Memory effects are ubiquitous in nature and the class of memory circuit elements - which includes memristors, memcapacitors and meminductors - shows great potential to understand and simulate the associated fundamental physical processes. Here, we show that such elements can also be used in electronic schemes mimicking biologically-inspired computer architectures, performing digital logic and arithmetic operations, and can expand the capabilities of certain quantum computation schemes. In particular, we will discuss few examples where the concept of memory elements is relevant to the realization of associative memory in neuronal circuits, spike-timing-dependent plasticity of synapses, digital and field-programmable quantum computing.
In this paper, we then focus on applications of memory circuit elements in all three computing paradigms.
In the case of analog computation, it was recently shown that electronic circuits with memory circuit elements can simulate processes typical of biological systems such as the adaptive behavior of unicellular organisms, learning and associative memory. The concept of “learning circuits” has also been implemented recently using VO2 as memory element. Here, we first briefly review existing models of neural computing with memristors and then focus on the spike-timing-dependent plasticity (SPDT) property of biological synapses. In particular, we show SPDT using first-order memristive systems and formulate a model of a second-order memristive synapse which resembles closer the operation of a real biological synapse.
It was proposed by Lehtonen and Laiho and experimentally demonstrated by Borghetti et al. that memristors can be employed in classical logic operations. In fact, two memristors are enough to compute any Boolean function. In this paper, we demonstrate that the combination of memcapacitors with memristors allows us to realize all basic logic operations (NOT, OR, AND) as well as many other operations (XOR, multi-input OR, AND, etc.) in a much simpler way than in existing approaches. Moreover, more complex operations, such as addition, can be performed in a straightforward way by using sequences of the elementary logic operations mentioned above. In fact, using memristor emulators - circuits consisting of a digital potentiometer, an analog-to-digital converter and a microcontroller - that emulate the properties of virtually any memristive system we have demonstrated experimentally all basic logic gates (NOT, OR, AND) and addition of two one-bit numbers. Using memristive crossbar arrays arithmetical operations with memory circuit elements can be highly parallelized and can possibly compete with present-day approaches.
Finally, in the case of quantum computation we discuss specific quantum computing schemes where meminductors and memcapacitors could be used to generate an essentially infinite number of programmable interaction Hamiltonians between two or more qubits inductively or capacitively coupled, in a manner we could term field-programmable quantum computation, the quantum analog of the well-established classical field-programmable gate array. This opens up the possibility of expanding both our fundamental understanding of circuit quantum electrodynamics (QED) as well as the optimization of quantum computing algorithms.
Field-programmable quantum computation - One of the possible applications of meminductors and memcapacitors is related to qubit coupling. In superconducting quantum computation schemes, phase and charge qubits are coupled capacitively while flux qubits are coupled inductively. Memcapacitors and meminductors can be used in such schemes to provide a controllable interaction between superconducting qubits.
We have addressed all three different paradigms of computation - neuromorphic (analog), digital and quantum - and shown the potential the three classes of memory elements, namely memristors, memcapacitors and meminductors offer in all three cases. In particular, we have discussed memristive neural networks that can perform associative memory, synaptic spike-timing-dependent plasticity with both first- and second-order memristors, classical logic and arithmetic with memristors and memcapacitors, and field programmable quantum computation with meminductors and memcapacitors with both charge and flux qubits. Clearly, these are only a small number of possible applications for these memory elements.With the increasing research into actual materials and devices that behave as memristors, memcapacitors and meminductors, we thus anticipate many more ideas could be implemented in actual systems and circuits thus offering a wider range of opportunities even in hybrid computational schemes involving any two or even all three paradigms.
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