Quantum Compiler for Topological Quantum Computation

This paper presents a novel approach to topological quantum computation – Dynamic Topological Quantum Circuit Compilation (DTQCC). The core claim is that by continuously monitoring the decoherence performance of a topological quantum circuit, its topology can be dynamically adjusted to achieve enhanced quantum computing efficiency and resilience. This is achieved through a mechanism that establishes a topological decoherence model, utilizes machine learning algorithms to predict decoherence rates, and subsequently, adjusts quantum gate operations and topological qubit connections in real-time to minimize the detrimental effects of decoherence. Unlike previous topological quantum computing methods which largely relied on fixed topologies, the proposed DTQCC framework introduces a dynamic adaptation strategy, significantly improving the adaptability and scalability of topological quantum systems. The core mathematical framework is presented, detailing the equations governing decoherence prediction and topological reconfiguration. We explore the key elements of the system, including the decoherence model formulation, the machine learning algorithm utilized for prediction, and the dynamic reconfiguration strategies. The goal is to demonstrate a pathway towards more robust and efficient topological quantum computation.This paper presents a novel approach to topological quantum computation – Dynamic Topological Quantum Circuit Compilation (DTQCC). The core claim is that by continuously monitoring the decoherence performance of a topological quantum circuit, its topology can be dynamically adjusted to achieve enhanced quantum computing efficiency and resilience. This is achieved through a mechanism that establishes a topological decoherence model, utilizes machine learning algorithms to predict decoherence rates, and subsequently, adjusts quantum gate operations and topological qubit connections in real-time to minimize the detrimental effects of decoherence. Unlike previous topological quantum computing methods which largely relied on fixed topologies, the proposed DTQCC framework introduces a dynamic adaptation strategy, significantly improving the adaptability and scalability of topological quantum systems. The core mathematical framework is presented, detailing the equations governing decoherence prediction and topological reconfiguration. We explore the key elements of the system, including the decoherence model formulation, the machine learning algorithm utilized for prediction, and the dynamic reconfiguration strategies. The goal is to demonstrate a pathway towards more robust and efficient topological quantum computation.

Sep 5, 20260 citations

Topological quantum computation

Giuseppe Mussardo

Springer eBooksJan 1, 20250 citations

Dynamic Topology-Dependent Quantum Computing Compilation

Jincheng Zhang

Quantum computing relies heavily on efficient compilation techniques to translate high-level quantum algorithms into low-level gate sequences suitable for specific quantum hardware. Traditional quantum compilation methods often rely on fixed, pre-defined topologies, which can be inefficient and inflexible when dealing with the inherent physical constraints and algorithmic variations present in real quantum devices. This work introduces a novel approach to quantum compilation that dynamically adapts the topology of quantum circuits based on reinforcement learning. We propose a "topology optimizer" that learns to optimize circuit topologies in real-time, considering factors such as quantum decoherence, quantum error correction, and resource limitations. The core mechanism involves iteratively adjusting the circuit's topology to minimize resource usage and error propagation. This dynamic approach promises to significantly improve the performance and practicality of quantum computing by aligning compilation strategies with the nuances of quantum hardware. The key equation representing this process is: $T^* = argmin_T \left[ \sum_{i=1}^{K} \rho_i(T) \cdot C_i \right]$ , where $T^*$ is the optimal topology, $T$ represents a candidate topology, $\rho_i(T)$ is the fidelity of the quantum circuit with topology $T$ for the $i$ -th qubit, and $C_i$ is the cost associated with that qubit. Furthermore, the error rate $ε(T)$ is defined as $ε(T) = \sum_{i=1}^{K} \delta_i(T)$ , where $\delta_i(T)$ represents the error introduced by the topology $T$ for the $i$ -th qubit. This framework offers a fundamentally new paradigm for quantum compilation.Quantum computing relies heavily on efficient compilation techniques to translate high-level quantum algorithms into low-level gate sequences suitable for specific quantum hardware. Traditional quantum compilation methods often rely on fixed, pre-defined topologies, which can be inefficient and inflexible when dealing with the inherent physical constraints and algorithmic variations present in real quantum devices. This work introduces a novel approach to quantum compilation that dynamically adapts the topology of quantum circuits based on reinforcement learning. We propose a "topology optimizer" that learns to optimize circuit topologies in real-time, considering factors such as quantum decoherence, quantum error correction, and resource limitations. The core mechanism involves iteratively adjusting the circuit's topology to minimize resource usage and error propagation. This dynamic approach promises to significantly improve the performance and practicality of quantum computing by aligning compilation strategies with the nuances of quantum hardware. The key equation representing this process is: $T^* = argmin_T \left[ \sum_{i=1}^{K} \rho_i(T) \cdot C_i \right]$, where $T^*$ is the optimal topology, $T$ represents a candidate topology, $\rho_i(T)$ is the fidelity of the quantum circuit with topology $T$ for the $i$-th qubit, and $C_i$ is the cost associated with that qubit. Furthermore, the error rate $ε(T)$ is defined as $ε(T) = \sum_{i=1}^{K} \delta_i(T)$, where $\delta_i(T)$ represents the error introduced by the topology $T$ for the $i$-th qubit. This framework offers a fundamentally new paradigm for quantum compilation.

Aug 31, 20260 citations

Topological Quantum Computation and Quantum Compilation

Joren Brunekreef

A central problem in realizing universal quantum computers is dealing with decoherence effects, which can destroy the vulnerable quantum states present in the internal registers. Several schemes have been developed that provide resistance to decoherence, leading to theories of fault-tolerant quantum computation. One such scheme is the theory of topological quantum computation, which encodes qubit states in robust topological properties of certain quantum systems. However, fault-tolerant theories typically only provide a finite set of primitive gates, from which we must then form approximations to arbitrary quantum gates. The Solovay-Kitaev algorithm describes a procedure for accomplishing this, and proves that the number of primitive gates required to approximate an arbitrary gate is only polylogarithmic in the desired degree of accuracy. In this thesis, we first outline the basic theory of quantum computation. Secondly, we describe the general problem of quantum compilation, list several possible strategies for relevant optimizations, and outline a proof of the Solovay-Kitaev theorem. Next, we give an introduction to the theory of topological quantum computation by anyons, with special focus on Fibonacci-anyons. Finally, we list some numerical results of an implementation of the Solovay-Kitaev algorithm when applied to a Fibonacci-anyon model and analyze the performance gains obtained through applications of the proposed optimizations.A central problem in realizing universal quantum computers is dealing with decoherence effects, which can destroy the vulnerable quantum states present in the internal registers. Several schemes have been developed that provide resistance to decoherence, leading to theories of fault-tolerant quantum computation. One such scheme is the theory of topological quantum computation, which encodes qubit states in robust topological properties of certain quantum systems. However, fault-tolerant theories typically only provide a finite set of primitive gates, from which we must then form approximations to arbitrary quantum gates. The Solovay-Kitaev algorithm describes a procedure for accomplishing this, and proves that the number of primitive gates required to approximate an arbitrary gate is only polylogarithmic in the desired degree of accuracy. In this thesis, we first outline the basic theory of quantum computation. Secondly, we describe the general problem of quantum compilation, list several possible strategies for relevant optimizations, and outline a proof of the Solovay-Kitaev theorem. Next, we give an introduction to the theory of topological quantum computation by anyons, with special focus on Fibonacci-anyons. Finally, we list some numerical results of an implementation of the Solovay-Kitaev algorithm when applied to a Fibonacci-anyon model and analyze the performance gains obtained through applications of the proposed optimizations.

Aug 26, 20140 citations

Topological Quantum Compilation Using Mixed-Integer Programming

Pavel Rytir, Phillip C. Burke, Christos Aravanis +2 more

We introduce the Mixed-Integer Quadratically Constrained Quadratic Programming framework for the quantum compilation problem and apply it in the context of topological quantum computing. In this setting, quantum gates are realized by sequences of elementary braids of quasiparticles with exotic fractional statistics in certain two-dimensional topological condensed matter systems, described by effective topological quantum field theories. We specifically focus on a non-semisimple version of topological field theory, which provides a foundation for an extended theory of Ising anyons and which has recently been shown by Iulianelli et al., Nature Communications {\bf 16}, 6408 (2025), to permit universal quantum computation. While the proofs of this pioneering result are existential in nature, the mixed integer programming provides an approach to explicitly construct quantum gates in topological systems. We demonstrate this by focusing specifically on the entangling controlled-NOT operation, and its local equivalence class, using braiding operations in the non-semisimple Ising system. This illustrates the utility of the Mixed-Integer Quadratically Constrained Quadratic Programming for topological quantum compilation.We introduce the Mixed-Integer Quadratically Constrained Quadratic Programming framework for the quantum compilation problem and apply it in the context of topological quantum computing. In this setting, quantum gates are realized by sequences of elementary braids of quasiparticles with exotic fractional statistics in certain two-dimensional topological condensed matter systems, described by effective topological quantum field theories. We specifically focus on a non-semisimple version of topological field theory, which provides a foundation for an extended theory of Ising anyons and which has recently been shown by Iulianelli et al., Nature Communications {\bf 16}, 6408 (2025), to permit universal quantum computation. While the proofs of this pioneering result are existential in nature, the mixed integer programming provides an approach to explicitly construct quantum gates in topological systems. We demonstrate this by focusing specifically on the entangling controlled-NOT operation, and its local equivalence class, using braiding operations in the non-semisimple Ising system. This illustrates the utility of the Mixed-Integer Quadratically Constrained Quadratic Programming for topological quantum compilation.

quant-pharXiv:2511.09513IEEE Transactions on Quantum EngineeringNov 13, 20250 citations

T^* = argmin_T \left[ \sum_{i=1}^{K} \rho_i(T) \cdot C_i \right]

, where

T^*

is the optimal topology,

T

represents a candidate topology,

\rho_i(T)

is the fidelity of the quantum circuit with topology

T

for the

i

-th qubit, and

C_i

is the cost associated with that qubit. Furthermore, the error rate

ε(T)

is defined as

ε(T) = \sum_{i=1}^{K} \delta_i(T)

, where

\delta_i(T)

represents the error introduced by the topology

T

for the

i

-th qubit. This framework offers a fundamentally new paradigm for quantum compilation.