The seemingly endless progress of microelectronics has been a result of the semiconductor industry’s ability to continuously scale down the transistor, which is the fundamental computing component of the modern computer. Scaling of the transistor to low-nanometer scales is limited by effects such as gate leakage, drain induced barrier lowering, and the extreme power dissipation. Molecular quantum cellular automata (QCA) is an exploratory computing paradigm in which information is encoded in the electronic charge configuration of a QCA cell. The charge interaction between neighbouring cells enables the transmission and processing of information. The underlying building block of any QCA circuit is the QCA cell, which is constructed with either a single molecule or a set of coupled quantum dots (in quantum-dot cellular automata (QCA)) or metallic islands (in metallic-island QCA). Members of our lab have developed a QCA design and simulation tool called QCADesigner. This tool is being used to evaluate this emerging technology by looking a circuits and computer architectures that can be implemented with QCA. For more information about QCADesigner, go to http://www.mina.ubc.ca/qcadesigner
Conference Proceedings: 2014 Conference on Optoelectronic and Microelectronic Materials Devices
Abstract: Simulations of quantum-dot cellular automata (QCA) on classical computers are highly limited due to the exponential growth in resources required for the numerical simulation of quantum mechanics involving networks of finite state nodes. Recent advancements in computing based on networks of flux-qubits, and in particular the platform technology developed by D-Wave Systems Inc., have made it possible to explore QCA networks that are intractable on classical machines. However, the embedding of such networks onto the available processor architecture is a key challenge in setting up such simulations. In this work, two approaches to embedding QCA circuits are characterized: a dense placement algorithm that uses a routing method based on negotiated congestion; and a heuristic method implemented in D-Wave’s SAPI package. Both embedding methods are characterized using a set of basic QCA benchmark circuits of various sizes and complexities. When including diagonal interactions only in the case of an inverter, both methods were able to embed a 4-bit 2-1 multiplexer circuit containing 192 non-driver QCA cells onto the 512 qubit D-Wave Vesuvius chip architecture. Including diagonal interactions for all cells, both methods successfully embedded a serial adder circuit containing 126 non-driver cells.
Published on: arXiv:1207.7008v1.
Date: July 2012
Abstract: Quantum-dot Cellular Automata (QCA) provides a basis for classical computation without transistors. Many simulations of QCA rely upon the so-called Intercellular Hartree Approximation (ICHA), which neglects the possibility of entanglement between cells. Here, we present computational results that treat small groups of QCA cells with a Hamiltonian analogous to a quantum mechanical Ising-like spin chain in a transverse field, including the effects of intercellular entanglement. When energy relaxation is included in the model, we find that intercellular entanglement changes the qualitative behaviour of the system, and new features appear. In clocked QCA, isolated groups of active cells experience oscillations in their polarization states as information propagates. Additionally, energy relaxation tends to bring groups of cells to an unpolarized ground state. This contrasts with the results of previous simulations which employed the ICHA. The ICHA is a valid approximation in the limit of very low tunneling rates, which can be realized in lithographically defined quantum-dots. However, in molecular and atomic implementations of QCA, entanglement will play a greater role. The degree to which entanglement poses a problem for memory and clocking depends upon the interaction of the system with its environment, as well as the system’s internal dynamics.
Journal: Journal of Computational Electronics, vol. 9, no. 1, pp. 16-30
Date: March 2010
Abstract: Molecular quantum-dot cellular automaton (QCA) offers an alternative paradigm for computing at the nano-scale. QCA circuits require an external clock which can be generated using a network of submerged electrodes to synchronize information flow and provide the required power to drive the computation. In this paper, the effect of electrode separation and applied potential on the likelihood of different QCA cell states of molecular cells located above and in between two adjacent electrodes is analyzed. Using this analysis, estimates of operational ranges are developed for the placement, applied potential, and relative phase between adjacent clocking electrodes to ensure that only those states that are used in the computation are energetically favorable. Conclusions on the trade-off between cell size, cell-to-cell distance, and applied clocking potential are drawn and the temperature dependence of the operation of fundamental QCA building blocks is considered.
Journal: Physical Review B, vol. 80, no. 11, pp. 115422 1-7
Date: September 2009
Abstract: We present a first-principles calculation of the emission current in a single-walled carbon nanotube electron source. We have employed the nonequilibrium Green’s function and Fisher-Lee’s transmission formulation to describe electronic transport through the system. The simulation results reproduce the trends observed in experimental data closely and, in particular, the current saturation and deviation from the Fowler-Nordheim behavior. The proposed numerical approach is useful whenever a region of vacuum is present in the system Hamiltonian.
Conference Proceedings: in Proceedings of the 1st IEEE International Workshop on Design and Test of Nano Devices, Circuits and Systems, pp. 49-52, Cambridge, MA, USA
Date: September 2008
Abstract: Quantum-dot cellular automata (QCA) is one of several emerging nanoscale devices that is targeted at scalable molecular electronics. In this paper, the tolerance to cell displacements of a QCA interconnect is analyzed in order to determine limits on allowable displacements, as well as to identify the important failure mechanisms. Numerical simulations using the coherence vector formalism are performed for a short length of QCA interconnect under various conditions. Contrary to previous work, our results indicate that wider interconnects display a higher sensitivity to cell displacements due to the formation of cell clusters, which are more prominent in wider interconnects as a result of the increased number of cells.
Conference Proceedings: in Proceedings of the 2008 IEEE International Conference on Nanotechnology, pp. 327-330, Arlington, TX, USA
Date: April 2008
Abstract: Molecular quantum-dot cellular automata (QCA) is an emerging computing paradigm which utilizes electrostatic coupling between electronic conﬁgurations in neighboring molecules to perform information processing. A simulation tool for this technology, QCADesigner, exists and allows designers to quickly layout and simulate QCA circuits constructed with up to thousands of QCA cells. However, in general, large quantum mechanical systems are not suitable for efﬁcient simulation on a classical computer, and as a result, QCADesigner uses the Hartree-Fock approximation to reduce the computational complexity of the simulation. Under certain circumstances, this approximation can lead to the incorrect ground state and hence, produce logically incorrect results at the outputs. In this work, we provide examples of problem circuits and propose a method to identify areas that must be simulated using the full Hamiltonian.
Journal: Journal on Emerging Technologies in Computing Systems, vol. 3, no. 1, article 2, pp. 1-14
Date: April 2007
Abstract: We analyze the behavior of quantum-dot cellular automata (QCA) building blocks in the presence of random cell displacements. The QCA cells are modeled using the coherence vector description and simulated using QCADesigner. We evaluate various fundamental circuits: the wire, the inverter, the majority gate, and the two-wire crossing approaches: the coplanar crossover and the multilayer crossover. Our results show that different building blocks have different displacement tolerances. The coplanar crossover and inverter perform the weakest. The wire is the most robust. We have found displacement tolerances to be a function of circuit layout and geometry rather than cell size.
Conference Proceedings: in Proceedings of the 22nd IEEE International Symposium on Defect and Fault Tolerance in VLSI Systems, pp. 487-495, Rome, Italy
Date: September 2007
Abstract: This paper analyzes the effect of random phase shifts in the underlying clock signals on the operation of several basic quantum-dot cellular automata (QCA) building blocks. Such phase shifts can result from manufacturing variations or from uneven path lengths in the clocking network. While previous literature has proposed various clock distribution architectures and also provided analysis of manufacturing variations on QCA layouts, so far no literature is available on the characterization of effects resulting from the lack of phase synchronization in the QCA clocks. We perform numerical simulations of these basic building blocks using two different simulation engines available in the QCADesigner tool. We assume that the phase shifts are characterized by a Gaussian distribution with a mean value of ipi/2, where i is the clock number. Our results indicate that the sensitivity of building blocks to phase shifts depends primarily on the layout of the building block, and that most building blocks were able to operate properly under random phase shifts characterized by sigma= 5% pi/2.
Conference Proceedings: in Proceedings of the SPIE Advanced Signal Processing Algorithms, Architectures, and Implementations XVI Conference, vol. 6313, no. 1, paper 631306, 9 pgs, San Diego, CA, USA
Date: August 2006
Abstract: Quantum-Dot Cellular Automata (QCA) is one of several proposed computational nanotechnology paradigms that are being investigated as alternatives to CMOS at the nano-scale. QCA has been reported to offer relatively low power consumption, and very high device density. In recent years, several researchers have started investigating relatively complex circuit architectures using QCA. Such design efforts have highlighted the crosstalk problem in QCA and the lack of research in this area. This paper explores the nature of crosstalk in QCA. We show how crosstalk can be amplified due to several parameters including wire length and the distance between adjacent cells. We develop a model and method that allows us to test for crosstalk using a set of test vectors. We also propose a set of cell placement guidelines and design geometries that help to minimize QCA crosstalk in large circuits.
Conference Proceedings: in Proceedings of the Canadian Conference on Electrical and Computer Engineering, pp. 2128-2131, Ottawa, ON, Canada
Date: May 006
Abstract: This paper presents the model and implementation of a new simulation engine, within the existing QCADesigner simulation tool, that will be used to simulate clocked molecular QCA cells and circuits. The clocking mechanism uses a layer of patterned electrodes to switch the cells by controlling the electrostatic potential energy of the different electronic configurations of the cells. The simulation engine models each QCA cell in the circuit using a three-state Hamiltonian. This Hamiltonian is projected onto a basis of generators of the special unitary group SU(3). The Bloch equation is solved to determine the time evolution of the coherence vector in this basis. Interaction with the environment is modelled using a density matrix approach and a relaxation-time approximation. We apply the Hartree-Fock approximation to model the interactions between cells that are assumed to be through expectation values in order to make the problem computationally feasible
Journal: Nanotechnology, vol. 16, no. 11, pp. 2525-2529
Date: November 2005
Abstract: This paper investigates the simulation of charging a semiconductor quantum-dot cellular automata (QCA) cell in the presence of impurity atoms. The complete conﬁguration space of the cell and the impurities is analysed using the canonical partition function. Limits on the size and location of the impurity region are determined. Within these limits, it is shown that the semiconductor QCA cell can be controllably charged. Using these results, it is shown that a short wire consisting of three QCA cells can operate with high logical correctness at cryogenic temperatures.
Conference Proceedings: in Proceedings of Application-Specific Systems, Architectures and Processors Conference, pp. 288-293, Samos, Greece
Date: July 2005
Abstract: We describe the design and layout of a simple 4-bit processor based on quantum dot cellular automata (QCA) using the QCADesigner design tool. The processor design is based on an accumulator architecture which reduces the required hardware complexity and allows for reasonable simulation times. Our aim is to provide evidence that QCA has potential applications in future computers provided that the underlying technology is made feasible.
Journal: IEEE Transactions on Nanotechnology, vol. 3, no. 4, pp. 443-450
Date: December 2004
Abstract: The basic Boolean primitive in quantum cellular automata (QCA) is the majority gate. In this paper, a method for reducing the number of majority gates required for computing three-variable Boolean functions is developed to facilitate the conversion of sum-of-products expression into QCA majority logic. Thirteen standard functions are introduced to represent all three-variable Boolean functions and the simplified majority expressions corresponding to these standard functions are presented. We describe a novel method for using these standard functions to convert the sum-of-products expression to majority logic. By applying this method, the hardware requirements for a QCA design can be reduced. As an example, a 1-bit QCA adder is constructed with only three majority gates and two inverters. The adder is designed and simulated using QCADesigner, a design and simulation tool for QCA. We will show that the proposed method is very efficient and fast in deriving the simplified majority expressions in QCA design.
Journal: IEEE Transactions on Nanotechnology, vol. 3, no. 2, pp. 249-255
Date: June 2004
Abstract: We examine a novel quantum-dot cellular automata device concept using the interaction of resonant tunneling currents through a system of four quantum wells. The interaction of resonant tunneling currents forces the total current to flow predominantly in the wells along one of the two diagonals, effectively polarizing the cell. We refer to this device concept as split current quantum cellular automata (SCQCA). A free cell will settle to a random diagonal, whereas charge interactions between adjacent cells will cause the polarization to synchronize between cells. In contrast with the standard QCA cell, this device does not require tunneling between dots. Electron tunneling occurs along the vertical direction, where highly controllable deposition techniques are able to deposit very thin films and effectively tune the device parameters. Clocking of an SCQCA cell is performed by controlling the bias across the device, and none of the potential barriers between the dots need to be controlled. We believe this device concept lends itself to fabrication using currently available fabrication technologies.
Journal: IEEE Transactions on Nanotechnology, vol. 3, no. 1, pp. 26-31
Date: March 2004
Abstract: This paper describes a project to create a novel design and simulation tool for quantum-dot cellular automata (QCA), namely QCADesigner. QCA logic and circuit designers require a rapid and accurate simulation and design layout tool to determine the functionality of QCA circuits. QCADesigner gives the designer the ability to quickly layout a QCA design by providing an extensive set of CAD tools. As well, several simulation engines facilitate rapid and accurate simulation. This tool has already been used to design full-adders, barrel shifters, random-access memories, etc. These verified layouts provide motivation to continue efforts toward a final implementation of QCA circuits.
Conference Proceedings: in Proceedings of the 4th IEEE Conference on Nanotechnology, pp. 216-219, München, Germany
Date: August 2004
Abstract: In this paper, we propose an alternative heterostructure device geometry to realize a semiconductor quantum cellular automata (QCA) cell. This device, called a split current quantum cellular automata (SCQCA) cell, has some attractive features which may enable the fabrication and circuit realization of QCA systems with current fabrication technologies. We present the device model and simulation results by incorporating this model in QCADesigner, a design and simulation tool for QCA. The simulations consist of the two cell interaction, showing the nonlinear cell-cell response function, a short wire, as well as the majority gate created with a cross pattern of five QCA cells.
Conference Proceedings: in Proceedings of the 37th IEEE Asilomar Conference on Signals, Systems and Computers, vol. 2, pp. 1435-1439, Monterey, CA, USA
Date: November 2003
Abstract: In this paper, we discuss arithmetic structures based on quantum cellular automata (QCA). By taking advantage of the unique capabilities of QCA we are able to design interesting computational architectures. We describe important design considerations and show how addition and multiplication circuits can be implemented using QCADesigner, a QCA design tool which has been developed in our laboratory. QCA technology allows, among other things, the implementation of majority boolean gates and interconnecting “wires” that support cross-overs on the same fabrication level. One of the important challenges with QCA design is working within a different cost function from standard transistor circuits. These differences arise from the device level latching inherent in QCA. This latching makes the total delay of a circuit directly proportional to the maximum number of clocking zones between input and output and the number of gates.
Conference Proceedings: in Proceedings of the 3rd IEEE Conference on Nanotechnology, vol. 2, pp. 461-464, San Francisco, CA, USA
Date: August 2003
Abstract: In this paper, a novel quantum-dot cellular automata (QCA) adder design is presented that reduces the number of QCA cells compared to previously reported designs. The proposed one-bit QCA adder structure is based on a new algorithm that requires only three majority gates and two inverters for the QCA addition. By connecting n one-bit QCA adders, we can obtain an n-bit carry look-ahead adder with the reduced hardware while retaining the simple clocking scheme and parallel structure of the original carry look-ahead approach. The proposed adder is designed and simulated using the QCA Designer tool for the four-bit adder case. The proposed design requires only about 70% of the hardware compared to previous designs with the same speed and clocking performance.
Conference Proceedings: in Proceedings of the 2003 Nanotechnology Conference and Trade Show“, vol. 2, pp. 160-163, San Francisco, CA, USA
Date: February 2003
Abstract: One of the most novel and powerful emerging nanotechnologies is quantum computing. This paper proposes a design for a parallel random-access memory (RAM) using Quantum-Dot Cellular Automata (QCA). QCA has the potential of becoming the technology of choice at the nano-scale. The RAM design is based on a simple 2-dimensional grid of identical memory cells, addressed by row using a QCA decoder. The proposed memory has storage capacity > 1.6 Gbit/cm2.
Conference Proceedings: in Proceedings of the IEEE Emerging Telecommunications Technologies Conference, 5 pgs, Dallas, TX, USA
Date: September 2002
Abstract: The use of quantum-dots is a promising emerging technology for implementing digital systems at the nano-scale level. Recently studied computational paradigms for quantum-dot technology include the use of locally connected quantum-dot cellular automata (QCA). This technique is based on the interaction of electrons within quantum dots that take advantage of quantum phenomena; the same phenomena that may prove problematic in future integrated circuit technologies as feature sizes continue to decrease. This paper proposes layouts for a carry-look-ahead adder and barrel shifter based on QCA. The potential application in telecommunications technologies of QCA and the proposed devices is widespread and clear. By taking full advantage of the unique features of this technology, we are able to create complete circuits on a single layer of QCA. Such devices are expected to function with ultra low power consumption and very high operating speeds.