Perspectives of quantum annealing: Methods and implementations (1903.06559v1)

Abstract: Quantum annealing is a computing paradigm that has the ambitious goal of efficiently solving large-scale combinatorial optimization problems of practical importance. However, many challenges have yet to be overcome before this goal can be reached. This perspectives article first gives a brief introduction to the concept of quantum annealing, and then highlights new pathways that may clear the way towards feasible and large scale quantum annealing. Moreover, since this field of research is to a strong degree driven by a synergy between experiment and theory, we discuss both in this work. An important focus in this article is on future perspectives, which complements other review articles, and which we hope will motivate further research.

• The paper presents a theoretical framework converting optimization problems into spin-glass Hamiltonians and discusses the impact of small energy gaps on computational efficiency.
• The paper demonstrates that non-stoquastic Hamiltonians and inhomogeneous field driving can reduce disruptive phase transitions, potentially enabling exponential speedup.
• The paper highlights reverse annealing and counter-diabatic driving as promising strategies to overcome decoherence and enhance the search for global minima.

Perspectives on Quantum Annealing: Methods and Implementations

Quantum annealing presents a promising alternative for solving large-scale combinatorial optimization problems by employing quantum mechanical processes. The paper "Perspectives of quantum annealing: Methods and implementations" offers a comprehensive analysis of the current state of quantum annealing, highlighting both methodological and implementation perspectives. This essay discusses the main points highlighted by the authors, providing an expert review tailored for researchers in the field.

Overview of Quantum Annealing

Quantum annealing is a classical optimization technique where a quantum system is driven toward its ground state. The optimization problem is encoded into a Hamiltonian, with the solution corresponding to the system's minimum energy state. A typical quantum annealing protocol involves the gradual transformation of an initial Hamiltonian with an easy-to-prepare ground state to a problem Hamiltonian, following the adiabatic theorem. This process ideally finds the global minimum of the given problem.

Main Contributions

1. Theoretical Framework: The paper discusses how optimization problems can be transformed into spin-glass-like Hamiltonians, revealing challenges in transitioning efficiently from initial to final states due to phase transitions and small energy gaps. These transitions directly affect computational complexity and feasibility, as exponential time is required to tunnel through small gaps.
2. Non-stoquastic Hamiltonians: Unlike conventional stoquastic Hamiltonians, non-stoquastic ones have arbitrary signs in their off-diagonal elements, potentially offering a quantum computational advantage. The paper outlines how this can reduce first-order transitions to second-order ones, implying exponential speedup.
3. Inhomogeneous Field Driving: By controlling quantum fields spatially, rather than globally, transitions can be smoothed, potentially reducing computational difficulty by moderating the number of qubits involved in transitions at any one time.
4. Reverse Annealing: Emphasizes a strategy where the annealing begins from a potentially near-optimal solution, encouraging a local search around the neighborhood of this solution to ensure closer proximity to the global minimum, rather than a full-space exploration from a ground state.
5. Counter-diabetic Driving and Shortcuts: Employing shortcuts to adiabaticity or counter-diabatic driving techniques offers potential methods to overcome the inherent limitations of adiabatic quantum computing, suggesting novel approaches to enhance protocol efficiencies beyond adiabatic conditions.
6. Implementations: The paper discusses the primary implementation medium—superconducting qubits—and addresses their constraints, including coherence time and connectivity. It also explores alternative mediums like trapped ions and neutral atoms, which might provide better lattice connectivity or coherence properties under certain conditions, albeit with their own intrinsic challenges.

Implications and Future Directions

The findings point towards the notion that addressing the limitations of current quantum annealers, such as coherent control and novel Hamiltonian structures, is essential for realizing substantial computational gains. The exploration of experimental flexibility in device design and the introduction of sophisticated quantum control techniques stand as promising endeavors toward achieving quantum computationally-active systems.

To advance quantum annealing further, intense methodological research is necessary, focused on algorithmic strategies to enhance energy gap management and decoherence mitigation. Experimentally, pushing the limits of existing platforms in terms of qubit connectivity and error management is imperative. Furthermore, compiling and benchmarking diverse algorithmic instances can provide a better understanding of where quantum annealing excels over classical annealing.

In conclusion, while current quantum annealing implementations offer a glimpse into the potential of quantum computation, fulfilling its capability will require both theoretical breakthroughs and engineering innovations. Continued exploration into novel Hamiltonian formulations and auxiliary qubit technologies will leverage quantum annealing's full potential as a competitive solver of complex, large-scale optimization problems.