Neuromorphic, Digital and Quantum Computation with Memory Circuit Elements

Yuriy V. Pershin; Massimiliano Di Ventra

Source-linked AI summary

Neuromorphic, Digital and Quantum Computation with Memory Circuit Elements

Yuriy V. Pershin, Massimiliano Di Ventra

arXiv:1009.6025v3Sep 30, 2010cond-mat.mes-hallq-bio.NCquant-ph

TL;DR

The paper examines how memory circuit elements can extend computation beyond storage across neuromorphic, digital, and quantum settings. It develops examples using memristive, memcapacitive, and meminductive systems, including associative learning, STDP, logic and arithmetic, and programmable qubit interactions. These examples show potential for biologically inspired circuits, integrated memory and computation, and field-programmable quantum computation.

Problem
Memory circuit elements are primarily associated with physical memory effects and storage, while their use across neuromorphic, digital, and quantum computation requires examination.
Method
The paper analyzes and demonstrates computational schemes based on memristive, memcapacitive, and meminductive systems for neural, classical logic, arithmetic, and quantum operations.
Results
The examples support associative and Hebbian learning, STDP, basic and extended logic, one-bit arithmetic, and programmable interaction Hamiltonians between coupled qubits.
Takeaways & Limitations
Memory elements can combine memory and computation in neuromorphic and digital circuits while offering a route toward field-programmable quantum computation.

Abstract

from arXiv · show

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.

I. INTRODUCTION

Memory circuit elements retain internal-state history and can support neuromorphic, digital, and quantum computation. The paper highlights associative learning, simpler and faster logic and arithmetic, and programmable quantum interactions.

I. INTRODUCTION: Memristive, memcapacitive, and meminductive systems retain memory of past states through internal variables influenced by voltage, charge, current, or flux.They are distinguished by current-voltage, charge-voltage, and flux-current variable pairs.
I. INTRODUCTION: Memory elements may support analog, digital, and quantum computation beyond information storage.The paper treats these three computational paradigms as its central subject.
I. INTRODUCTION: The paper discusses memristive models for associative memory and spike-timing-dependent plasticity in neural circuits.It also introduces a second-order memristive model for STDP.
I. INTRODUCTION: A memcapacitive-memristive scheme realizes basic and extended logic operations more simply and speeds up one-bit addition.The scheme integrates computing and memory on the same platform.
I. INTRODUCTION: Meminductive and memcapacitive systems could generate an essentially infinite number of programmable interaction Hamiltonians for coupled qubits.The paper terms this possibility field-programmable quantum computation.

II. NEURAL COMPUTATION WITH MEMRISTIVE SYSTEMS

Memristive systems can model neural computation by exploiting synapse-like behavior and internal dynamics. The paper discusses associative Hebbian learning and two schemes for implementing STDP, including one that does not require overlapping pulses.

II. NEURAL COMPUTATION WITH MEMRISTIVE SYSTEMS: Memristive systems can mimic aspects of biological synapses in neuromorphic circuits for adaptive behavior, learning by association, and pattern recognition.Their nanometer-scale realizations may support possible scaling of these elements.
II. NEURAL COMPUTATION WITH MEMRISTIVE SYSTEMS: Two memristive schemes realize spike-timing-dependent plasticity: a bipolar first-order system with overlapping pulses and an intrinsic second-order system without temporal overlap.The intrinsic model uses two state variables and decaying internal processes.

A. Memristive neural networks and Hebbian learning

Memristive neural networks use electronic neurons and memristive synapses to implement associative memory and Hebbian learning through timing-dependent memristance changes.

Network architecture: A simple network uses three electronic neurons connected by two memristive synapses, with neurons sending forward and backward pulses.The neurons monitor inputs and generate signals of controlled intensity and shape.
Synaptic update mechanism: The memristive synapse changes resistance only when forward and backward pulses overlap under the specified threshold conditions.With α = 0 and suitable Vt, isolated forward pulses do not modify memristance.
Synaptic update mechanism: Maximum memristance change occurs at perfect pulse overlap, δt = 0.The timing dependence is illustrated for opposite-polarity square pulses applied to a first-order memristive system.
Associative memory: During learning, simultaneous activation of both inputs drives synapse S2 from a high-resistance to a low-resistance state, implementing Hebbian learning.After learning, either input can activate the output neuron in the demonstrated associative-memory experiment.

B. Spike-timing-dependent plasticity

Biological synapses exhibit plasticity that depends on the relative timing of pre- and post-synaptic signals, extending beyond simple Hebbian learning.

Timing-dependent plasticity: Biological synapses show time-resolved plasticity that is more complicated than the simple Hebbian rule.The paper contrasts this complexity with the simpler overlap-based learning behavior discussed earlier.
Timing-dependent plasticity: Post-synaptic firing before pre-synaptic firing produces long-term depression, with synaptic strength decreasing according to their time difference.The passage identifies this timing order as LTD.
Timing-dependent plasticity: Post-synaptic firing after pre-synaptic firing produces long-term potentiation, increasing synaptic strength according to the timing difference.The supplied passage introduces this opposite timing relationship as LTP.

1) STDP with first-order memristive systems:

First-order memristive systems can realize STDP with bipolar action-potential pulses, while pulse-width choices constrain network modeling.

1) STDP with first-order memristive systems:: STDP is realized by applying bipolar pulses corresponding to pre-synaptic and post-synaptic action potentials.The approach uses first-order memristive systems whose resistance changes during pulse overlap.
1) STDP with first-order memristive systems:: Pulse widths of approximately 20 ms are needed to obtain STDP on time scales similar to biological synapses.This requirement follows because memristance modification is possible only while pulses overlap.
1) STDP with first-order memristive systems:: Non-linear pulses more closely reproduce biological variation in synaptic strength, whereas rectangular double pulses are easier to generate.The comparison concerns pulse generation convenience versus similarity to biological plasticity.
1) STDP with first-order memristive systems:: Wide pulses may require revised neural-network rules because multiple pre-synaptic pulses shorter than the pulse width are not clearly modeled.The publication explicitly limits its discussion to possible STDP realizations with memristive synapses.

2) STDP with second-order memristive systems:

Second-order memristive systems use two internal state variables to model STDP, with one variable tracking pulse separation and the other governing memristance changes. Numerical results show memristance changes resembling experimentally observed biological synaptic weight changes, while solid-state implementations remain needed.

2) STDP with second-order memristive systems:: Second-order memristive systems describe synapses with two internal state variables, including y for tracking the time separation between pulses.The model uses x and y as internal state variables.
2) STDP with second-order memristive systems:: The variable y relaxes with decay constant τ, while memristance changes when |y| reaches the threshold y_t.The model assumes short pre-synaptic and post-synaptic square pulses of the same polarity.
2) STDP with second-order memristive systems:: Numerically calculated memristance changes as a function of pulse interval resemble synaptic weight changes observed in biological synapses.The calculation is presented in Fig. 4 for a pair of rectangular pulses separated by δt.
2) STDP with second-order memristive systems:: Second-order systems can implement neuron firing with short single rectangular pulses and no additional hardware, unlike systems using only first-order memristive elements.The paper notes that this functionality is straightforward in memristor emulators.
2) STDP with second-order memristive systems:: Solid-state second-order memristive systems still need to be developed, although their implementation in memristor emulators is straightforward.The presented equations are described as one of the simplest models exhibiting STDP, with abrupt threshold functions replaceable by sigmoids.

III. LOGIC GATES AND ARITHMETICS WITH MEMORY

The proposed memory-element circuit combines memristive systems with a memcapacitive system to perform Boolean logic and arithmetic. Its demonstrated operations include the basic Boolean gates and one-bit addition, while the reported multi-bit extension is straightforward.

III. LOGIC GATES AND ARITHMETICS WITH MEMORY: The circuit combines an array of memristive systems, a memcapacitive system, a load resistor, and drivers for logic and arithmetic operations.Memristive states encode 1 as ON and 0 as OFF.
III. LOGIC GATES AND ARITHMETICS WITH MEMORY: Four memristor emulators demonstrated the full set of basic Boolean logic operations and addition of two one-bit numbers.The paper states that multi-bit extension is straightforward but does not report it experimentally.
III. LOGIC GATES AND ARITHMETICS WITH MEMORY: Charging the memcapacitive system through input memristive systems and discharging it through output systems controls circuit operation.Because of circuit symmetry, each memristive system can serve as an input or output.
III. LOGIC GATES AND ARITHMETICS WITH MEMORY: The realization substitutes a usual 10µF capacitor for the memcapacitive system because its models are not yet well developed and emulator noise reduction remains important.The paper later discusses advantages of replacing the regular capacitor with a memcapacitor.
III. LOGIC GATES AND ARITHMETICS WITH MEMORY: The circuit uses threshold-type bipolar memristive systems whose resistance changes only when the applied voltage exceeds the threshold voltage V_t.The circuit operation is organized through initialization, charging, and related elementary operations.

D1 DR

The paper demonstrates memristive and memcapacitive schemes for Boolean logic and one-bit arithmetic, using capacitor-mediated operations and experimentally validating the resulting signals. The one-bit adder combines AND and XOR operations, while the architecture is intended to scale through stored intermediate states and parallelization.

Basic logic operations: The proposed scheme implements NOT, OR, AND, and XOR logic using combinations of memristive systems and a capacitor.NOT uses four steps; OR and AND use five steps; XOR uses eleven steps.
Basic logic operations: The NOT gate uses capacitor charging through an input memristive system to determine whether the output memristive system switches state.The capacitor reaches a sufficiently high voltage to switch the output only when the input is 1.
Basic logic operations: The OR and AND gates were experimentally demonstrated with correct truth tables using five-step pulse sequences.The AND sequence uses 10 ms charging pulses and 25 ms pulses for the remaining operations.
Arithmetic operations: 16 steps implement addition of two one-bit numbers by storing AND in M3 and XOR in M4, compared with 87 steps in an earlier approach.The carry flag is encoded in M4 for the one-bit addition.
Arithmetic operations: The scheme can extend straightforwardly to n-bit addition, while memcapacitive storage and crossbar architectures may reduce steps and parallelize operations.Crossbar implementation may require nonlinear memristive systems or additional access devices to suppress unwanted currents.

IV. QUANTUM COMPUTATION WITH MEMORY ELEMENTS

The paper proposes using memcapacitive and meminductive elements to make superconducting-qubit couplings controllable after fabrication. These elements can vary interaction Hamiltonians and tank-circuit frequencies, enabling field-programmable quantum computation, though practical realization must address decoherence.

Field-programmable quantum computation: Memcapacitive and meminductive systems are proposed as controllable interactions for superconducting charge, phase, and flux qubits.Charge and phase qubits are coupled capacitively, whereas flux qubits are coupled inductively.
Charge qubits: Replacing a charge-qubit coupling capacitor with a memcapacitive system allows its capacitance, and therefore the interaction Hamiltonian, to be preset.A controllable voltage source Vab sets the memcapacitive state.
Charge qubits: For N interacting qubits, changing one coupling produces different interaction Hamiltonians and system evolutions, yielding many interaction schemes.The paper connects this reconfigurability to quantum algorithms benefiting from novel hardware functionality.
Flux qubits: A flux-qubit tank circuit using meminductance and memcapacitance changes its frequency according to ω = 1/√(LMCM), thereby changing the qubit interaction Hamiltonian.The tank circuit may be current- or voltage-controlled.
Field-programmable quantum computation: The proposed architectures are termed field-programmable quantum computation because programmable couplings generate different computation schemes.Practical implementation must avoid additional decoherence from real memcapacitive and meminductive elements.

V. CONCLUSIONS

The paper concludes that memristive, memcapacitive, and meminductive systems have potential across neuromorphic, digital, and quantum computation. It also identifies substantial implementation challenges, including neural connectivity, parallelization, and qubit decoherence.

Conclusions: The paper addresses neuromorphic, digital, and quantum computation using memristive, memcapacitive, and meminductive systems.Examples include memristive neural networks, classical logic and arithmetic, and field-programmable quantum computation.
Conclusions: Quantum-computation applications discussed include meminductive and memcapacitive systems used with both charge and flux qubits.The paper anticipates additional opportunities, including effective meminductive behavior from a micromechanical resonator embedded in a DC SQUID.
Challenges: Further work is needed to realize high neural connectivity, effectively parallelize logic and arithmetic, and reduce qubit decoherence.The paper notes that a human-brain neuron has approximately 7000 synaptic connections.