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Journal of Applied Physics

Fault tolerance calculations for clocked quantum-dot cellular automata devices

Mahfuza Khatun, Travis Barclay, Ioan Sturzu, P. Douglas Tougaw

Published Nov 1, 2005• 19 citations
Publisher

Abstract

We present a numerical study of fault tolerance properties in quantum-dot cellular automata (QCA) devices. A full-basis quantum method is used for calculations of the Hamiltonian, and a statistical model has been introduced to simulate the influence of position defects of the dots within cells on the logical output. Combined effects of temperature and cell defects on a shift register have been studied. Uniform and normal distributions have been used for the cell defect simulations. Normal distribution simulations produce realistic results compared to the uniform distribution. In order to show the operational limit of a device, parameters such as “displacement factor” and “success rate” are introduced. Results show that the fault tolerance of a QCA device is strongly dependent on temperature as well as on the cell defects. The robustness of a shift register is also dependent on the size of the device.

DOI
10.1063/1.2128473

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We present a numerical study of fault tolerance properties in quantum-dot cellular automata (QCA) devices. A full-basis quantum method is used for calculations of the Hamiltonian, and a statistical model has been introduced to simulate the influence of position defects of the dots within cells on the logical output. Combined effects of temperature and cell defects on a shift register have been studied. Uniform and normal distributions have been used for the cell defect simulations. Normal distribution simulations produce realistic results compared to the uniform distribution. In order to show the operational limit of a device, parameters such as “displacement factor” and “success rate” are introduced. Results show that the fault tolerance of a QCA device is strongly dependent on temperature as well as on the cell defects. The robustness of a shift register is also dependent on the size of the device.
Molecular quantum-dot cellular automata (QCA) may provide low-power, high-speed computational hardware for processing classical information. Simulation and modeling play an important role in the design of QCA circuits because fully coherent models of QCA scale exponentially with the number of devices, and such models are severely limited in size. For larger circuits, approximations become necessary. In the era of fault-tolerant quantum computation, however, it may become possible to model large QCA circuits without such limitations. This work explores the use of the noisy-intermediate scale quantum (NISQ) variational quantum eigensolver (VQE) method for estimating the ground state of QCA circuits. This is relevant because the computational result of a QCA calculation is encoded in the circuit’s ground state. In this study, VQE is used to model logic circuits, including binary wires, inverters, and majority gates. VQE models are performed by ideal simulators, noisy simulators, and actual quantum hardware. This study demonstrates that VQE may indeed be used to model molecular QCA circuits. It is observed that using modern NISQ hardware, results are still quite sensitive to noise, so measures should be taken to minimize noise. These include simplifying the ansatz circuit whenever possible and using low-noise hardware.
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The probability models of 2 different quantum cellular automaton (QCA) adders are based on the theory of probabilistic transfer matrix and circuit partition. The effect of individual component on the overall fault-tolerance is fully analyzed at the same level. The simulation shows that the effect of the wire is minor when the success probability is low, while the overall fault-tolerance rises sharply once the success probability is high. And the inverter is considered to be a major factor that affects the overall fault-tolerance in the variation range of parameter. Frobenbius norm of the overall error probabilistic transfer matrix is employed to study the fault-tolerance difference. The result shows that the overall fault-tolerance of QCA adder consisting of 5-input majority is superior to the other. Such fault-tolerance analyses should be used for a better characterization of QCA circuit design and fault-tolerance improvement.
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This paper explores the potential of Quantum Cellular Automata (QCA) for simulating complex systems with enhanced efficiency compared to their classical counterparts. Classical Cellular Automata (CCA) face limitations when modeling systems exhibiting quantum phenomena or requiring computational power for intricate simulations. QCA, leveraging the principles of quantum mechanics, offers a fundamentally different approach. This work details the design of a QCA where cells are represented by qubits, and the governing rules are defined by quantum gates. The core argument presented is that QCA's inherent parallelism and superposition capabilities can lead to significant speedups in simulating complex systems. This research proposes a novel methodology for applying QCA to various complex systems, highlighting its potential advantages and exploring the theoretical foundations underpinning this approach. The investigation focuses on the theoretical aspects of QCA design and simulation, without the need for experimental validation.