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Noiseles holonomic quantum computation with higher-j physical spin

Linus Odenhall

Published Jan 1, 2026• 0 citations
OpenAlex

Abstract

Quantum information and quantum computation is an area of quantum mechanics which utilizes quantum properties of particles in schemes for computation. These quantum schemes have been shown to improve computational capabilities for some systems. In quantum computation, the decoherence problem is a limiting factor. Decoherence is the process of loss of quantum information due to interaction from the environment, which puts a limit to how long a quantum computation is valid. There are ways to limit the effect of decoherence. The idea of a noiseless subsystem is to encode the quantum information in a smaller subsystem of the physical system that is not affected by decoherence. Holonomic quantum computation encodes quantum information in holonomies, making it more robust and less affected by decoherence. In this report, these two concepts are combined by encoding one logical qubit in three physical spin-1 particles. The approach to combine these concepts is entirely analytical. A Hamiltonian acting on the physical system is derived. To achieve a result which is possible to implement experimentally, the analytical derivation utilizes permutation operators to derive the Hamiltonian, which is known to be implementable experimentally. A resulting Hamiltonian to implement the scheme is derived, using only permutaion operators. Both a one-qubit gate and a two-qubit gate is derived, which forms a universal set allowing all possible quantum computation. The resulting scheme seems to only use two-body interactions. The project has shown that holonomic quantum computation in a noiseless subsystem using threephysical spin-1 particles is possible. The resulting scheme only using two-body interactions is of a large interest since this simplifies the experimental implementation.

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Quantum information and quantum computation is an area of quantum mechanics which utilizes quantum properties of particles in schemes for computation. These quantum schemes have been shown to improve computational capabilities for some systems. In quantum computation, the decoherence problem is a limiting factor. Decoherence is the process of loss of quantum information due to interaction from the environment, which puts a limit to how long a quantum computation is valid. There are ways to limit the effect of decoherence. The idea of a noiseless subsystem is to encode the quantum information in a smaller subsystem of the physical system that is not affected by decoherence. Holonomic quantum computation encodes quantum information in holonomies, making it more robust and less affected by decoherence. In this report, these two concepts are combined by encoding one logical qubit in three physical spin-1 particles. The approach to combine these concepts is entirely analytical. A Hamiltonian acting on the physical system is derived. To achieve a result which is possible to implement experimentally, the analytical derivation utilizes permutation operators to derive the Hamiltonian, which is known to be implementable experimentally. A resulting Hamiltonian to implement the scheme is derived, using only permutaion operators. Both a one-qubit gate and a two-qubit gate is derived, which forms a universal set allowing all possible quantum computation. The resulting scheme seems to only use two-body interactions. The project has shown that holonomic quantum computation in a noiseless subsystem using threephysical spin-1 particles is possible. The resulting scheme only using two-body interactions is of a large interest since this simplifies the experimental implementation.
Quantum information processing requires a high degree of isolation from the detrimental effects of the environment as well as an extremely precise level of control on the way quantum dynamics unfolds in the information-processing system. In this paper, we show how these two goals can be ideally achieved by hybridizing the concepts of noiseless subsystems and of holonomic quantum computation. An all-geometric universal computation scheme based on non-adiabatic and non-Abelian quantum holonomies embedded in a four-qubit noiseless subsystem for general collective decoherence is proposed. The implementation details of this synergistic scheme along with the analysis of its stability against symmetry-breaking imperfections are presented.
Quantum-information processing requires a high degree of isolation from the detrimental effects of the environment as well as an extremely precise level of control of the way quantum dynamics unfolds in the information-processing system. In this paper we show how these two goals can be ideally achieved by hybridizing the concepts of noiseless subsystems and of holonomic quantum computation. An all-geometric universal computation scheme based on nonadiabatic and non-Abelian quantum holonomies embedded in a four-qubit noiseless subsystem for general collective decoherence is proposed. The implementation details of this synergistic scheme along with the analysis of its stability against symmetry-breaking imperfections are presented.
A constructive scheme has been devised to enable mapping of any quantum computation into a spintronic circuit in which the computation is encoded in a basis that is, in principle, immune to quantum decoherence. The scheme is implemented by an algorithm that utilizes multiple physical spins to encode each logical bit in such a way that collective errors affecting all the physical spins do not disturb the logical bit. The scheme is expected to be of use to experimenters working on spintronic implementations of quantum logic. Spintronic computing devices use quantum-mechanical spins (typically, electron spins) to encode logical bits. Bits thus encoded (denoted qubits) are potentially susceptible to errors caused by noise and decoherence. The traditional model of quantum computation is based partly on the assumption that each qubit is implemented by use of a single two-state quantum system, such as an electron or other spin-1.2 particle. It can be surprisingly difficult to achieve certain gate operations . most notably, those of arbitrary 1-qubit gates . in spintronic hardware according to this model. However, ironically, certain 2-qubit interactions (in particular, spin-spin exchange interactions) can be achieved relatively easily in spintronic hardware. Therefore, it would be fortunate if it were possible to implement any 1-qubit gate by use of a spin-spin exchange interaction. While such a direct representation is not possible, it is possible to achieve an arbitrary 1-qubit gate indirectly by means of a sequence of four spin-spin exchange interactions, which could be implemented by use of four exchange gates. Accordingly, the present scheme provides for mapping any 1-qubit gate in the logical basis into an equivalent sequence of at most four spin-spin exchange interactions in the physical (encoded) basis. The complexity of the mathematical derivation of the scheme from basic quantum principles precludes a description within this article; it must suffice to report that the derivation provides explicit constructions for finding the exchange couplings in the physical basis needed to implement any arbitrary 1-qubit gate. These constructions lead to spintronic encodings of quantum logic that are more efficient than those of a previously published scheme that utilizes a universal but fixed set of gates.
Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of (N - 2)/N. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.
Abstract Adiabatic holonomic gates possess the geometric robustness of adiabatic geometric phases, i.e., dependence only on the evolution path of the parameter space but not on the evolution details of the quantum system, which, when coordinated with decoherence-free subspaces, permits additional resilience to the collective dephasing environment. However, the previous scheme [Phys. Rev. Lett. 95 130501 (2005)] of adiabatic holonomic quantum computation in decoherence-free subspaces requires four-body interaction that is challenging in practical implementation. In this work, we put forward a scheme to realize universal adiabatic holonomic quantum computation in decoherence-free subspaces using only realistically available two-body interaction, thereby avoiding the difficulty of implementing four-body interaction. Furthermore, an arbitrary one-qubit gate in our scheme can be realized by a single-shot implementation, which eliminates the need to combine multiple gates for realizing such a gate.
Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, nonadiabatic holonomic quantum computation in decoherence-free subspaces, which avoids a long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize nonadiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.