Silicon based Quantum Computation C191 Final Project Report Cheuk Chi Lo Kinyip Phoa Department of Electrical Engineering Computer Science 0 University of California Berkeley Dec 8 2005 1 Abstract Silicon the most widely used semiconducting material used in the electronics industry has attracted considerable attention in recent years as a candidate for implementing large scale solid state quantum computers In this paper we review several silicon based quantum computation proposals namely shallow donor qubits deep donor qubits and the silicon 29 qubit schemes The feasibility technological challenges and prospects of each scheme are discussed We observe that silicon processing requirements as required by silicon quantum computer architectures converges with those as projected by the International Technology Roadmap for Semiconductors ITRS in the near future 2 Table of Contents Abstract 1 Table of Contents 2 Introduction 3 Silicon based Quantum Computation Schemes Scheme I Shallow Donor Qubits I 3 Scheme II Shallow Donor Qubits II 6 Scheme III Deep Donor Qubits 8 Scheme IV Silicon 29 Qubits 11 Summary and Conclusions 13 References 14 3 Introduction Silicon transistors the heart of almost all classical computers are by far the most abundant man made artifacts in history Due to the blossom of the semiconductor electronics industry we have gained an enormous amount of insight about silicon in the past three decades its electrical mechanical and thermal properties both theoretically and experimentally Moreover engineers have also established an impressive array of tools to process silicon We understand and know how to handle silicon better than anything else From the perspective of constructing quantum computers silicon or more precisely silicon28 28Si is an ideal host substrate for spin based qubits due to the long decoherence time of impurity qubit spins Moreover the extremely taxing requirements of quantum computation implies that in any operational quantum computers classical electronics should be used when quantum phenomena is not required such as the transmission of classical signals to a human operator or the amplification of a qubit state measurement result the measured result is also a classical signal Silicon which most classical computers are built out of provides us with the perfect platform to integrate the quantum and the classical worlds How exactly do we go about building a quantum computer with silicon What are the challenges What has been done And what are the prospects These are the questions that we attempt to address in this paper However before we start delving deeper into silicon quantum computers we should establish a list of figures of merits or a checklist to see how good is silicon standing up to the task DiVincenzo s Checklist In 1998 David P DiVincenzo and Daniel Loss discussed several developments of quantum system regarding error correction entanglement and decoherence They listed five criteria which must be satisfied to implement a quantum computer in the laboratory These criteria were 1 1 The system has a well defined Hilbert space representing the quantum information 2 The states of the system can be initialized to a simple fiducial state 3 The coupling to the environment should be weak enough that computations can be finished before the states become decoherent 4 There must be some precisely defined unitary transformations to manipulate the states 5 There must be some methods for reading out the results of the computations to a classical environment Later a sixth criterion was added requiring the system under consideration be scalable that a large number of qubits could be implemented In this paper the basic features of the various silicon quantum computation schemes will be described in accordance to DiVincenzo s checklist Scheme I Shallow Donor Qubits I Overview The first silicon based quantum computation scheme was proposed by Bruce Kane in 1998 2 often referred to as the Kane computer in literature In this scheme the nuclear spins of shallow donors are used to encode quantum information serving as the qubit Donor nuclear spin has a particular advantage in that it has exceptionally long decoherence times in a pure Silicon 28 28Si host substrate Magnetic resonance techniques is used to manipulate the spin state of the donor nucleus while the resonance frequency can be fine tuned by controlling the hyperfine interaction of the nucleus with the donor electron Thus cryogenic operation is required in order for the donor electron to remain bounded to the donor impurity Qubit qubit interaction is performed by donor electron mediated exchange interaction of neighboring qubits or by the magnetic dipolar interaction 3 After qubit state manipulation is accomplished the state read out can be accomplished by the transfer of the donor nuclear spin to the donor electron and the electron spin is then determined Checklist 1 Representation of Qubit Quantum information can be encoded into the nuclear spin of impurity atoms in a silicon host substrate One criterion for the selection of the donor impurity species are that it should be a shallow donor meaning a small donor ionization energy Ed Small donor ionization energies 4 translate to large Bohr radii which mean that qubit qubit interaction is greater through the electron mediated nuclear spin interaction In addition a good donor qubit should have a net nuclear spin I of Magneti 1 2 as the Eleme Natural Bohr nuclear c Ed Isotope nt abundance radii spin I moment meV Group atom a0 N 28 Si IV 92 2297 0 0 29 1 Si IV 4 6832 2 0 55529 30 Si IV 3 0872 0 0 31 1 P V 100 2 1 13160 45 18 2 75 3 As V 100 2 1 43947 54 16 6 121 5 Sb V 57 21 2 3 3634 43 18 6 123 7 Sb V 42 79 2 2 5498 43 18 6 209 9 Bi V 100 2 4 1106 71 14 5 representation of a qubit As can be seen from Table 1 the natural candidate would be 31P The basic architecture of the system is shown in Figure 1 Table 1 Properties of relevant elements for silicon quantum computers Refs 3 and 4 Figure 1 The qubit is represented by the donor nucleus spin embedded in a silicon 28 lattice Electrodes A gate are added on top of the qubit to tune the hyperfine interaction strength of the electron and nucleus and hence the resonance frequency of the nucleus spin Checklist 2 State Initialization Although a DC magnetic field BDC is always present for magnetic resonance and hence nuclear spin state manipulation the spin flip time for donor nucleus might be too long for the purpose of