Spin-based quantum computation in multielectron quantum dots

Abstract

In a quantum computer the hardware and software are intrinsically connected because the quantum Hamiltonian (or more precisely its time development) is the code that runs the computer. We demonstrate this subtle and crucial relationship by considering the example of electron-spin-based solid state quantum computer in semiconductor quantum dots. We show that multielectron quantum dots with one valence electron in the outermost shell do not behave simply as an effective single spin system unless special conditions are satisfied. Our work compellingly demonstrates that a delicate synergy between theory and experiment (between software and hardware) is essential for constructing a quantum computer.PACS numbers: 03.67. Lx, 85.30.Vw Ever since the pioneering work on quantum computation and quantum error correction [1][2][3][4] To help overcome these difficulties, more theoretical work is needed to explore the optimal operating regimes, figure out the operational constraints and tolerances, and discover potential sources of errors, just to name a few directions [15][16][17][18]. While the optical and atomic physics based architectures have been crucial in demonstrating the proof of principle for quantum computation, it is generally believed that solid state QC architectures, with their obvious advantage of controllable scale-up possibilities, offer the most promising potential for realistic large scale QC hardwares. The fundamental problem plaguing the solid state QC architectures has been the fact that the basic quantum bit (qubit), the QC building block, has not been compellingly demonstrated in any solid state QC architectures, although there is no reason to doubt that they exist in nature. Thus, the construction of successful QC hardwares has faced the somewhat embarrassing dichotomy: the architectures (ion traps, etc.) demonstrating existence of quantum bits cannot be easily scaled up, while the architectures (solid state QCs) which may be easily scaled up have not yet experimentally demonstrated quantum bits! Quantum computation with fermionic spins is considered to be a potentially promising prospect for solid state quantum computers [9][10][11][12]19]. Among the many proposed solid state QC architectures the spin quantum computer has several intrinsic advantages: (1) A fermionic spin, being a quantum two-level system, is a natural qubit with its spin up and down states; (2) it is fairly straightforward to carry out single-qubit operations on spin up and down levels by applying suitable magnetic fields (or through a purely exchange-based scheme [15]); (3) two-qubit operations can, in principle, be carried out rather easily (in theory, at least) by using the exchange interaction between two neighboring spins; (4) quantum spin is fairly robust and does not decohere easily (typical electron spin relaxation times in solids are many orders of magnitude longer [20] than the momentum relaxation time)-in particular, electron spin relaxation times could be microseconds in semiconductors [21].Our work presented in this...

Screening of charged impurities with multielectron singlet-triplet spin qubits in quantum dots

“…Previous studies considered this splitting, which is an effective exchange energy, for six electrons using a frozencore approximation. 28 We will improve upon these early results both by increasing the number of electrons to include the N = 10 and N = 14 cases, and by relaxing the assumption that the core electrons are frozen. In order to both test and improve upon the frozen-core approximation, we will use the cutoff approximation as in Sec.…”

“…In other words, one can consider the "frozen-core" approximation in which one keeps only multi-particle states for which all but two of the electrons fill up the Fock-Darwin states below the valence orbital. 28 Another technique is to simply neglect all configurations involving single-particle orbitals above some cutoff level. This is referred to as "full CI" within the orbital cutoff.…”

“…30), there occurs some anomalous behavior arising from the spatial dependence of the phase of the relevant valence orbital. 31 In contrast to previous theoretical studies of multielectron DQDs 32-34 or multi-electron qubits, 28,29,35 our focus is on how charge noise affects singlet-triplet qubits in a DQD. However, our results also give some new insights pertaining to the multi-electron quantum dot system in the absence of charge impurities, and so has some direct bearing on these earlier works.…”

“…Experimental studies of spin blockade 25,26 and excitation spectra 27 have already been performed in multi-electron DQDs. On the theoretical side, early work analyzed some of the subtleties involved with qubit manipulation in the context of multi-electron dots, 28,29 highlighting, for example, the need for an external magnetic field in the case of singlet-triplet qubits in order to ensure that the qubit is well defined. We shall see that the use of multi-electron dots for spin-based quantum computation merits further consideration because of the favorable behavior of such qubits in the presence of charge impurities.…”

Few-body spin couplings and their implications for universal quantum computation

“…This is achievable, e.g., by using local magnetic fields [1,20,21,33,34], by ferroelectric gates [35], or by optical rectification [36]. It is important to emphasize that the last two methods [35,36] do not require magnetic field control, hence overcome at least in part the problems with EQC raised in Refs.…”