High-fidelity adiabatic quantum computation using the intrinsic Hamiltonian of a spin system: Application to the experimental factorization of 291311 (1706.08061v1)

Abstract: In previous implementations of adiabatic quantum algorithms using spin systems, the average Hamiltonian method with Trotter's formula was conventionally adopted to generate an effective instantaneous Hamiltonian that simulates an adiabatic passage. However, this approach had issues with the precision of the effective Hamiltonian and with the adiabaticity of the evolution. In order to address these, we here propose and experimentally demonstrate a novel scheme for adiabatic quantum computation by using the intrinsic Hamiltonian of a realistic spin system to represent the problem Hamiltonian while adiabatically driving the system by an extrinsic Hamiltonian directly induced by electromagnetic pulses. In comparison to the conventional method, we observed two advantages of our approach: improved ease of implementation and higher fidelity. As a showcase example of our approach, we experimentally factor 291311, which is larger than any other quantum factorization known.

• The paper introduces a method that uses the intrinsic Hamiltonian of spin systems to achieve high-fidelity adiabatic quantum computation.
• It experimentally factors 291311 into its prime components 523 and 557, showcasing improved precision and efficiency.
• The study employs Energy Landscape Manipulation to enhance scalability and robustness, paving the way for practical quantum technologies.

High-Fidelity Adiabatic Quantum Computation for Factoring: Insights from NMR Spin Systems

The paper "High-fidelity adiabatic quantum computation using the intrinsic Hamiltonian of a spin system: Application to the experimental factorization of 291311" presents a novel approach to adiabatic quantum computation (AQC) utilizing nuclear magnetic resonance (NMR) spin systems. It targets the improvement of both the fidelity and ease of implementation by employing the intrinsic Hamiltonian of spin systems, a significant departure from the traditional methods that rely on the average Hamiltonian technique and Trotter's formula.

Key Contributions

1. Intrinsic Hamiltonian Utilization: The research introduces a method that harnesses the intrinsic Hamiltonian of spin systems to represent problem Hamiltonians while implementing an adiabatic drive using exogenous electromagnetic pulses. This innovation addresses the challenges faced by the conventional average Hamiltonian approach, particularly the issues related to maintaining adiabaticity and achieving high fidelity.
2. Experimental Factorization of 291311: The authors demonstrate their method through the experimental factorization of the integer 291311. The system managed to derive the correct prime factors, 523 and 557, showcasing the applicability and precision of the proposed method. This is notably larger than many numbers previously factored using quantum algorithms.
3. Energy Landscape Manipulation (ELM): To overcome the limitations of realistic quantum systems, the paper employs ELM techniques. These techniques enable the transformation of a computational Hamiltonian to one that maintains the same ground state but is more feasible for experimental realization.
4. Scalability and Robustness: The methodology highlights the potential for scalability due to the reduced requirement for control pulses and improved resilience against noise. This robustness is particularly relevant when projecting applications to larger qubit systems where noise and decoherence present growing challenges.

Implications and Future Directions

The implications of this research are multi-faceted, spanning both theoretical and practical dimensions of quantum computing. On the theoretical front, the ability to factor large integers using AQC mechanisms without exiting the ground state suggests enhanced opportunities for scalability and reliability in quantum computing applications. On a practical level, the research sets the stage for developing more efficient quantum annealing processes and influencing superconducting qubit designs that integrate non-stoquastic and $k$-local terms.

Future research could expand on applying this high-fidelity adiabatic approach to other computational problems, such as discrete optimization tasks and simulating complex quantum systems beyond factoring. In parallel, there is potential for further refining ELM techniques to match even broader classes of Hamiltonians to physical systems, thereby broadening the scope and applicability of AQC in diverse quantum architectures, including NV-centers and optical lattice systems.

The ongoing advancements in NMR technology and control techniques will be instrumental in translating these theoretical constructs into practical devices. The current results offer a pathway to circumvent the scalability issues that have traditionally hindered quantum adiabatic computing, emphasizing the important role of intrinsic Hamiltonians in pragmatic quantum computational strategies.