Quantum Computation with Quantum Dots and Terahertz Cavity Quantum Electrodynamics

A quantum computer processes quantum information which is stored in “quantum bits” (qubits). [1] If a small set of fundamental operations, or “universal quantum logic gates,” can be performed on the qubits, then a quantum computer can be programmed to solve an arbitrary problem [2]. The explosion of interest in quantum computation can be traced to Shor’s demonstration in 1994 that a quantum computer could efficiently factorize large integers [3]. Further boosts came in 1996, with the proof that quantum error correcting codes exist [4,5]. It has since been shown that if the quantum error rate is below an accuracy threshold, quantum information can be stored indefinitely [6]. The implementation of a large-scale quantum computer is recognized to be a technological challenge of unprecendented proportions. The qubits must be wellisolated from the decohering influence of the environment, but must also be manipulated individually to initialize the computer, perform quantum logic operations, and measure the result of the computation [7]. Implementations of universal quantum logic gates and quantum computers have been proposed using atomic beams [8], trapped atoms [9] and ions [10], bulk nuclear magnetic resonance [11], nanostructured semiconductors [12–15] and Josephson junctions [16,17]. In schemes based on trapped atoms and ions, qubits couple with collective excitations or cavity photons. Such long-range coupling enables two-bit gates involving an arbitrary pair of qubits, which makes programming straightforward. However, in the atomic and ionic schemes [9,10], the gates must be performed serially, whereas existing error correcting schemes require some degree of parallelism. In semiconductor and superconductor schemes which have been proposed [12–17], only nearest-neighbor qubits can be coupled, and significant overhead is involved in coupling distant qubits. However, some of these schemes have the important advantage that gate operations can be performed in parallel. It is widely agreed that a solid-state quantum computer, if it can be realized, will be the only way to produce a quantum computer containing, for example, 10 qubits. The remainder of this paper describes what is, to our knowledge, the first proposal for a semiconductorbased quantum computer in which quantum gates can be effected between an arbitrary pair of qubits. The qubits consist of the lowest electronic states of speciallyengineered quantum dots (QDs) and are coupled by Terahertz cavity photons. The proposal combines ideas from the atomic and ionic implementations described above with recent developments in the spectroscopy of doped semiconductor nanostructures at Terahertz frequencies [18–20].