Abstract not found

Quantum computers offer the prospect of computation that scales exponentially with data size. Unfortunately, a single bit error can corrupt an exponential amount of data. Quantum mechanics can seem more suited to science fiction than system engineering, yet small quantum devices of 5 to 7 bits have nevertheless been built in the laboratory, 1,2 100-bit devices are on the drawing table now, and emerging quantum technologies promise even greater scalability. 3,4 More importantly, improvements in quantum error-correction codes have established a threshold theorem, 5 according to which scalable quantum computers can be built from faulty components as

In the formalism of measurement based quantum computation we start with a given fixed entangled state of many qubits and perform computation by applying a sequence of measurements to designated qubits in designated bases. The choice of basis for later measurements may depend on earlier measurement outcomes and the final result of the computation is determined from the classical data of all the measurement outcomes. This is in contrast to the more familiar gate array model in which computational steps are unitary operations, developing a large entangled state prior to some final measurements for the output. Two principal schemes of measurement based computation are teleportation quantum computation (TQC) and the so-called cluster model or one-way quantum computer (1WQC). We will describe these schemes and show how they are able to perform universal quantum computation. We will outline various possible relationships between the models which serve to clarify their workings. We will also discuss possible novel computational benefits of the measurement based models compared to the gate array model, especially issues of parallelisability of algorithms. 1

In this article we present a classification scheme for quantum computing technologies that is based on the characteristics most relevant to computer systems architecture. The engineering trade-offs of execution speed, decoherence of the quantum states, and size of systems are described. Concurrency, storage capacity, and interconnection network topology influence algorithmic efficiency, while quantum error correction and necessary quantum state measurement are the ultimate drivers of logical clock speed. We discuss several proposed technologies. Finally, we use our taxonomy to explore architectural implications for common arithmetic circuits, examine the implementation of quantum error correction, and discuss cluster-state quantum computation.

These ‘lecture notes ’ are based on joint work with Samson Abramsky. I will survey and informally discuss the results of [3, 4, 5, 12, 13] in a pedestrian not too technical way. These include: • ‘The logic of entanglement’, that is, the identification and abstract axiomatization of the ‘quantum information-flow ’ which enables protocols such as quantum teleportation. 1 To this means we defined strongly compact closed categories which abstractly capture the behavioral properties of quantum entanglement. • ‘Postulates for an abstract quantum formalism ’ in which classical informationflow (e.g. token exchange) is part of the formalism. As an example, we provided a purely formal description of quantum teleportation and proved correctness in abstract generality. 2 In this formalism types reflect kinds, contra the essentially typeless von Neumann formalism [25]. Hence even concretely this formalism manifestly improves on the usual one. • ‘A high-level approach to quantum informatics’. 3 Indeed, the above discussed work can be conceived as aiming to solve: von Neumann quantum formalism � high-level language low-level language. I also provide a brief discussion on how classical and quantum uncertainty can be mixed in the above formalism (cf. density matrices). 4

The paper discusses teleportation in the context of comparing quantum and topological points of view. 1

Advances in quantum devices have brought scalable quantum computation closer to reality. We focus on the system-level issues of how quantum devices can be brought together to form a scalable architecture. In particular, we examine promising silicon-based proposals. We discover that communication of quantum data is a critical resource in such proposals. We find that traditional techniques using quantum SWAP gates are exponentially expensive as distances increase and propose quantum teleportation as a means to communicate data over longer distances on a chip. Furthermore, we find that realistic quantum error-correction circuits use a recursive structure that benefits from using teleportation for long-distance communication. We identify a set of important architectural building blocks necessary for constructing scalable communication and computation. Finally, we explore an actual layout scheme for recursive error correction, and demonstrate the exponential growth in communication costs with levels of recursion, and that teleportation limits those costs.

We prove an accuracy threshold theorem for fault-tolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla states are protected by a concatenated error-detecting code and the preparation is aborted if an error is detected. The proof applies to independent stochastic noise but (in contrast to proofs of the quantum accuracy threshold theorem based on concatenated error-correcting codes) not to strongly-correlated adversarial noise. Our rigorously established lower bound on the accuracy threshold, 1.04 × 10 −3, is well below Knill’s numerical estimates.

Abstract not found

Fault-tolerant logical operations for qubits encoded by CSS codes are discussed, with emphasis on methods which apply to codes of high rate, encoding k qubits per block with k> 1. It is shown that the logical qubits within a given block can be prepared by a single recovery operation in any state whose stabilizer generator separates into X and Z parts. Optimized methods to move logical qubits around and to achieve controlled-not and Toffoli gates are discussed. It is found that the number of time-steps required to complete a fault-tolerant quantum computation is the same when k> 1 as when k = 1. 1