Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation

Abstract

Quantum information processing has witnessed significant advancements through the application of qubit-based techniques within universal gate sets. Recently, exploration beyond the qubit paradigm to $d$-dimensional quantum units or qudits has opened new avenues for improving computational efficiency. This paper delves into the qudit-based approach, particularly addressing the challenges presented in the high-fidelity implementation of qudit-based circuits due to increased complexity. As an innovative approach towards enhancing qudit circuit fidelity, we explore algebraic relations, such as the Yang-Baxter-like turnover equation, that may enable circuit compression and optimization. The paper introduces the turnover relation for the three-qutrit time propagator and its potential use in reducing circuit depth. We further investigate whether this relation can be generalized for higher-dimensional quantum circuits, including a focused study on the one-dimensional spin-1 Heisenberg model. Our work outlines both rigorous and numerically efficient approaches to potentially achieve this generalization, providing a foundation for further explorations in the field of qudit-based quantum computing.

References in corpus (57)

• Non-Abelian Anyons and Topological Quantum Computation
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• Topological quantum memory
• Two-Bit Gates are Universal for Quantum Computation
• Quantum cryptography with 3-state systems
• Optimal eavesdropping in cryptography with three-dimensional quantum states
• Exponential suppression of bit or phase flip errors with repetitive error correction
• Multi-valued Logic Gates for Quantum Computation
• Quantum codes on a lattice with boundary
• A universal qudit quantum processor with trapped ions
• Realization of an Error-Correcting Surface Code with Superconducting Qubits
• Efficient Toffoli Gates Using Qudits
• Quantum Information Scrambling in a Superconducting Qutrit Processor
• Quantum key distribution with higher-order alphabets using spatially-encoded qudits
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Real- and imaginary-time evolution with compressed quantum circuits
• Enhanced fault-tolerant quantum computing in $d$-level systems
• Quantum computation based on d-level cluster states
• Artificial Intelligence and Machine Learning for Quantum Technologies
• Security of Quantum Key Distribution with Entangled Qutrits
• Magic state distillation in all prime dimensions using quantum Reed-Muller codes
• A Quantum solution to the Byzantine agreement problem
• Asymptotically Optimal Quantum Circuits for d-level Systems
• High-Fidelity Qutrit Entangling Gates for Superconducting Circuits
• Logical-qubit operations in an error-detecting surface code
• Parallel Quantum Simulation of Large Systems on Small Quantum Computers
• Native qudit entanglement in a trapped ion quantum processor
• Factoring with Qutrits: Shor's Algorithm on Ternary and Metaplectic Quantum Architectures
• Exceeding classical capacity limit in quantum optical channel
• Fast-forwarding of Hamiltonians and Exponentially Precise Measurements
• Criteria for Exact Qudit Universality
• Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
• A Very Small Logical Qubit
• Universal qudit gate synthesis for transmons
• Overcoming erasure errors with multilevel systems
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution
• Arithmetic Circuits for Multilevel Qudits Based on Quantum Fourier Transform
• Constant-Depth Circuits for Dynamic Simulations of Materials on Quantum Computers
• Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression
• Quantum time dynamics of 1D-Heisenberg models employing the Yang-Baxter equation for circuit compression
• Experimental realization of the Yang-Baxter Equation via NMR interferometry
• Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model
• An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation
• Direct Experimental Simulation of the Yang-Baxter Equation
• Steering random spin systems to speed up the quantum adiabatic algorithm
• Quantum error-correcting code for ternary logic
• Quantum computing hardware for HEP algorithms and sensing
• Numerical Gate Synthesis for Quantum Heuristics on Bosonic Quantum Processors
• Impacts of Noise and Structure on Quantum Information Encoded in a Quantum Memory
• Speedup of the Quantum Adiabatic Algorithm using Delocalization Catalysis
• Noise Improvements in Quantum Simulations of sQED using Qutrits
• Response of a quantum disordered spin system to a local periodic drive
• QuYBE -- An Algebraic Compiler for Quantum Circuit Compression
• Generalized Yang-Baxter Equations and Braiding Quantum Gates
• Lectures on Quantum Groups and Yang-Baxter Equations
• Excitation dynamics in inductively coupled fluxonium circuits

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