We describe a fast quantum computer based on optically controlled electron spins in charged quantum dots that are coupled to microcavities. This scheme uses broad-band optical pulses to rotate electron spins and provide the clock signal to the system. Non-local two-qubit gates are performed by phase shifts induced by electron spins on laser pulses propagating along a shared waveguide. Numerical simulations of this scheme demonstrate high-fidelity single-qubit and twoqubit gates with operation times comparable to the inverse Zeeman frequency.PACS numbers: 03.67. Lx, 32.80.Qk, 33.35.+r, 42.65.Re Quantum computers potentially allow improvement in computational speed over existing computers if an architecture is found with a fast clock rate and the ability to be scaled to many qubits and operations [1]. Electron spins of charged semiconductor quantum dots are promising candidates for such an architecture because of their potential integration into existing microtechnology. Most proposals for electron spin quantum computers [2,3,4,5], however, restrict logic operations to nearest-neighbors, limiting the computational clock rate. Optically mediated quantum logic [6,7,8,9] for two-qubit gates and fast single qubit rotations [10,11] may improve the overall clock rate of the system. Several previous works suggest techniques for fast single-qubit rotations of electron spins. Ground-state coherence generation via ultrafast pulses in molecular, atomic, and quantum dot spectroscopy [11,12,13,14,15,16] indicates the ability to control ground state populations and phases. This control is faster than that of microwave pulses or multiple, adiabatic narrow-band optical pulses. The application of ultrafast pulses to U(1) control of single quantum-dot qubits has been proposed [10]. Here we describe complete optical SU(2) control of single dots using similar techniques.There are also proposals for optically-mediated entanglement formation between two non-local qubits. One type of proposal uses coherently generated single photons [9,17], but requires precisely shaped optical pulses. Recent methods for the entanglement of atomic ensembles via simple optical pulses [18,19] have led to proposals for optically-mediated two-qubit gates based on small phase shifts of light via single qubits in cavities [8]. These latter techniques may be easier and faster than the use of coherently generated single photons. Here, we propose a unique way to combine both fast, SU(2) single-qubit rotations and fast, optically-mediated two-qubit gates on a single semiconductor chip. These elements may lead toward the fastest potentially-scalable quantum computing scheme of which the authors are aware. tecture. It is a square millimeter of a semiconductor chip patterned with cavities. Each cavity holds a single charged quantum dot and is connected to other cavities through a switched, circular waveguide. Each quantum dot can be individually addressed by focused optical pulses incident perpendicular to the plane of the chip to perform single qubit rotations. ...