Quantum optimization using variational algorithms on near-term quantum devices (1710.01022v2)

Abstract: Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed. With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupled-cluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits.

• The paper demonstrates the use of variational quantum eigensolver methods to tackle complex optimization problems on current quantum hardware.
• It details innovative strategies for mapping fermions to qubits and constructing efficient trial wavefunctions under hardware constraints.
• The study introduces quantum volume as a key metric to evaluate device performance and guide strategies for enhanced error mitigation.

Quantum Optimization Using Variational Algorithms on Near-Term Quantum Devices

The paper "Quantum optimization using variational algorithms on near-term quantum devices" explores the practical challenges and possibilities associated with utilizing current quantum computing technology to perform meaningful computations. Given that universal fault-tolerant quantum computers, which would require millions of physical qubits, are not yet feasible, this research focuses on the potential of near-term quantum devices that operate with several hundred qubits and limited error correction capabilities.

Variational Quantum Eigensolver (VQE) and Its Applications

A central topic in the paper is the exploration of the Variational Quantum Eigensolver (VQE), a hybrid quantum-classical algorithm particularly suited for optimization problems that are expensive for classical computation. VQE is promising for both classical and quantum optimization problems. The algorithm works by steering a highly entangled quantum state towards a target state, minimizing a cost function through variations of gate parameters. This approach is considered especially valuable for problems in quantum chemistry, such as finding molecular ground states or simulating molecular dynamics.

Mapping from Fermions to Qubits and Trial Wavefunctions

The paper outlines several obstacles and solutions, such as the mapping of fermions to qubits, which results in complex qubit correlations due to fermionic statistics. Different schemes like the Jordan-Wigner transformation are discussed to address this challenge. Coupled-cluster trial wavefunctions and heuristic wavefunctions are proposed as efficient methods to find molecular ground states. These methods consider both the problem-specific entanglement structure and hardware constraints, forming the core strategy for near-term quantum computing applications in chemistry.

Quantum Volume as a Metric for Quantum Computing Power

A significant component of the paper is the introduction of quantum volume as a metric for evaluating the power of quantum devices. Quantum volume considers the number of qubits, connectivity, execution of gate operations, and coherence to provide a quantitative measure of a quantum computer's capability to execute meaningful quantum circuits. This metric helps in assessing and comparing different quantum hardware platforms with varying architectures and error rates.

Implications and Future Directions

The implications of this research are crucial for the continued development and practical deployment of quantum technologies. While the numerical results presented indicate that even with error mitigation techniques, current error rates are an impediment, they also point toward possible improvements through hardware enhancement and algorithmic strategies. The research speculates on advancements in error mitigation, particularly through the adaptation of algorithms like VQE to work with shallow circuits which could function within the coherence time limits of contemporary quantum processors. Furthermore, it stresses the importance of improving coherence and qubit control while investigating new mappings and trial state preparations.

The paper hints at a future where significantly reduced error rates and expanded quantum volume could enable accurate simulation of larger and more complex chemical systems. This potential leap could facilitate crucial advancements in chemical reactions understanding and optimization, which are currently challenging for classical computation due to their exponential scaling complexity.

In summary, the research presented in this paper outlines a feasible path forward for making use of near-term quantum devices, focusing on hybrid algorithms like VQE. The advances in noise-resilient computation will pave the way for practical applications in quantum chemistry and materials science, ultimately bridging the gap to full-scale quantum computing.