746 research outputs found
An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation
Quantum states are very delicate, so it is likely some sort of quantum error
correction will be necessary to build reliable quantum computers. The theory of
quantum error-correcting codes has some close ties to and some striking
differences from the theory of classical error-correcting codes. Many quantum
codes can be described in terms of the stabilizer of the codewords. The
stabilizer is a finite Abelian group, and allows a straightforward
characterization of the error-correcting properties of the code. The stabilizer
formalism for quantum codes also illustrates the relationships to classical
coding theory, particularly classical codes over GF(4), the finite field with
four elements. To build a quantum computer which behaves correctly in the
presence of errors, we also need a theory of fault-tolerant quantum
computation, instructing us how to perform quantum gates on qubits which are
encoded in a quantum error-correcting code. The threshold theorem states that
it is possible to create a quantum computer to perform an arbitrary quantum
computation provided the error rate per physical gate or time step is below
some constant threshold value.Comment: 46 pages, with large margins. Includes quant-ph/0004072 plus 30 pages
of new material, mostly on fault-toleranc
Tailored codes for small quantum memories
We demonstrate that small quantum memories, realized via quantum error
correction in multi-qubit devices, can benefit substantially by choosing a
quantum code that is tailored to the relevant error model of the system. For a
biased noise model, with independent bit and phase flips occurring at different
rates, we show that a single code greatly outperforms the well-studied Steane
code across the full range of parameters of the noise model, including for
unbiased noise. In fact, this tailored code performs almost optimally when
compared with 10,000 randomly selected stabilizer codes of comparable
experimental complexity. Tailored codes can even outperform the Steane code
with realistic experimental noise, and without any increase in the experimental
complexity, as we demonstrate by comparison in the observed error model in a
recent 7-qubit trapped ion experiment.Comment: 6 pages, 2 figures, supplementary material; v2 published versio
Improving the tolerance of stochastic LDPC decoders to overclocking-induced timing errors: a tutorial and design example
Channel codes such as Low-Density Parity-Check (LDPC) codes may be employed in wireless communication schemes for correcting transmission errors. This tolerance to channel-induced transmission errors allows the communication schemes to achieve higher transmission throughputs, at the cost of requiring additional processing for performing LDPC decoding. However, this LDPC decoding operation is associated with a potentially inadequate processing throughput, which may constrain the attainable transmission throughput. In order to increase the processing throughput, the clock period may be reduced, albeit this is at the cost of potentially introducing timing errors. Previous research efforts have considered a paucity of solutions for mitigating the occurrence of timing errors in channel decoders, by employing additional circuitry for detecting and correcting these overclocking-induced timing errors. Against this background, in this paper we demonstrate that stochastic LDPC decoders (LDPC-SDs) are capable of exploiting their inherent error correction capability for correcting not only transmission errors, but also timing errors, even without the requirement for additional circuitry. Motivated by this, we provide the first comprehensive tutorial on LDPC-SDs. We also propose a novel design flow for timing-error-tolerant LDPC decoders. We use this to develop a timing error model for LDPC-SDs and investigate how their overall error correction performance is affected by overclocking. Drawing upon our findings, we propose a modified LDPC-SD, having an improved timing error tolerance. In a particular practical scenario, this modification eliminates the approximately 1 dB performance degradation that is suffered by an overclocked LDPC-SD without our modification, enabling the processing throughput to be increased by up to 69.4%, which is achieved without compromising the error correction capability or processing energy consumption of the LDPC-SD
Array-based architecture for FET-based, nanoscale electronics
Advances in our basic scientific understanding at the molecular and atomic level place us on the verge of engineering designer structures with key features at the single nanometer scale. This offers us the opportunity to design computing systems at what may be the ultimate limits on device size. At this scale, we are faced with new challenges and a new cost structure which motivates different computing architectures than we found efficient and appropriate in conventional very large scale integration (VLSI). We sketch a basic architecture for nanoscale electronics based on carbon nanotubes, silicon nanowires, and nano-scale FETs. This architecture can provide universal logic functionality with all logic and signal restoration operating at the nanoscale. The key properties of this architecture are its minimalism, defect tolerance, and compatibility with emerging bottom-up nanoscale fabrication techniques. The architecture further supports micro-to-nanoscale interfacing for communication with conventional integrated circuits and bootstrap loading
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