What is the combinatorial optimization problem? Take the famous Traveling Salesman Problem (TSP) as an example. Suppose a traveling salesman wants to visit n cities, he must choose the road he wants to take. The limit of the route is that each city can only go once, and finally he will return to his original city. The goal of path selection is to require the path length to be the minimum of all paths. This is a typical combinatorial optimization problem.
Broadly speaking, combinatorial optimization problem includes finding the "best" object from a limited set of objects. "Best" is measured by a given evaluation function, which maps objects to a certain score or cost, with the goal of finding the object with the highest evaluation score and the lowest cost. Combinatorial optimization often involves sorting, classification, screening and other issues.
Combinatorial optimization is widely used in real life, such as transportation, logistics, scheduling, finance and many other fields. Moreover, the complexity of classical algorithms corresponding to many combinatorial optimization problems is very high, and it is difficult for classical computers to find the optimal solutions of these problems quickly when the scale of the problems is large. Therefore, it is of great significance to use quantum computing to accelerate the solution of combinatorial optimization problems.
In the noisy mesoscale (NISQ) quantum era, reliable quantum operands will be limited by quantum noise (at present, quantum noise includes quantum decoherence, rotation error, etc.). Therefore, people are interested in the quantum-classical hybrid algorithm, which can optimize the parameters in the quantum circuit with the help of the classical optimizer, thus selecting the optimal evolutionary path and reducing the depth of the quantum circuit. A famous quantum-classical hybrid algorithm is the quantum approximate optimization algorithm (QAOA), which is expected to bring exponential acceleration to the approximate solution of combinatorial optimization problems.
The researchers said that in theory, if the quantum circuit is deep enough, QAOA can get a better approximate solution. But the error caused by quantum noise will accumulate with the increase of the depth of quantum circuit. When the depth of quantum circuit is large, the performance of QAOA will actually decrease. Therefore, it is a challenging task to show the advantages of QAOA algorithm on the current quantum computer. Reducing the line depth of QAOA algorithm is of great significance to show the advantages of QAOA algorithm on the current quantum computer.
In order to reduce the depth of quantum circuits, researchers put forward a new idea called "Shortcut to QAOA": (S-QAOA). Firstly, the extra two-body interaction is considered in S-QAOA, and the double gate related to YY interaction is added to the quantum circuit to compensate the non-adiabatic effect, thus accelerating the quantum annealing process and accelerating the optimization of QAOA. Secondly, the parameter freedom of two-body interaction (including ZZ interaction and YY interaction) is released, which enhances the representation ability of quantum circuit, thus reducing the depth of quantum circuit. The numerical simulation results show that compared with QAOA, S-QAOA can get better results when the quantum circuit is shallow.
Researchers improve the QAOA algorithm by introducing more two-body interaction and releasing parameter degrees of freedom, which reduces the line depth required by QAOA algorithm and makes QAOA algorithm more suitable for quantum computers with noise at present. Because the algorithm uses STA (Shortcut to Thermal Insulation) principle, researchers call it "Shortcut to QAOA".
The former quantum researcher said: "In S-QAOA, the degree of freedom of parameters is released by further optimizing the parameters with large gradient, but whether there is a better way to choose the most important parameters for optimization is still worth exploring and studying. Next, we will study more cases to verify and improve our ideas. We hope that our method can provide new methods and ideas for realizing quantum advantages as soon as possible. "