Discrete Cosine Transforms on Quantum Computers

A classical computer does not allow to calculate a discrete cosine transform on N points in less than linear time. This trivial lower bound is no longer valid for a computer that takes advantage of quantum mechanical superposition, entanglement, and interference principles. In fact, we show that it is possible to realize the discrete cosine transforms and the discrete sine transforms of size NxN and types I,II,III, and IV with as little as O(log^2 N) operations on a quantum computer, whereas the known fast algorithms on a classical computer need O(N log N) operations.Comment: 5 pages, LaTeX 2e, IEEE ISPA01, Pula, Croatia, 200

Engineering superpositions of displaced number states of a trapped ion

We present a protocol that permits the generation of a subtle with superposition with 2^(l+1) displaced number states on a circle in phase space as target state for the center-of-mass motion of a trapped ion. Through a sequence of 'l' cycles involving the application of laser pulses and no-fluorescence measurements, explicit expressions for the total duration of laser pulses employed in the sequence and probability of getting the ion in the upper electronic state during the 'l' cycles are obtained and analyzed in detail. Furthermore, assuming that the effective relaxation process of a trapped ion can be described in the framework of the standard master equation for the damped harmonic oscillator, we investigate the degradation of the quantum interference effects inherent to superpositions via Wigner function.Comment: 14 pages, 10 figure

Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions

Physical qubits in experimental quantum information processors are inevitably exposed to different sources of noise and imperfections, which lead to errors that typically accumulate hindering our ability to perform long computations reliably. Progress towards scalable and robust quantum computation relies on exploiting quantum error correction (QEC) to actively battle these undesired effects. In this work, we present a comprehensive study of crosstalk errors in a quantum-computing architecture based on a single string of ions confined by a radio-frequency trap, and manipulated by individually-addressed laser beams. This type of errors affects spectator qubits that, ideally, should remain unaltered during the application of single- and two-qubit quantum gates addressed at a different set of active qubits. We microscopically model crosstalk errors from first principles and present a detailed study showing the importance of using a coherent vs incoherent error modelling and, moreover, discuss strategies to actively suppress this crosstalk at the gate level. Finally, we study the impact of residual crosstalk errors on the performance of fault-tolerant QEC numerically, identifying the experimental target values that need to be achieved in near-term trapped-ion experiments to reach the break-even point for beneficial QEC with low-distance topological codes.Comment: 30 pages, 13 figures, 1 tabl

Synthesis and evaluation of fault-tolerant quantum computer architectures

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 241-247).Fault-tolerance is the cornerstone of practical, large-scale quantum computing, pushed into its prominent position with heroic theoretical efforts. The fault-tolerance threshold, which is the component failure probability below which arbitrarily reliable quantum computation becomes possible, is one standard quality measure of fault-tolerant designs based on recursive simulation. However, there is a gulf between theoretical achievements and the physical reality and complexity of envisioned quantum computing systems. This thesis takes a step toward bridging that gap. We develop a new experimental method for estimating fault-tolerance thresholds that applies to realistic models of quantum computer architectures, and demonstrate this technique numerically. We clarify a central problem for experimental approaches to fault-tolerance evaluation--namely, distinguishing between potentially optimistic pseudo-thresholds and actual thresholds that determine scalability. Next, we create a system architecture model for the trapped-ion quantum computer, discuss potential layouts, and numerically estimate the fault-tolerance threshold for this system when it is constrained to a local layout. Finally, we place the problem of evaluation and synthesis of fault-tolerant quantum computers into a broader framework by considering a software architecture for quantum computer design.by Andrew W. Cross.S.M