Primitive quantum gates for an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> discrete subgroup: Binary tetrahedral
Erik Gustafson, Henry Lamm, Felicity Lovelace, Damian Musk
Abstract
We construct a primitive gate set for the digital quantum simulation of the binary tetrahedral ($\mathbb{BT}$) group on two quantum architectures. This non-Abelian discrete group serves as a crude approximation to $SU(2)$ lattice gauge theory while requiring five qubits or one quicosotetrit per gauge link. The necessary basic primitives are the inversion gate, the group multiplication gate, the trace gate, and the $\mathbb{BT}$ Fourier transform over $\mathbb{BT}$. We experimentally benchmark the inversion and trace gates on ibm_nairobi, with estimated fidelities between 14%--55%, depending on the input state.
Topics & Concepts
TetrahedronQubitTRACE (psycholinguistics)Binary numberQuantum gateQuantum Fourier transformLattice (music)Quantum computerQuantumMathematicsDiscrete mathematicsPhysicsQuantum mechanicsArithmeticGeometryAcousticsLinguisticsPhilosophyQuantum and electron transport phenomenaLow-power high-performance VLSI designQuantum Computing Algorithms and Architecture