New Approach Enhances Variational Quantum Algorithms

A research team from Infineon Technologies AG, BASF Digital Solutions GmbH, Siemens AG, and Quantum Technology and Application Consortium (QUTAC) has developed a new approach to improve the performance of variational quantum algorithms. The team addressed the challenge of handling linear inequality constraints in these algorithms by omitting slack qubits and evaluating the inequality classically during parameter tuning.

This method simplifies the optimization process, reduces the number of local optima, and improves solution quality. The approach can be applied to any problem with linear inequality constraints and could potentially accelerate the development of practical quantum computing applications.

What are the Challenges in Embedding Integer Linear Inequalities for Variational Quantum Algorithms?

Variational quantum algorithms are a promising area of research in quantum computing. These algorithms use a combination of classical and quantum computing techniques to solve complex optimization problems. However, one of the challenges in implementing these algorithms is the handling of linear inequality constraints.

In traditional variational quantum algorithms, constraints are added to the problem objective through penalty terms. For linear inequality constraints, this process requires the use of additional slack qubits. These extra qubits increase the search space and complicate the parameter landscapes that the classical optimizers need to navigate. This can lead to difficulties in finding optimal solutions and slow convergence rates.

The research team of Maximilian Hess, Lilly Palackal, Abhishek Awasthi, and Karen Wintersperger from Infineon Technologies AG, BASF Digital Solutions GmbH, Siemens AG, and Quantum Technology and Application Consortium (QUTAC) have explored approaches to model linear inequalities for quantum algorithms without these drawbacks. Their main suggestion is to omit the slack qubits completely and evaluate the inequality classically during parameter tuning.

How Does the New Approach Improve Variational Quantum Algorithms?

The researchers tested their methods on Quantum Approximate Optimization Algorithm (QAOA) as well as on Trotterized adiabatic evolution and presented empirical results. As a benchmark problem, they considered different instances of the multiknapsack problem.

Their results showed that removing the slack bits from the circuit Hamiltonian and considering them only for the expectation value yields better solution quality than the standard approach. The tests were carried out using problem sizes up to 26 qubits.

This new approach can be applied to any problem with linear inequality constraints and is suitable for variational as well as digitized versions of adiabatic quantum computing. This means that it has the potential to significantly improve the performance of variational quantum algorithms in solving complex optimization problems.

What is the Impact of Slack Bits on Quantum Algorithms?

The incorporation of slack bits in quantum algorithms comes with two main challenges. The first is the requirement of qubits to accurately model the problem on the quantum hardware. The second is the convergence of the slack bits.

The addition of slack bits expands the solution space, making it more difficult for the algorithm to navigate and find the optimal solution. This can result in a higher number of local optima, causing the optimization process to get stuck at suboptimal solutions or to converge slowly. This issue becomes more prominent as the number of slack bits increases and as the problem size grows.

Furthermore, the interaction between the slack bits and the main variables of the problem can create intricate dependencies, making it challenging to find a balance between satisfying constraints and optimizing the objective function. This can lead to difficulties in converging to a solution that simultaneously satisfies all constraints and optimizes the objective function.

How Does the New Approach Address the Challenges of Slack Bits?

The researchers’ approach of omitting the slack qubits completely and evaluating the inequality classically during parameter tuning addresses the challenges associated with slack bits. By removing the slack bits from the circuit Hamiltonian and considering them only for the expectation value, the complexity of the optimization landscape is reduced.

This approach simplifies the optimization process and makes it easier for the algorithm to navigate the solution space and find the optimal solution. It also reduces the number of local optima, making it less likely for the optimization process to get stuck at suboptimal solutions or to converge slowly.

Furthermore, by evaluating the inequality classically during parameter tuning, the intricate dependencies between the slack bits and the main variables of the problem are eliminated. This makes it easier to find a balance between satisfying constraints and optimizing the objective function, leading to better solution quality.

What are the Implications of this Research for Quantum Computing?

This research has significant implications for the field of quantum computing. By addressing the challenges associated with slack bits, the researchers have developed a new approach that can significantly improve the performance of variational quantum algorithms in solving complex optimization problems.

This approach can be applied to any problem with linear inequality constraints and is suitable for variational as well as digitized versions of adiabatic quantum computing. This means that it has the potential to broaden the range of problems that can be effectively solved using variational quantum algorithms.

Furthermore, by reducing the complexity of the optimization landscape and simplifying the optimization process, this approach makes it easier to implement variational quantum algorithms and could potentially accelerate the development of practical quantum computing applications.