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IEEE Transactions on Applied Superconductivity

Classical and Quantum Operation Modes of the Reversible Josephson-Junction Logic Circuits

Vasili K. Semenov, G.V. Danilov, D. V. Averin

Published Jun 1, 2007• 35 citations
Publisher

Abstract

One of the most important features of the quantum computing circuits that distinguishes them from the traditional computational models is their full, physical and logical, reversibility at all stages of the calculations. This makes the large-scale architecture of potential quantum and classical reversible computers quite similar. The goal of this work is to analyze this similarity in the case of reversible superconducting logic circuits based on the recently suggested elementary gate, the nSQUID. Specifically, we present the results of numerical simulations and some limited measurements of a reversible 8-bit circular shift register fabricated at HYPRES, Inc., and working in the classical mode. The measured energy dissipation per bit operation per nSQUID is still about 20 times higher than the thermodynamic reversibility threshold of kBTIn 2 at T ap 4 K. We also discuss qualitatively operation of the reversible circuits of galvan- ically-coupled nSQUIDs in the quantum mode which provides the basis for implementation of "flying" superconducting qubits. Such qubits have several attractive features for Josephson-junction quantum logic devices beyond the single- or two-qubit circuits.

DOI
10.1109/tasc.2007.898260

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One of the most important features of the quantum computing circuits that distinguishes them from the traditional computational models is their full, physical and logical, reversibility at all stages of the calculations. This makes the large-scale architecture of potential quantum and classical reversible computers quite similar. The goal of this work is to analyze this similarity in the case of reversible superconducting logic circuits based on the recently suggested elementary gate, the nSQUID. Specifically, we present the results of numerical simulations and some limited measurements of a reversible 8-bit circular shift register fabricated at HYPRES, Inc., and working in the classical mode. The measured energy dissipation per bit operation per nSQUID is still about 20 times higher than the thermodynamic reversibility threshold of kBTIn 2 at T ap 4 K. We also discuss qualitatively operation of the reversible circuits of galvan- ically-coupled nSQUIDs in the quantum mode which provides the basis for implementation of "flying" superconducting qubits. Such qubits have several attractive features for Josephson-junction quantum logic devices beyond the single- or two-qubit circuits.
Prior to early this century, the semiconductor microprocessor can be scaled according to the Moore's law, basically doubling its performance in every 18 months. Only recently, the energy efficiency of semiconductor integrated circuits has become a concern than their computational capabilities since their power dissipation scales nonlinear with clock frequency. The specific energy dissipation per logic operation for a modern semiconductor computer is still over 6 orders of magnitude above the thermodynamic threshold kBTln2. It has been known for a long time that this thermodynamic limit on the energy dissipation per logic operation can be overcome by physically and logically reversible circuits. Reversible circuits based on nSQUIDs (negative SQUIDs) or dc SQUIDs (superconducting quantum interference device) with negative mutual inductance between the arms of the SQUID loop, are introduced and investigated in this thesis. First test reversible circuit contains one 8-stage shift register, cells that transfer the input data to the outputs. Dynamic of this circuit illustrates unique properties which agree well with theoretical analysis. Based on the knowledge from the study of shift register, a new timing belt clocking scheme built upon the moving vortices along long Josephson junction (LJJ) is introduced and analyzed. The test circuits for this new scheme contain two 8-stage shift registers, one with direct and the other with inverted outputs. The energy dissipation per nSQUID gate per bit measured for these test circuits at 4 K temperature is already below the thermodynamic threshold. A family of logical gates based on the new timing belt and nSQUIDs shift register are continued to be developed and these gates are capable of fundamentally low energy dissipation and the ability to operate in both irreversible and reversible modes. Moreover, the extremely low energy dissipation in these circuits makes them a natural candidate to support circuitry working in quantum mode with unique advantages.
We continue to develop a new Superconductor Flux Logic (SFL) family based on nSQUID gates with fundamentally low energy dissipation and the ability to operate in irreversible and reversible modes. Prospective computers utilizing the new gates can keep conventional logically irreversible architectures. In this case the energy dissipation is limited by fundamental thermodynamic laws and could be as low as a fewkBTs per logic operation. Highly exotic and less practical logically and physically reversible circuit architectures are more attractive for us because they enable a reduction of the specific energy dissipation well below the thermodynamic thresholdkBTln2. The reversible option is of interest to us because we can then experimentally demonstrate that all technical mechanisms of the energy dissipation could be cut below the fundamental thermodynamic limit. In other words, we like to set the energy dissipation record for all conventional digital technologies that (if measured inkBT) is about one million times below the best figures achieved in commercially available semiconductor circuits. Besides, we believe that diving below the thermodynamic threshold would have impressive scientific and philosophical impacts. In the paper we introduce a new timing belt clocking scheme and present new circuits. While we still work with test circuits, some of them contain two 8-stage shift registers, one with direct and the other with inverted outputs. The energy dissipation per nSQUID gate per bit measured at 4 K temperature is already below the thermodynamic threshold. We are confident that we passed through the critical phase of the project and we simply need more time to make more sophisticated circuits. The extremely low energy dissipation converts our circuits into a natural candidate to support circuitry for any sensors operating at milli-Kelvin temperatures.
Atomic-scale logic and the minimization of heating (dissipation) are both very high on the agenda for future computation hardware. An approach to achieve these would be to replace networks of transistors directly by classical reversible logic gates built from the coherent dynamics of a few interacting atoms. As superpositions are unnecessary before and after each such gate (inputs and outputs are bits), the dephasing time only needs to exceed a single gate operation time, while fault tolerance should be achieved with low overhead, by classical coding. Such gates could thus be a spin-off of quantum technology much before full-scale quantum computation. Thus motivated, we propose methods to realize the 3-bit Toffoli and Fredkin gates universal for classical reversible logic using a single time-independent 3-qubit Hamiltonian with realistic nearest neighbour two-body interactions. We also exemplify how these gates can be composed to make a larger circuit. We show that trapped ions may soon be scalable simulators for such architectures, and investigate the prospects with dopants in silicon.
Quantum information processing systems can be used in a variety of applications. Among proposed realizations of quantum bits nano-electronic circuits appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. In one limit, two logic states of the quantum bit differ by a Cooper pair charge, 2e, on a superconducting island. In the other limit different magnetic fluxes penetrate a superconducting loop in two states. Single-qubit and two-qubit logic operations can be performed by means of voltage or current pulses. Weak coupling to the environment allows a series of these elementary steps before the phase coherence is lost. To read out the result of the computation a quantum measurement is needed. For charge qubits this can be accomplished by coupling a single-electron transistor (SET) capacitively to the qubit. Monitoring the current in the transistor one can extract the information about the state of the qubit. We discuss recent experiments and present a suitable set of circuit parameters available with the present-day technology.
Today's industrial digital logic gates are reaching a technological limit and meanwhile, superconducting circuits produce fundamentally different technologies for the future of digital computing. The standard logic is irreversible and yet superconducting circuits allow digital reversible logic with a much higher energy efficiency per gate operation. Previous reversible gate circuits were “adiabatic,” meaning that they used adiabatic-clocking waveforms for their operation power. However, we are studying logic starting from a ballistic model, where ftuxons enable gates using only energy from their inertia. Our ftuxons are defined in Long Josephson Junctions (LJJs) and may travel ballistically, similar to a particle with negligible damping. Once a ftuxon's energy approaches close enough to the gate, a resonance is induced at the gate and the ftuxon loses its definite topology. Gates are comprised of the (few Josephson-penetration-depth long) ends of LJJs and a connecting circuit interface. Only after the resonance does a ftuxon get formed and yield the gate result without external power: a ftuxon for bit-state 0 or an antiftuxon for bit-state 1. Through earlier analysis of the numerically discovered phenomena we find that dynamics can be described with ftuxon- and antiftuxon-like excitations at the ends of LJJs within the gate. The bit-switching action in our gates is resonant indicating fundamentally different dynamics than the classic model of adiabatic reversible circuits. Our ballistic Reversible Fluxon Logic (RFL) gates have no added damping and calculated energy efficiencies of over 97%. Thus in our dynamical process the “bit energy” is preserved. However, irreversible logic completely dissipates this at each operation (e.g., charging energy in CMOS or SFQ energy in irreversible SFQ logic). An RFL gate can achieve a fast gate operation since its resonance is only few JJ plasma periods. We also describe the CNOT in our technology. It is enabled by a couple of vital gates: A IDSN logic gate, similar to our other ballistic gates, and a Store-aNd-Launch (SNL) timing gate to ensure proper synchronization of the bits. The latter allows bit storage followed by launching of a data ftuxon using an adiabatic pulse from a clock ftuxon with lower energy than the data ftuxon for good CNOT efficiency.
It has been realized that quantum computing is one of the latest technologies using reversible logic. It is observed that increasing growth of transistor density, power consumption will reach their limits in conventional technologies. In conventional Circuits during the logic operations bits of information is erased resulting dissipation of energy in significant amount. Thus, if Circuits are designed so that information bits can be preserved, the power use can be reduced. In case of reversible logic computation, the information bits are not lost. We can use reversible logic technology for minimizing the power consumption, heat dissipation, increasing speed etc. This paper describes various logic gates based on reversible logic like Toffoli, Peres, Fredkin, and Feynman etc. A comparative between classical and quantum logic gates is also given on various parameters along with limitations of conventional computing.