A Preliminary Study on Implementation of Five-Qubit Quantum Information Processing in Silicon Devices

INTRODUCTION<br/>An electrode-driven Silicon (Si) quantum dot (QD) system can be adopted to design scalable quantum processors with well-established industrial fabrication technologies [<i>Nat. Electron. </i><b>5</b>, 184 (2022)]. Recently, there have been experimental efforts to understand the physics of electron-spin qubits in Si QD systems whose confinement is manipulated with human controls, including a successful implementation of entangling logic operations up to six qubits [<i>Nature </i><b>609</b>, 919 (2022)]. Device designs & control engineering of physical systems consisting of many QDs, however, are still critical issues that must be uncovered with computational modeling to secure the scalability of quantum processors. Here we study the control engineering needed to initialize the linear five QD (FQD) system in Si and show the initialized spin states can be controlled to produce the magic state, one of quantum resource for realization of fault-tolerant quantum computing [<i>Nature </i><b>510</b>, 351 (2014)].<br/><br/>METHODS<br/>Device simulations are conducted for the realistically sized Si FQD system with our multi-scale modeling approach integrating the bulk physics & the parabolic effective mass approximation. Qubits are encoded to electron spins that are created with quantum confinement driven by gate biases imposed on top electrodes. A static magnetic field is applied with a lateral gradient to make the Zeeman-splitting energies of electron ground states distinguishable. Once a set of five Zeeman-splitting energies and exchange interactions between nearest QDs is obtained from device simulations, the time-response of spin qubits is obtained from solutions of a time-dependent Schrödinger equation that is described with the Heisenberg spin Hamiltonian.<br/><br/>RESULTS AND DISCUSSION<br/>We rigorously explored appropriate sets of biases imposed on the top electrodes, with which the FQD can be stably created satisfying the symmetric-biasing condition. Figuring out the bias condition that fills a single electron to each QD (qubit initialization), we engineered the sizes of nine electrodes to calibrate the distance between nearest electron spins to ~100nm. When the system is initialized, the five Zeeman-splitting energies come clearly distinguishable, and the four exchange interactions between nearest electron spins turn out to be weak enough to guarantee the individual address of five qubits. Then, as an application example, we show how a specific type of 5-qubit magic states can be prepared in the Si FQD platform, where we also present the detailed guideline of controls required to implement the non-Clifford <i>T</i>-gate and the Hadamard gate that are essential to generate the magic state. Robustness of the secured 5-qubit circuit (and so the magic state) to charge noise is also confirmed by simulation results that are obtained with unintentional random fluctuations in exchange energies.