A practical quantum computer must not merely store information, but also process it. To prevent errors introduced by noise from multiplying and spreading, a fault-tolerant computational architecture is required. Current experiments are taking the first steps toward noise-resilient logical qubits. But to convert these quantum devices from memories to processors, it is necessary to specify how a universal set of gates is performed on them. The leading proposals for doing so, such as magic-state distillation and colour-code techniques, have high resource demands. Alternative schemes, such as those that use high-dimensional quantum codes in a modular architecture, have potential benefits, but need to be explored further.

/pdf/roads-towards-fault-tolerant-universal-quantum-computation-4c57b0upnl.pdf

Roads towards fault-tolerant universal quantum computation

A machine equivalent to Turing machine, that is more intuitive in its working is defined. Three derivation rules are added to Elementary Arithmetic of Godel and his incompleteness theorems are proved without using any metalanguage. Two axioms are added to Zermelo-Fraenkel theory to derive the Continuum Hypothesis and to split the unit interval into infinitesimals.

Foundations of Computer Science

: This is the final report for the AFRL/RI in-house project Cluster State Quantum Computation. Under this project investigations were conducted which included: (i) the development and characterization of a new multipli-entangled photon source that increased the usable number of photon pairs by a factor of six over conventional entangled photon sources; (ii) design of multi-layer superconducting number-resolving photon detector, (iii) a theoretical and experimental investigation into the requirements of imperfect (non-unit fidelity) two-qubit linear optical photonic gates; (iv) a theoretical investigation of entanglement and nonlocality addressing the issue of why nature does not take advantage of the algebraically allowed maximum correlations amongst collections of qubits, and (v) a theoretical investigation into the a 2.25X more efficient means to generate linear cluster states. This latter investigation led to a patent for probabilistic cluster state generator, also discussed in this report.

Cluster State Quantum Computation

Sorting is a common task in a wide range of applications from signal and image processing to switching systems. For applications that require high performance, sorting is often performed in hardware with application-specified integrated circuits or field-programmable gate arrays. Hardware cost and power consumption are the dominant concerns. The usual approach is to wire up a network of compare-and-swap units in a configuration called the Batcher (or bitonic) network. Such networks can readily be pipelined. This paper proposes a novel area-efficient and power-efficient approach to sorting networks, based on “unary processing.” In unary processing, numbers are encoded uniformly by a sequence of one value (say 1) followed by a sequence of the other value (say 0) in a stream of 0’s and 1’s with the value defined by the fraction of 1’s in the stream. Synthesis results of complete sorting networks show up to 92% area and power saving compared to the conventional binary implementations. However, the latency increases. To mitigate the increased latency, this paper uses a novel time-encoding of data. The approach is validated with two implementations of an important application of sorting: median filtering. The result is a low cost, energy-efficient implementation of median filtering with only a slight accuracy loss, compared to conventional implementations.

Low-Cost Sorting Network Circuits Using Unary Processing

We analyze the resource overhead of recently proposed methods for universal fault-tolerant quantum computation using concatenated codes. Namely, we examine the concatenation of the 7-qubit Steane code with the 15-qubit Reed-Muller code, which allows for the construction of the 49- and 105-qubit codes that do not require the need for magic state distillation for universality. We compute a lower bound for the adversarial noise threshold of the 105-qubit code and find it to be 8.33 × 10(−6). We obtain a depolarizing noise threshold for the 49-qubit code of 9.69 × 10(−4) which is competitive with the 105-qubit threshold result of 1.28 × 10^(−3). We then provide lower bounds on the resource requirements of the 49- and 105-qubit codes and compare them with the surface code implementation of a logical T gate using magic state distillation. For the sampled input error rates and noise model, we find that the surface code achieves a smaller overhead compared to our concatenated schemes.

/pdf/overhead-analysis-of-universal-concatenated-quantum-codes-4wmn258v0m.pdf

Overhead analysis of universal concatenated quantum codes

Developing a scalable quantum computer as a single processing unit is challenging due to technology limitations. A solution to deal with this challenge is distributed quantum computing where several distant quantum processing units are used to perform the computation. The main design issue of this approach is costly communication between the processing units. Focused on this issue, in this paper, an efficient partitioning approach is proposed which combines both gate and qubit teleportation concepts in an efficient manner to minimize the communication. Experimental results show the proposed approach on average reduces the communication cost by about 29.5% in comparison with the best approaches in the literature.

Automated window-based partitioning of quantum circuits

Nonlinear digital filters play an important role in digital signal processing applications. In this brief, a novel architecture is proposed for the hardware implementation of fixed and runtime variable window length one-dimensional median filters. In the proposed architecture, the maximum working clock frequency is almost independent of the median filter window length, whereas the hardware complexity is proportional to the number of samples in the window. This feature enables the construction of filters with relatively large window lengths with negligible reduction in the maximum clock frequency, whereas in previous architectures, the maximum clock frequency significantly drops as the window length is increased. The benchmark results show the efficiency of the proposed architecture in comparison with state-of-the-art techniques.

High-Speed Hardware Implementation of Fixed and Runtime Variable Window Length 1-D Median Filters

One-way quantum computer simulation

In one-way quantum computation (1WQC) model, universal quantum computations are performed using measurements to designated qubits in a highly entangled state The choices of basis for these measurements as well as the structure of the entanglements specify a quantum algorithm Although a number of methods have been proposed to simulate quantum circuit model on classical computers, no efficient tool has been developed to simulate the 1WQC model directly In this paper, some techniques such as qubit elimination, implicit and in-place matrix-vector multiplication and pattern reordering are utilized to considerably reduce the time and memory needed for the simulations These techniques were implemented in a tool called One-Way Quantum computation Simulator (OWQS) Experimental results validate the efficiency of the proposed approach

OWQS: One-Way Quantum Computation Simulator

In the one-way quantum computation (1WQC) model, computations are done by correlated sequences of entanglement, measurement and local corrections commands. As scalable and reliable quantum computers have not been implemented yet, the only widely available tools for designing and testing quantum algorithms are quantum computation simulators. However, simulating quantum computations on a standard classical computer in most cases requires very large memory and time. Recently, an array-based simulator, called one-way quantum computation simulator (OWQS) has been proposed to directly simulate the 1WQC model. OWQS outperforms the previously proposed quantum computation simulators to simulate the 1WQC model. In this paper, OWQS is modified in a way that it utilizes the graph-based representation of system states using algebraic decision diagram (ADD) in order to benefit from the similarities in the quantum states of 1WQC. This simulator is called graph-based OWQS, GOWQS. Experimental results validate the considerable improvement of the proposed simulator as compared to OWQS.

GOWQS: Graph-based one-way quantum computation simulator

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