PACS 03.67. Lx, 68.65.Hb, 68.90.+g For application of quantum dots (QDs) in quantum computers, a precise control of self-assembled QDs was achieved in position and size. On a GaAs surface, atomic force microscope lithography is performed to fabricate nano-scaled oxide dots. When the oxide dots are suitably detached from the substrate, holes of the same size are formed. By overgrowing InGaAs on such a hole-patterned surface, one single quantum dot, whose size depends on the hole, is formed on the site of each hole. An ordered array of differently sized QDs can be fabricated as the qubits of all-optical quantum computer using electron spins of coupled QDs.1 Introduction Quantum computer (QC) research, which appeared in 1980's, has become more and more popular due to the discovery of quantum algorithms and the developments of experimental techniques in recent years [1]. Some physical implementations of quantum gates are proposed and demonstrated. Among them, solid state systems have an advantage of scalability, which is necessary for practical tasks. As a candidate of solid state QC, an electron system in semiconductor nanostructures is further advantageous of relatively controllable individual quantum states, which are particularly important in quantum gate operation. Accordingly, many QC schemes based on semiconductor quantum dots (QDs) have been proposed and studied [2,3]. To construct QC by using QDs, one of the most important challenges is to realize an arbitrarily ordered QD array, because self-assembled QDs grown in the Stranski−Krastanov (S−K) mode are usually randomly distributed. Although some techniques were developed, there are still many problems for them to be applied in QC. Defining holes by electron beam lithography is one of the widely used techniques, but the obtained dots are mostly still larger than 50 nm in diameter with an interdot distance above 100 nm [4,5] due to the proximity effect of the resist against electron beam. The large lateral separation prevents QDs from effective interdot coupling, which is fundamental in QC made of QDs. Scanning tunneling microscope (STM) lithography was also used to control self-assembled QDs [6]. The guiding element of the QD position is some unknown deposit, introducing defect-rich growth of QDs and then degradation of the QD coherence, which is fatal in QC. Selfassembly itself is sometimes capable of growing a rather ordered QD array [7], prospective due to an enhanced optical non-linearity, but it is impossible to prepare differently sized QDs at the same time. In this work, we use atomic force microscopy (AFM) oxidation to help controlling QDs. It is firstly advantageous of little defects and impurity. We can fabricate QD arrays with a size homogeneity of ±5%. The precision and reproducibility are satisfactory to the application in QC.