We consider bosonization of supersymmetry in the context of Wess-Zumino quantum mechanics. Our motivation for this investigation is the flexibility the bosonic fock space affords as any classical probability distribution can be realized on it making it a versatile framework to work with for quantum processes. We proceed by constructing a minimal bosonization of a system with one bosonic and two fermionic degrees of freedom. We iterate this process to construct a tower of SUSY systems that is akin to unfolded Adinkras. We then identify an osp(2|2) symmetry of the system constructed. To build an irreducible representation of the system we induce representations across the sectors, a first to our knowledge, as the previous work have focused on induction only within the bosonic sector. First, we start with a fermionic representation using Clifford algebras and then induce a representation to gl(2|2) and restrict it to osp(2|2). In the second method, we induce a representation from that of the bosonic sector. In both cases, our representations are in terms of qubit operators that provide a way to solve SUSY problems using quantum information based approaches. Depending upon the direction of induction the representations are suitable for implementation on a hybrid qubit and fermionic or bosonic quantum computers.
We consider bosonization of supersymmetry in the context of Wess-Zumino quantum mechanics. Our motivation for this investigation is the flexibility the bosonic fock space affords as any classical probability distribution can be realized on it making it a versatile framework to work with for quantum processes. We proceed by constructing a minimal bosonization of a system with one bosonic and two fermionic degrees of freedom. We iterate this process to construct a tower of SUSY systems that is akin to unfolded Adinkras. We then identify an osp(2|2) symmetry of the system constructed. To build an irreducible representation of the system we induce representations across the sectors, a first to our knowledge, as the previous work have focused on induction only within the bosonic sector. First, we start with a fermionic representation using Clifford algebras and then induce a representation to gl(2|2) and restrict it to osp(2|2). In the second method, we induce a representation from that of the bosonic sector. In both cases, our representations are in terms of qubit operators that provide a way to solve SUSY problems using quantum information based approaches. Depending upon the direction of induction the representations are suitable for implementation on a hybrid qubit and fermionic or bosonic quantum computers.
Supersymmetry (SUSY), originally proposed in particle physics, refers to a dual relation that connects fermionic and bosonic degrees of freedom in a system. Recently, there has been considerable interest in applying the idea of SUSY to topological phases, motivated by the attempt to gain insights from the fermion side into the boson side and vice versa. We present a systematic study of this construction when applied to band topology in noninteracting systems. First, on top of the conventional tenfold way, we find that topological insulators and superconductors are divided into three classes depending on whether the supercharge can be local and symmetric, must break a symmetry to preserve locality, or needs to break locality. Second, we resolve the apparent paradox between the nontriviality of free fermions and the triviality of free bosons by noting that the topological information is encoded in the identification map. We also discuss how to understand a recently revealed SUSY entanglement duality in this context. These findings are illustrated by prototypical examples. In this paper, we shed light on band topology from the perspective of SUSY.
Supersymmetry (SUSY) postulates that for every fermion there is boson of equal mass (i.e. energy). In quantum mechanics this comes about because for every quantum Hamiltonian there is a partner Hamiltonian that has the same energy spectrum above the ground state of the original system. In particle physics, one “sector” is populated by bosons and the other sector by fermions and SUSY predicts that the lowest lying fermion state is energetically degenerate with the first excited boson state. Evidence for SUSY has proven to be elusive and it is now believed that SUSY is a broken symmetry. In January 2009 at a conference dedicated to Bob Wyatt, we began to look at SUSY as a way to develop new computational methods and approaches. Up until now, SUSY has been more of a mathematical technique that has been used more or less as a way to obtain stationary solutions to the Schrödinger equation for a variety of T&F Cat # K11224, Chapter 4, Page 54, 15-9-2010 one-dimensional potential systems. In this chapter, we will discuss some of the work we have been doing in developing “SUSY” inspired methods for performing quantum many-body calculations and quantum scattering calculations. We begin with a brief overview of the SUSY theory and some of its elementary results. We then discuss how we have used the approach to develop both analytical and numerical solutions of the stationary Schrödinger equation. Finally, we conclude by discussing our recent extension of SUSY to higher dimensions and for scattering theory.
In the present paper, we will concern ourselves with the extended phase-space quantum mechanics of particles which have both bosonic and fermionic degrees of freedom, i.e., the quantum field theory in (0 + 1) dimensions in q -(position) and p -(momentum) spaces, exhibiting supersymmetry. We present ( N = 2) realization of extended supersymmetry algebra and discuss the vacuum energy and topology of super-potentials. Shape invariance of exactly solvable extended SUSY potentials allows us to obtain analytic expressions for the entire energy spectrum of an extended Hamiltonian with, for example, Scarf potential without ever referring to an underlying differential equation.
Abstract: This paper proposes a novel paradigm for quantum artificial intelligence: the design and implementation of Supersymmetric Quantum Neural Networks (S-QNNs) that explicitly integrate superalgebraic structures into quantum circuit-based AI architectures. By embedding the symmetry principles of supersymmetry—captured by quantum superalgebras such as osp(1∣2) and sl(1∣1)—into the computational fabric of quantum neural networks, we aim to create models that exhibit both structural elegance and computational efficiency. The resulting framework allows for interpretable, energy-efficient, and mathematically grounded learning systems that leverage both fermionic (discrete) and bosonic (continuous) quantum states to encode and process information. This interdisciplinary approach opens new directions for building explainable and scalable quantum AI systems, particularly in the era of Noisy Intermediate-Scale Quantum (NISQ) devices. Keywords: Supersymmetric Neural Networks, Quantum Superalgebras, Quantum AI, Hybrid Quantum-Classical Learning, osp(1|2), sl(1|1), Interpretable AI, Quantum Symmetry, NISQ
Recent experimental results by Metz, Jolie and collaborators have led to renewed interest in the notion of dynamical supersymmetry in fermion many-body systems. By considering the general problem of constructing a boson-fermion realization for Lie algebras with generators expressed in terms of fermion and bifermion operators, also when favored pairs dictate the structure of collective bosons, we demonstrate that dynamical “supersymmetry without bosons” can indeed emerge in a fermion system without any Pauli Violations. Our construction of the general realization utilizes the identification of a physical subspace and allows one to identify the images of single particle transfer operators uniquely, unlike the situation in phenomenological applications of dynamical supersymmetry.
Supersymmetric models are grounded in the intriguing concept of a hypothetical symmetry that relates bosonic and fermionic particles. This symmetry has profound implications, offering valuable extensions to the Standard Model of particle physics and fostering connections to theories of quantum gravity. However, lattice studies exploring the non-perturbative features of these models, such as spontaneous supersymmetry breaking and real-time evolution encounter significant challenges, particularly due to the infamous sign problem. The sign problem obstructs simulations on classical computers, especially when dealing with high-dimensional lattice systems. While one potential solution is to adopt the Hamiltonian formalism, this approach necessitates an exponential increase in classical resources with the number of lattice sites and degrees of freedom, rendering it impractical for large systems. In contrast, quantum hardware offers a promising alternative, as it requires in principle a polynomial amount of resources, making the study of these models more accessible. In this context, we explore the encoding of lower-dimensional supersymmetric quantum mechanics onto qubits. We also highlight our ongoing efforts to implement and check the model supersymmetry breaking on an IBM gate-based quantum simulator with and without shot noise, addressing the technical challenges we face and the potential implications of our findings for advancing our understanding of supersymmetry.