossing the threshold into practical quantum advantages.

Furthermore, the exploration of novel quantum technologies, such as semiconductor-based qubits, spin ensembles, and hybrid systems, presents a compelling outlook. These approaches promise to bridge current limitations and scale quantum architectures towards broader applicability.

Conclusion

In conclusion, the paper positions quantum computers as imminent universal quantum simulators capable of simulating complex quantum systems. While challenges remain, particularly in error correction and coherence times, the ongoing advancements in both theoretical and experimental fronts are paving the way for a new era of quantum simulations. The realization of scalable, high-fidelity quantum processors will likely redefine computational capabilities across various scientific domains.