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arXiv:quant-ph/9711034 · Journal of Experimental and Theoretical Physics Letters

Single-electron computing without dissipation

A. M. Bychkov, L. А. Openov, Igor Semenihin

Published Aug 1, 1997• 14 citations
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Abstract

The possibility of performing single-electron computing without dissipation in an array of tunnel-coupled quantum dots is studied theoretically, taking the spin gate NOT (inverter) as an example. It is shown that the logical operation can be implemented at the stage of unitary evolution of the electron subsystem, although complete switching of the inverter cannot be achieved in a reasonable time at realistic values of model parameters. The optimal input magnetic field is found as a function of the interdot tunneling energy and intradot Coulomb repulsion energy.

DOI
10.1134/1.567471

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•Jan 1, 2019•0 citations
The possibility of performing single-electron computing without dissipation in an array of tunnel-coupled quantum dots is studied theoretically, taking the spin gate NOT (inverter) as an example. It is shown that the logical operation can be implemented at the stage of unitary evolution of the electron subsystem, although complete switching of the inverter cannot be achieved in a reasonable time at realistic values of model parameters. The optimal input magnetic field is found as a function of the interdot tunneling energy and intradot Coulomb repulsion energy.
We propose an implementation of a universal set of one- and two-quantum-bit gates for quantum computation using the spin states of coupled single-electron quantum dots. Desired operations are effected by the gating of the tunneling barrier between neighboring dots. Several measures of the gate quality are computed within a recently derived spin master equation incorporating decoherence caused by a prototypical magnetic environment. Dot-array experiments that would provide an initial demonstration of the desired nonequilibrium spin dynamics are proposed.
A quantum computer based on an asymmetric coupled-dot system has been proposed and shown to operate as a controlled-NOT gate. The basic ideas are the following. (1) The electron is localized in one of the asymmetric coupled dots. (2) The electron transfer takes place from one dot to the other when the energy levels of the coupled dots are set to be close. (3) The Coulomb interaction between the coupled dots mutually affects the energy levels of the other coupled dots. The decoherence time of the quantum computation and the measurement time are estimated. The proposed system can be realized by developing the technology of the single-electron memory using Si nanocrystals, and a direct combination of the quantum circuit and the conventional circuit is possible.
Abstract We studied the dynamics of a pair of single-electron double quantum dots (DQDs) under longitudinal and transverse static magnetic fields and time-dependent harmonic modulation of their interaction couplings. We propose to modulate the tunnel coupling between the QDs to produce one-qubit gates and the exchange coupling between DQDs to generate entangling gates, the set of operations required for quantum computing. We developed analytical approximations to set the conditions to control the qubits and applied them to numerical calculations to test the accuracy and robustness of the analytical model. The results shows that the unitary evolution of the two-electron state performs the designed operations even under conditions shifted from the ideal ones.
Rising energy demand from data-center and AI applications has renewed interest in reversible computation, where logic need not dissipate heat at every step if information is uncomputed. Implementations have so far been classical: adiabatic CMOS recovers part of the switching energy but still moves thousands of kBTk_BTkB​T per logic node at room temperature. Here we propose classical reversible logic implemented by coherent spin dynamics in a spin quantum-dot array, with inputs and outputs in classical basis states and no algorithmic use of superposition. The same spin stores, transports, and computes, with unitary rotation replacing irreversible switching. The universal building block is an iToffoli gate driven by DC voltage pulses and exchange between hole spins in Ge/SiGe quantum dots. Simulations with realistic model parameters reproduce the Toffoli truth table and yield a testable error landscape. Because shuttling transports the bit without measurement, logic and data movement remain unitary until readout. Millivolt pulses on femtofarad gates with superconducting lines dissipate only dielectric loss and have no thermodynamic floor. With the loss parameters assumed for a demonstrated device the gate energy is ∼102 kBTln⁡2\sim 10^{2}\,k_BT\ln 2∼102kB​Tln2 at 4 K; at a design point within reach of existing devices it can fall below the Landauer scale kBTln⁡2k_BT\ln 2kB​Tln2, five to seven orders of magnitude less than a CMOS Toffoli. The same semiconductor hardware therefore serves both purposes, supporting quantum algorithms when superposition is used and classical reversible logic otherwise.
The Toffoli–Fredkin (TF) gate is a universal reversible logic gate capable of performing logic operations without dissipating energy. Here, we show that a linear array of three quantum dots, each hosting a single electron, can realize the TF gate, if we encode logic bits in the spin polarization of the electrons and allow nearest neighbor exchange coupling. The dynamics of the TF gate is realized by selectively driving spin resonances in the coupled spin system with an ac magnetic field. The conditions for gate operation are established, and an estimate of the switching speed and gate error are provided.
Spin and topological-qubit based quantum computers require an easily scalable and highly sensitive method for readout and manipulation, for which Dispersive Gate Sensing (DGS) is a promising candidate [1, 2]. DGS enables sensing of single electron tunneling events in a mesoscopic system by measuring a reflected Radio Frequency (RF) signal from a resonator capacitively coupled to one of the system’s gate electrodes. From the resonator’s perspective, the system is modeled as an effective ‘parametric capacitance’ [3]. Motivated by its viability for qubit readout and control, we measure transport characteristics of a semiconducting-superconducting hybrid charge island system using this method. Doing so, we observe a spin degeneracy modulation of interdot tunnel couplings resulting from hybridization of a dot orbital with a subgap state of the superconductor, measured entirely within Coulomb blockade. Without DC measurement, we also track a subgap state’s energy via voltage intervals between island charge states as a function of field. Subsequently, we attempt to correlate changes in the resonator’s internal dissipation with coherence of tunneling into the superconducting island. In particular, we collapse a superconducting island’s lowest energy state to the Fermi level by applying a magnetic field. Contrary to expectations, internal dissipation in the resonator did not change dramatically with field, in fact decreasing at charge degeneracy points at all field strengths. We corroborate measurements with existing theory, augmented by simple analytical and numerical models demonstrating that coherence factors of superconducting quasiparticle states and the degeneracy of dot orbitals modulate parametric capacitance. A master equation model of finite temperature interdot tunneling is solved, agreeing with experimental evidence that Sisyphus dissipation is negligible when a dot orbital is hybridized with multiple independent quasiparticle states. To be employed in quantum computers, a full understanding of all phenomena contributing to a DGS signal in these hybrid systems is critical. Hence, these results mark a step towards unambiguous readout of Majorana parity in topological qubits [4].