Variational Quantum Eigensolver Enables Practical Quantum Computing on NISQ Devices

Quantum computers promise to revolutionise computation by tackling problems beyond the reach of even the most powerful classical machines, but building these machines presents significant challenges. Kang-Min Hu, Min Namkung, and Hyang-Tag Lim, working to overcome these hurdles, demonstrate a pathway towards practical quantum computation using light. Their research focuses on the variational quantum eigensolver, a powerful algorithm particularly suited to current, limited quantum hardware, and adapts it for implementation on photonic systems. This approach leverages the unique advantages of photons, their ability to operate at room temperature and maintain quantum information for extended periods, to create a more stable and scalable platform for solving complex problems in fields like materials science and fundamental physics.

Photonic Variational Quantum Algorithm Development

Scientists are actively developing variational quantum algorithms (VQAs), particularly the variational quantum eigensolver (VQE), to leverage near-term quantum computers for problems intractable for classical computers. A key focus is photonic quantum computing, which offers advantages such as room-temperature operation, potential scalability, and the ability to generate complex quantum states. Research encompasses error mitigation, algorithm optimization, and exploration of diverse quantum hardware architectures. Photonic quantum computing utilizes technologies like orbital angular momentum of light for encoding qubits, integrated photonics for building scalable processors, and Hong-Ou-Mandel interference for manipulating qubits.

VQAs combine classical optimization with quantum computation, with VQE being prominent for finding the ground state energy of quantum systems, applicable to quantum chemistry, materials science, and drug discovery. Researchers are applying VQAs to diverse areas including quantum chemistry, materials science, drug discovery, and quantum battery optimization, as well as quantum simulation and excited state calculations. Algorithmic techniques include natural gradient methods, constrained VQE, error mitigation, and adaptive VQE, all aimed at improving accuracy and efficiency. Challenges remain in scaling quantum computers while maintaining coherence and fidelity, and in developing manufacturing processes for complex quantum circuits. Research focuses on high-dimensional entanglement using orbital angular momentum, integrated photonic circuits, quantum Fisher information for measurement optimization, and error-resilient algorithms. Companies like PsiQuantum and IBM Quantum are contributing to this progress, alongside numerous academic research groups.

Photonic VQE Accurately Estimates Molecular Ground States

Recent research demonstrates the potential of photonic systems for practical quantum computation by implementing the variational quantum eigensolver (VQE). Scientists have successfully used VQE to estimate ground state energies for quantum chemistry and many-body physics problems, showcasing the algorithm’s versatility and accuracy. The inherent advantages of photonic platforms, including room-temperature operation and low decoherence, contribute to its scalability. Experiments involved simulating VQE for molecules like H2, HeH+, and LiH, with results closely matching theoretical ground state energies.

The team extended the VQE framework to tackle problems in many-body physics, constructing a Hamiltonian for a two-qubit antiferromagnetic Heisenberg model. Notably, they demonstrated VQE’s application to integer factorization, efficiently factoring the number 35 using a constant-depth quantum circuit. To enhance accuracy, scientists explored error-mitigation techniques like zero-noise extrapolation and employed classical optimization methods such as gradient descent and particle swarm optimization. These advancements demonstrate a comprehensive approach to building practical and reliable quantum algorithms for a range of computational challenges.

Photonic VQE Advances Towards Practical Quantum Computation

This work demonstrates significant progress in the photonic implementation of the variational quantum eigensolver (VQE), establishing its potential for near-term quantum computation. Researchers successfully applied photonic VQE to problems spanning quantum chemistry, many-body physics, and integer factorization, even in the presence of noise, confirming its viability as a promising approach for noisy intermediate-scale quantum (NISQ) devices. The inherent advantages of photonic systems, room temperature operation, low decoherence, and support for high-dimensional encoding, contribute to its scalability and suitability for complex quantum networks. These advancements position photonic VQE as a platform with considerable potential for practical applications, notably in the design of new drug molecules and the discovery of advanced battery materials. Furthermore, the research extends beyond ground state energy estimation, exploring methods to compute excited state energies, crucial for understanding photochemical reactions and optical material properties. While acknowledging limitations such as the barren plateau problem, this work represents a pivotal step in the advancement of quantum information science and technology.

Photonic VQE Implementation

Scientists are pioneering new approaches to quantum computation by implementing the variational quantum eigensolver (VQE) on photonic systems, addressing limitations posed by noisy intermediate-scale quantum (NISQ) devices. They harness the unique advantages of photonic platforms for scalable, high-dimensional quantum computation. The work begins with a thorough theoretical overview of the VQE framework, detailing Hamiltonian approximation, ansatz construction, and Pauli measurement grouping. Researchers developed methods for grouping Pauli measurements to optimize data acquisition and streamline the computational process.

They also investigated error mitigation techniques, specifically zero-noise extrapolation and Pauli noise error-mitigation, to improve the resilience of VQE in realistic experimental settings. Experimental implementations of photonic VQE were carried out across diverse use cases, ranging from quantum chemistry and many-body systems to integer factorization. The team demonstrated that photonic systems efficiently realize small-scale VQE with few qubits, and naturally support qudit-based implementations, expanding the computational capabilities of VQE.