#LipkinMeshkovGlickModel

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Lipkin Meshkov Glick Model on Neutral Atom Quantum Computer

Lipkin Meshkov Glick Model

Variational-quantum-eigensolver algorithm for neutral atom quantum computer Lipkin-Meshkov-Glick model simulation. Spin systems' ground-state energy is measured up to 15 spins. Encoding strategies include an individual spin encoding where each spin is represented by one qubit and an efficient Grey code encoding that takes a logarithm of spins. This more efficient encoding and zero-noise extrapolation enhance simulated energy accuracy to perfect answers.

A fundamental theoretical framework for analysing quantum systems having a finite number of two-level atomic quantum states is Lipkin-Meshkov-Glick (LMG). The 1960s-founded organisation studied nuclear giant monopoles and many-body physics computer simulations. It is now a key test location for many-body physics approximation methods. Because it is non-trivial but precisely solved, it is ideal for computational confirmation.

In Bose-Einstein condensates, quantum correlations, and statistical mechanics with spin relationships, the LMG model works. It is increasingly used in quantum thermodynamics to build and test thermodynamic cycles, notably for quantum phase transitions. Comparative studies of quantum Otto and Carnot cycle performance metrics have used it.

Physics: Benchmarking Heat Engine and Quantum Computing Improvements with a Common Theoretical Model

Recent scientific advances are illuminating quantum technologies' potential using two Lipkin-Meshkov-Glick model studies. An LMG model-based study evaluates neutral atom quantum computers, while another examines the quantum Otto machine. These simultaneous discoveries show how swiftly quantum thermodynamics and computing power are advancing.

Maxing Out Quantum Heat Engine Efficiency

The quantum Otto machine's quantum heat correlations, performance, and efficiency were studied in Optical and Quantum Electronics using the discrete sides of the LMG model as its working medium. Quantum heat engines (QHEs) may produce a “paradigm shift” in technology and outperform thermal machines. Otto engines are popular because they clearly separate heat and work exchange in their phases.

The LMG model was examined for symmetric cross-interaction and magnetic field spin interactions. Key study findings include:

Symmetrical heat correlations were always found around the coupling of the symmetric cross-interaction in anisotropic XY, Ising, or mixed ferromagnetism models.

Although the maximum boundaries varied, two or three sides of the mixed ferromagnetic working substance functioned symmetrically.

The two-sided mixed ferromagnetism model became more efficient as the exchange parameter climbed.

The discovery that a three-sided spin interaction can accurately manage the system's anisotropy parameter led to the QHE or quantum refrigerator. Mixed ferromagnetic situations were more efficient and anisotropic than Ising. An optimal Carnot efficiency can be achieved with fewer “atoms” (two-side spin interaction) in a QHE, but it decreases with more atoms.

When the external magnetic field was stronger than the exchange coupling, symmetric cross-interaction coupling was needed to maintain heat correlations and avoid adiabatic process disruptions.

The study also examined certain operations:

The two-side mixed ferromagnetism LMG model developed a QHE with positive work done and heat absorbed and negative heat released under low external magnetic field coupling and particular exchange coupling. The system ended thermodynamically when the symmetric cross-interaction increased beyond a certain range.

The device can operate as a QR for the two-side anisotropic XY system at zero symmetric cross-interaction (work done and heat emitted negative, heat absorbed positive) and a QHE when coupling is enhanced. Increased exchange coupling and external magnetic field coupling can make the two-side anisotropic XY system a heater (negative heat absorbed).

In the three-side LMG model, a QHE was obtained by setting (\gamma) to -1, whereas a QR was obtained by setting (\gamma) to 0 (Ising model) or 1 (anisotropic XY model). Increased exchange coupling parameter may result in an accelerator operation around zero symmetric cross-interaction in these latter cases. In general, two sides had higher work output limits than three sides.

This study suggests that customised quantum matter like the LMG model can work as a working medium in quantum thermodynamic cycles, possibly producing more work than traditional engines, when employed between comparable thermal reservoirs.

Benchmarking Quantum Computers with LMG

A neutral atom quantum computer was used to simulate the LMG model using the Variational Quantum Eigensolver (VQE) algorithm in another work. The LMG model is ideal for testing new and old quantum computers since it is solvable. It achieves the same goal for quantum machines 60 years after being applied to classical systems in the 1960s.

Besides technological breakthroughs, the research team examined the ground-state energy of spin systems with up to 15 spins:

We directly contrasted a very successful Grey code encoding that requires a number of qubits scaling logarithmically with spins and a spin encoding (one spin per qubit). With appropriate encoding, three qubits may replicate 15 spins.

Zero-noise extrapolation (ZNE) improved performance for the researchers. ZNE reduces gate errors, improving simulated energy accuracy beyond intrinsic physical gate fidelities. They used SIIM and FIIM ZNE for this.

Neutral atom processor breakthroughs included moving Caesium (Cs) atoms for dynamic qubit connection and fast optical control beam scanning. Executing quantum algorithms with these qualities increased two-qubit gate fidelity to 0.971(1).

ZNE agreed well with theoretical ground-state energies for up to seven spins and roughly 5% for nine spins, but larger systems still have concerns. VQE convergence was prone to entrapment in local energy minima, especially for the 15-spin system, even in noise-free simulations. This advises using more advanced adaptive optimisation methods and expanding the search to more beginning circumstances.

This paper shows how neutral atom quantum computers can simulate complex many-body spin models, highlighting the importance of good encoding and noise reduction approaches in quantum computation. The challenges of larger systems underscore the need for quantum error correction and robust optimisation advances.