Quantum Annealing Shows Superiority in Solving Complex Problems

Quantum annealing, a process involving quantum tunneling, is used in quantum computing and other fields to find the lowest energy configuration of a complex system. It is particularly useful in solving complex problems in mathematics, computer science, and statistical physics. Quantum annealing has been observed in the frustrated magnet α-CoV 2O6, which quickly converges towards the lowest-energy state in a transverse field. However, real materials are complex and difficult to model, making it challenging to observe many-body quantum annealing phenomena. The compound α-CoV 2O6 has been suggested as a potential material for realizing quantum annealing, but further investigation is needed.

What is Quantum Annealing and its Applications?

Quantum annealing is a process that involves quantum tunneling among possible solutions. It has state-of-the-art applications not only in quickly finding the lowest energy configuration of a complex system but also in quantum computing. This process is particularly useful in solving complex problems in various fields, from mathematics and computer science to statistical physics. The prototypical problem for studying lowest-energy configurations in many-body systems is likely probing the ground state of a correlated Ising model.

The annealing of a complex Ising spin system towards its optimal state can be time-consuming and typically characterized by a relaxation time constant τ. For thermal or classical annealing, τ rapidly approaches infinity as temperature T decreases to 0 K, following a thermally activated Arrhenius form. At low temperatures, this classical form hinders the system from converging towards the lowest-energy configuration, resulting in reduced work efficiency. In contrast, quantum annealing (QA) with a transverse field exhibits superiority over classical annealing, resulting in a much shorter τ that is temperature-independent as T approaches 0 K.

How are Quantum Annealing Phenomena Observed?

In a study of the frustrated magnet α-CoV 2O6, which consists of a triangular arrangement of ferromagnetic Ising spin chains without evident structural disorder, quantum annealing phenomena were observed. This resulted from time-reversal symmetry breaking in a tiny transverse field. Below 1 K, the system exhibits no indication of approaching the lowest-energy state for at least 15 hours in zero transverse field but quickly converges towards that configuration with a nearly temperature-independent relaxation time of about 10 seconds in a transverse field of about 35 mK.

Many-body simulations show qualitative agreement with the experimental results and suggest that a tiny transverse field can profoundly enhance quantum spin fluctuations, triggering a rapid quantum annealing process from topological metastable Kosterlitz-Thouless phases at low temperatures.

What are the Challenges in Quantum Annealing?

Real materials are typically highly complex systems that are difficult to model due to the numerous perturbation interactions arising from structural imperfections. Thus, experimentalists and materials scientists have been making significant efforts to search for ultra-clean materials that exhibit precisely solvable models, allowing for the observation of well-defined many-body phenomena.

However, there exists only one reported example of an Ising spin glass LiHo xY1-xF4 that exhibits many-body QA phenomena. The site-mixing disorder of Ho and Y introduces interaction randomness, making it challenging to create a precise microscopic model of this system. Moreover, in this compound, QA phenomena are only visible at very low temperatures, much lower than ΔE=0.54 K, due to the weak couplings between the rare-earth magnetic moments.

What are the Potential Materials for Realizing Quantum Annealing?

The frustrated spin-chain compound Ca 3Co2O6 has no apparent structural disorder and was predicted to exhibit QA using a DWAVE QA computer, but no measurable effect of QA has been observed in this material. Therefore, further investigation and exploration of other candidate materials for realizing QA is required.

Previous studies on α-CoV 2O6 have suggested that the compound can experimentally realize the spatially anisotropic triangular lattice of ferromagnetic Ising spin chains with no apparent structural disorder. High-quality single crystals of this compound are available for further investigation. However, no reports on quantum effects of transverse magnetic fields have been made in α-CoV 2O6.

How Can Quantum Annealing be Enhanced?

In α-CoV 2O6, under zero applied transverse field and at temperatures below about 2 K, the frustrated spin system has a strong tendency to get stuck in metastable Kosterlitz-Thouless (KT) phases characterized by the appearance of topological vortices and antivortices around the domain walls. By contrast, a small transverse field achieved by breaking the time-reversal symmetry in an applied transverse magnetic field can profoundly enhance quantum mechanical tunneling at low temperatures, triggering QA towards the optimum state with a short and nearly temperature-independent relaxation time.

What is the Spin Hamiltonian in α-CoV 2O6?

In α-CoV 2O6, the 28 electronic states of Co2+ 4F linearly superpose into 14 doublets under the crystal electric field and spin-orbit coupling, preserving the time-reversal symmetry as described by the Kramers theorem. The lowest-lying doublet is the ground state, and the next doublet is the first excited state. The energy gap between these two doublets is about 100 K, much larger than the energy scale of the magnetic interactions. Therefore, the ground doublet can be treated as an effective spin-1/2 system.