Quantum Computing Probes Supersymmetry with Reduced Parameters in 6 Analyses
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John Kerfoot and colleagues at University of Liverpool perform variational quantum eigensolver (VQE) analyses for supersymmetric quantum mechanics with differing superpotentials. The work addresses a key challenge in lattice SSB, a severe sign problem, by using hybrid quantum-classical algorithms. An adaptive ansatz construction algorithm minimising the number of variational parameters was developed, reducing the computational demands on both classical and quantum resources and enhancing the practicality of these calculations on near-term, noisy quantum processors. Preliminary VQE results obtained from IBM quantum devices further illuminate the accuracy, limitations, and computational cost associated with this approach, including the benefits of error mitigation techniques. Adaptive ansatz construction streamlines quantum simulation of spontaneous supersymmetry breaking A six-fold reduction in the number of variational parameters is now possible for quantum simulations of spontaneous supersymmetry breaking (SSB). Previously, this was unattainable due to the exponential growth of computational demands. This adaptive ansatz construction algorithm facilitates more complex supersymmetric quantum mechanics calculations on near-term, noisy quantum computers. Traditional methods struggle with these systems because of a severe sign problem hindering lattice calculations. The sign problem arises from the oscillatory nature of the fermionic determinant in lattice field theories, leading to cancellations and exponentially increasing statistical errors as the system size grows. This makes accurate numerical simulations intractable using classical Monte Carlo methods, particularly in regimes where SSB is expected to occur. Supersymmetry, a theoretical framework postulating a symmetry between bosons and fermions, predicts the existence of partner particles for each known particle. Spontaneous breaking of this symmetry is a crucial mechanism in many extensions of the Standard Model of particle physics, potentially explaining phenomena like dark matter and the hierarchy problem. Preliminary results utilising real IBM quantum devices demonstrate the feasibility of this approach, paving the way for exploring SSB in a Hamiltonian formalism and offering insights into the accuracy and resource requirements of such simulations. Three distinct superpotentials, Harmonic Oscillator, Anharmonic Oscillator, and Double Well, were used in the analyses, each influencing the interaction between bosonic and fermionic particles within the system. The Hamiltonian, a mathematical description of the system’s energy, was digitised and mapped onto qubits, the basic units of quantum information, enabling simulations on IBM quantum devices. This mapping typically involves representing fermionic operators using the Jordan-Wigner or Bravyi-Kitaev transformation, which introduces complexities in the quantum circuit construction. Error mitigation techniques were also explored to improve accuracy, but initial simulations involved a limited number of qubits and a simplified representation of the physical system. A clear demonstration of scalability to more complex scenarios remains outstanding. The choice of superpotential directly impacts the potential energy landscape and, consequently, the nature of the SSB.
The Harmonic Oscillator represents a simple quadratic potential, while the Anharmonic Oscillator introduces non-linearities, and the Double Well potential features two minima, promoting a more pronounced symmetry breaking pattern. Adaptive quantum algorithms address computational barriers in symmetry breaking analysis Variational quantum eigensolvers are now employed to tackle longstanding problems in particle physics, specifically spontaneous supersymmetry breaking, a phenomenon where fundamental symmetries appear to vanish. Computational demands are demonstrably reduced, although a full assessment of quantum advantage remains elusive. The complex mathematical issue known as the ‘sign problem’ makes exploring spontaneous supersymmetry breaking notoriously difficult using conventional computing, as symmetry, a cornerstone of particle physics, seems to disappear. The VQE algorithm operates by preparing a trial quantum state (the ansatz) with adjustable parameters, measuring its energy, and then optimising these parameters using a classical optimisation algorithm to minimise the energy expectation value. This iterative process continues until the lowest energy state, approximating the ground state of the system, is found. This approach circumvents these limitations by employing a hybrid quantum-classical algorithm, intelligently minimising the complexity of quantum circuits and reducing the demands on available quantum hardware. An ansatz is an initial educated guess at a solution. The adaptive ansatz construction is crucial because the size of the quantum circuit, and therefore the computational cost, grows rapidly with the number of variational parameters. By systematically reducing these parameters while maintaining accuracy, the researchers have significantly improved the feasibility of simulating SSB on current quantum hardware. A new computational route for exploring spontaneous supersymmetry breaking, a challenging area of theoretical physics, has been established. Applying a variational quantum eigensolver to supersymmetric quantum mechanics characterised the interaction between bosonic and fermionic particles using the three superpotentials: Harmonic Oscillator, Anharmonic Oscillator, and Double Well. The superpotentials define the potential energy landscape experienced by the system, influencing the nature of the symmetry breaking. The use of multiple superpotentials allows for a systematic investigation of how different potential shapes affect the SSB pattern and the associated ground state energy. Further investigation will focus on expanding the simulations to include a greater number of qubits and more intricate physical models. This will allow for a more thorough evaluation of the algorithm’s performance and potential for uncovering new insights into SSB. Future work could explore the use of more sophisticated error mitigation techniques, such as zero-noise extrapolation or probabilistic error cancellation, to further improve the accuracy of the simulations. Ultimately, the goal is to determine whether quantum computers can provide a significant advantage over classical methods in studying SSB and other complex phenomena in particle physics, potentially leading to a deeper understanding of the fundamental laws of nature. Researchers successfully used a variational quantum eigensolver to simulate spontaneous supersymmetry breaking, a complex process in particle physics, with reduced computational demands. This achievement matters because it offers a potential pathway to study systems currently intractable for classical computers, utilising IBM quantum devices and adaptive ansatz construction to minimise circuit complexity.
The team characterised interactions between particles using three superpotentials, demonstrating the feasibility of this approach in the noisy intermediate-scale quantum (NISQ) era. Future work will focus on increasing qubit numbers and refining error mitigation techniques to further validate this method and explore its application to more complex physical models. 👉 More information🗞 Simulating Supersymmetric Quantum Mechanics Using Variational Quantum Algorithms🧠 ArXiv: https://arxiv.org/abs/2603.18749 Tags: