Scalable silicon quantum computers will require a material perfection that has never been attempted. Ground state wavefunctions for conduction electrons orbiting individual phosphorous donors must be polarized electronically and coupled to nearest neighbors with great precision. Elimination of all randomizing influences can be achieved only with a fully epitaxial structure; and we believe that output circuitry must also be integrated into the qubit arrays in order to achieve the uniformity needed for large-scale integration. A process that could potentially accomplish this will be outlined, based on scanning tunneling microscope (STM) removal of individual hydrogen atoms from the H-terminated silicon surface followed by phosphine dosing and ultra-low-temperature overgrowth. Self-ordering of PH3 molecules onto extended areas of bare silicon should permit patterning of planar single-electron transistors along with P-donor qubits in the same lithographic step. Initial plans for an experiment to characterize exchange coupling under gate control will be described.
Scalable silicon quantum computers will require a material perfection that has never been attempted. Ground state wavefunctions for conduction electrons orbiting individual phosphorous donors must be polarized electronically and coupled to nearest neighbors with great precision. Elimination of all randomizing influences can be achieved only with a fully epitaxial structure; and we believe that output circuitry must also be integrated into the qubit arrays in order to achieve the uniformity needed for large-scale integration. A process that could potentially accomplish this will be outlined, based on scanning tunneling microscope (STM) removal of individual hydrogen atoms from the H-terminated silicon surface followed by phosphine dosing and ultra-low-temperature overgrowth. Self-ordering of PH3 molecules onto extended areas of bare silicon should permit patterning of planar single-electron transistors along with P-donor qubits in the same lithographic step. Initial plans for an experiment to characterize exchange coupling under gate control will be described.
Scalable silicon quantum computers will require a material perfection that has never been attempted. Ground state wavefunctions for conduction electrons orbiting individual phosphorous donors must be polarized electronically and coupled to nearest neighbors with great precision. Elimination of all randomizing influences can be achieved only with a fully epitaxial structure; and we believe that output circuitry must also be integrated into the qubit arrays in order to achieve the uniformity needed for large-scale integration. A process that could potentially accomplish this will be outlined, based on scanning tunneling microscope (STM) removal of individual hydrogen atoms from the H-terminated silicon surface followed by phosphine dosing and ultra-low-temperature overgrowth. Self-ordering of PH3 molecules onto extended areas of bare silicon should permit patterning of planar single-electron transistors along with P-donor qubits in the same lithographic step. Initial plans for an experiment to characterize exchange coupling under gate control will be described.
We discuss progress towards the fabrication and demonstration of a prototype silicon-based quantum computer. The devices are based on a precise array of 31P dopants embedded in 28Si. Fabrication is being pursued via two complementary pathways – a ‘top-down’ approach for near-term production of few-qubit demonstration devices and a ‘bottom-up’ approach for large-scale qubit arrays. The ‘top-down’ approach employs ion implantation through a multi-layer resist structure which serves to accurately register the donors to metal control gates and single-electron transistor (SET) read-out devices. In contrast the ‘bottom-up’ approach uses STM lithography and epitaxial silicon overgrowth to construct devices at an atomic scale. Techniques for qubit read-out, which utilise coincidence measurements on novel twin-SET devices, are also presented.
Presents recent results on two different approaches to realize a solid-state quantum computer based in silicon, using phosphorus atoms as qubits. In the first approach the device is built from the 'bottomup' using a combination of atomic lithography with a scanning tunneling microscope and high quality silicon epitaxial growth using molecular beam epitaxy. In the second approach ion implantation is used to implant the phosphorus atoms from the 'top-down'. In both cases surface control electrodes are fabricated by conventional electron beam lithography. Techniques for qubit read-out utilising coincidence measurements on twin single electron transistors are also presented.
The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel-posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited.
Practical quantum computers require a large network of highly coherent qubits, interconnected in a design robust against errors. Donor spins in silicon provide state-of-the-art coherence and quantum gate fidelities, in a platform adapted from industrial semiconductor processing. Here we present a scalable design for a silicon quantum processor that does not require precise donor placement and leaves ample space for the routing of interconnects and readout devices. We introduce the flip-flop qubit, a combination of the electron-nuclear spin states of a phosphorus donor that can be controlled by microwave electric fields. Two-qubit gates exploit a second-order electric dipole-dipole interaction, allowing selective coupling beyond the nearest-neighbor, at separations of hundreds of nanometers, while microwave resonators can extend the entanglement to macroscopic distances. We predict gate fidelities within fault-tolerance thresholds using realistic noise models. This design provides a realizable blueprint for scalable spin-based quantum computers in silicon.Quantum computers will require a large network of coherent qubits, connected in a noise-resilient way. Tosi et al. present a design for a quantum processor based on electron-nuclear spins in silicon, with electrical control and coupling schemes that simplify qubit fabrication and operation.
The discovery of efficient quantum algorithms a decade ago has shown that a quantum computer encoding and processing information quantum mechanically, can solve important problems intractable with conventional computers. The invention of quantum error correction principle, makes quantum computation possibly fault-tolerant against the decoherence of information carriers. Thereafter, intensive research activities have been made toward the implementation of quantum computation with various realistic quantum systems. Among them, the most attractive implementation proposals are using silicon-based materials, which have the advantage of borrowing the existing ingenuity and resources accumulated during the development of modern microelectronics. In this dissertation we investigate several theoretical aspects of a silicon- based quantum computer in which qubits are represented by the spins of electrons bound to phosphorous donors in silicon. Encoding each qubit in terms of three neighboring donor electron spins, we can realize universal quantum gate operations with only the Heisenberg exchange coupling J S1 •S2 between neighboring donors. Therefore, studying the exchange coupling for a phosphorous donor pair in silicon is of central importance for providing the experimentalists with qualitative insights and quantitative guidance for building such a silicon quantum computer. After giving some general considerations on the quantum computer architecture, we develop the necessary theoretical tools. A multi-valley effective mass equation is derived and discussed, to handle impurities in a multi-valley semiconductor. Then we apply it to solve a single Si:P donor embedded in our quantum computer architecture. We show that the width of the silicon quantum well can significantly influence the energy splitting and charge distributions of the ground state. Oscillation of level splitting is observed as the quantum well width or donor position is varied at atomic scale. Elementary gate operations for 3-donor-spin qubits involve a neighboring pair of donors at each step. The exchange coupling in Heisenberg model hamiltonian, defined as the energy splitting of the lowest singlet and triplet states, has to be calculated from the realistic two-donor hamiltonian. We discuss several popular methods to solve the two-donor problem and develop an appropriate extended Hartree-Fock method that can give reliable results for a well-separated donor pair subject to tunable coupling. This method is first applied to a Si:P donor pair in the framework of hydrogenic effective mass theory, to study how to tune the exchange coupling with simple gate potentials. A followed study shows that under a parallel electric field the singlet and triplet states exhibit very different polarization behaviors. This difference can be exploited to measure the state of an electron spin. We also show that, a perpendicular electric field cannot tune the exchange coupling efficiently. Then we apply the realistic multi-valley effective mass equation, coupled with a realistic modeling of the potential generated by gate electrodes, to a pair of phosphorous donors in silicon quantum well. By varying the gate electrode voltages, the exchange coupling can be tuned with exponential efficiency in a wide range. We find that, for best performance, we need to set the quantum well width to be around 10 nm, and the donor separation to be around 10 a∗ b---- 24nm in the doping plane. We analyze in detail an adiabatic half-swap operation between neighboring donor spins. The gate operation time is estimated to be 0.2 ns, which satisfies the constraints put by the donor spin decoherence time and by the validity of adiabatic approximation. The interference between different valley components could lead to oscillations of exchange coupling as donor positions are shifted by occasion. We find the exchange oscillation persists even with only two relevant valleys for donors in a strongly-strained silicon quantum well. It is also shown that the oscillation induced by changing donor separation at atomic scale is strongly suppressed as donors approach each other. Finally, we study the entanglement issue in quantum computing context. We analyze the low-energy Hilbert space for a pair of qubits encoded by localized electron spins and suggest a suitable measure to describe the entanglement between qubits involving indistinguishable electrons and in the presence of leakage errors. The dynamics of inter-qubit entanglement during a gate operation is also studied.