Quantum Calculations Become More Efficient with Paired Gate Optimisation
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Joona V. Pankkonen and colleagues at Aalto University present Two-Gate Fraxis (TGF) and Two-Gate FQS (TGFQS), extensions to existing single-qubit optimisation techniques. These new methods simultaneously optimise two single-qubit gates, constructing a quartic local cost function to achieve potentially lower final relative error in tasks such as finding ground state energies and preparing quantum states. Numerical experiments demonstrate that TGF and TGFQS, when employing specific gate pairing strategies, frequently outperform their single-gate predecessors, even with limited measurement data, although this enhanced performance requires increased computational effort. The methods represent a key step towards realising the potential of quantum computation. Two-Gate quantum circuits sharply reduce error rates in complex simulations Two-Gate Fraxis and Two-Gate FQS frequently achieve a lower final relative error to the ground state energy or infidelity than their single-gate counterparts, with improvements ranging from modest gains to approximately two orders of magnitude lower error in benchmark tests. This performance surpasses previous limitations where optimising circuits required sequential updates of individual quantum gates, restricting the efficiency of larger computations. Traditional variational quantum algorithms, such as Variational Quantum Eigensolver (VQE), often rely on optimising parameters of a quantum circuit iteratively. Each iteration typically adjusts one or a few parameters at a time, guided by measurements of the quantum system. This sequential approach can become inefficient as the number of parameters increases, leading to slow convergence or getting trapped in local optima. A new approach was employed, constructing an exact quartic local cost function and optimising it using classical methods, enabling more efficient exploration of optimisation pathways despite increased computational demands per gate update. Benchmark tests across various systems, including a four-qubit Fermi-Hubbard model and transverse-field Ising models with eight, ten, and twelve qubits, consistently showed these optimisers outperformed their single-gate counterparts. Random and half-shifted gate pairing strategies yielded the lowest relative error to the ground state energy, even with finite shot counts of 4096, 8192, and 16384 shots on Fermi-Hubbard and transverse-field Ising model Hamiltonians. The Fermi-Hubbard model is a fundamental model in condensed matter physics, used to describe interacting electrons in a lattice, while the transverse-field Ising model is a widely studied model in quantum magnetism. Achieving accurate ground state energies for these models is computationally challenging for classical computers, making them ideal benchmarks for quantum algorithms. However, this enhanced performance necessitates 18 to 50 circuit evaluations per updated gate, representing a trade-off between optimisation power and computational cost and currently limiting scalability to sharply larger, more complex quantum circuits. The construction of the quartic local cost function is central to the improved performance of TGF and TGFQS. In standard single-qubit optimisation methods, the cost function is typically quadratic, reflecting the optimisation of a single gate parameter. By considering two gates simultaneously, the interaction between them introduces higher-order terms, leading to the quartic cost function. This more complex function captures the correlations between the two gates, allowing for a more accurate and efficient optimisation process. The optimisation is then performed using classical optimisation algorithms, such as gradient descent or more sophisticated methods like the Nelder-Mead simplex algorithm. The choice of gate pairing strategy, how the two gates are selected for simultaneous optimisation, also plays a crucial role. The researchers found that random and half-shifted pairings consistently yielded the best results, suggesting that these strategies effectively explore the parameter space and avoid getting stuck in local minima. Balancing optimisation efficacy with computational demands in near-term quantum devices Refinement of techniques for optimising quantum circuits is key for unlocking the potential of near-term quantum devices. While demonstrably reducing errors in benchmark tests, these new methods demand a greater number of circuit evaluations per gate update, creating a tension between optimisation power and the practical limitations of current hardware. Quantum computers are rapidly evolving, meaning today’s hardware limitations are not necessarily tomorrow’s roadblocks. The number of circuit evaluations required for each gate update directly impacts the overall runtime of the optimisation process. Current quantum devices are limited in the number of operations they can perform before decoherence, the loss of quantum information, occurs. Therefore, minimising the number of circuit evaluations is crucial for achieving meaningful results on these devices.
The Aalto University team developed methods that simultaneously refine two single-qubit gates, a contrast to prior approaches limited by optimising one gate at a time. Simultaneously optimising constructs a more complex, quartic local cost function, a mathematical measure of calculation error, and utilises classical optimisation tools to find solutions. The concept of a ‘local’ cost function is important because it allows the optimisation to focus on a specific region of the parameter space, rather than attempting to search the entire space. This is particularly useful in high-dimensional problems, where the search space can be vast. These techniques offer demonstrably better results on complex problems like molecular modelling and quantum state preparation, important areas for future applications. Molecular modelling, for example, can be used to simulate the properties of molecules and materials, aiding in the discovery of new drugs and materials. Quantum state preparation is essential for many quantum algorithms, as it involves creating a specific quantum state that encodes the solution to a problem. Numerical experiments reveal frequently lower error rates when simulating spin and molecular systems, and preparing quantum states. Future research will likely focus on mitigating the increased computational cost associated with TGF and TGFQS. This could involve developing more efficient classical optimisation algorithms or exploring techniques for reducing the number of circuit evaluations required per gate update. Furthermore, investigating the performance of these methods on larger and more complex quantum systems is crucial for assessing their scalability and potential impact on real-world applications. The development of hybrid quantum-classical algorithms, where quantum and classical computers work together, is also a promising avenue for overcoming the limitations of current quantum hardware and unlocking the full potential of quantum computation. The research demonstrated that optimising two single-qubit gates simultaneously, using methods termed TGF and TGFQS, frequently achieved lower error rates than optimising one gate at a time when simulating complex systems like molecular Hamiltonians. This matters because more accurate simulations accelerate materials discovery and improve quantum algorithms essential for future technologies. Experiments utilising spin systems and quantum state preparation showed improvements with random or half-shifted gate pairing strategies, though at the cost of increased computation. Future work will likely explore ways to reduce this computational burden and assess the scalability of these techniques on larger quantum systems. 👉 More information 🗞 Two-Gate Extensions of Free Axis and Free Quaternion Selection for Sequential Optimization of Parameterized Quantum Circuits 🧠 ArXiv: https://arxiv.org/abs/2603.25876 Tags: