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arXiv:2112.15517 · Physical Review Applied

Swap Test with Quantum Dot Charge Qubits

Yen-Wei Li, N. Barraza, G. Alvarado Barrios, E. Solano, F. Albarrán-Arriagada

Published Jul 20, 2022• 7 citations
arXivHTMLPDF

Abstract

We propose the implementation of the swap test using a charge qubit in a double quantum dot. The swap test is a fundamental quantum subroutine in quantum machine learning and other applications for estimating the fidelity of two unknown quantum states by measuring an auxiliary qubit. Our proposal uses a controlled three-qubit gate, which is natural to quantum dot charge qubits. It allows us to implement a swap test with a circuit depth of six layers, and an estimated gate time of less than 3 ns, that is below the coherence time of double quantum dots. This work paves the way for enhancing the toolbox of quantum machine learning developments in semiconductor qubits.

DOI
10.1103/physrevapplied.18.014047

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•Aug 11, 2015•0 citations
We propose the implementation of the swap test using a charge qubit in a double quantum dot. The swap test is a fundamental quantum subroutine in quantum machine learning and other applications for estimating the fidelity of two unknown quantum states by measuring an auxiliary qubit. Our proposal uses a controlled three-qubit gate, which is natural to quantum dot charge qubits. It allows us to implement a swap test with a circuit depth of six layers, and an estimated gate time of less than 3 ns, that is below the coherence time of double quantum dots. This work paves the way for enhancing the toolbox of quantum machine learning developments in semiconductor qubits.
Abstract The swap test is a quantum algorithm capable of computing the absolute value of the scalar product of two arbitrary wavefunctions. Scalar products represent a crucial ingredient to many quantum machine learning (QML) methods, but their evaluation is not straightforward at all. For this reason, many research efforts have been made without achieving an efficient and robust implementation. Here, we present an integrated photonic circuit designed to implement the swap test algorithm. Our approach relies solely on linear optical integrated components and qudits, represented by single photons from an attenuated laser beam propagating through a set of waveguides. By utilizing 23 spatial degrees of freedom for the qudits, we can configure all the necessary arrangements to set any two-qubit state and perform the swap test. This simplifies the requirements on the circuitry elements and eliminates the need for non-linearity, heralding, or post-selection to achieve multi-qubit gates. Our photonic swap test circuit successfully encodes two qubits and estimates their scalar product with a measured root mean square error smaller than 0.05. This result paves the way for the development of integrated photonic architectures capable of performing QML tasks with robust devices operating at room temperature.
In this theoretical manuscript I propose a scheme for entangling a single-electron-semiconductor spin qubit with a single-electron-semiconductor charge qubit in a triangular triple-quantum-dot configuration. Two out of three quantum dots are used to define a single-electron-semiconductor charge qubit. Furthermore, the spin qubit is embedded in the Zeeman sublevels of the third quantum dot. Combining single-qubit gates with entangling controlled-not gates allows one to construct a swap gate and therefore to use the semiconductor spin qubit as a long-lived memory for the semiconductor charge qubit.
The spin of an electron confined in semiconductor quantum dots is currently a promising candidate for quantum bit (qubit) implementations. Taking advantage of the existing CMOS integration technologies, such devices can offer a platform for large scale quantum computation. However, a quantum mechanical framework bridging a device's physical design and operational parameters to the qubit's energy space is lacking. Furthermore, the spin to charge coupling introduced by intrinsic or induced spin-orbit interaction (SOI) exposes the qubits to charge noise compromising their coherence properties and inducing quantum gate errors. We present here a comodeling framework for double quantum dot (DQD) devices and their charge noise environments. We use a combination of an electrostatic potential solver, full configuration interaction quantum mechanical methods, and two-level-fluctuator models to study the quantum gate performance in realistic device designs and operation conditions. We utilize the developed models together alongside the single electron solutions of the quantum dots to simulate one- and two-qubit gates in the presence of charge noise. We find an inverse correlation between quantum gate errors and quantum dot confinement frequencies. We calculate X-gate fidelities >97>97%>97 in the simulated Si-MOS devices at a typical TLF density of ${10}^{11}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. We also find that exchange driven two-qubit SWAP gates show higher sensitivity to charge noise with fidelities down to 9191%91 in the presence of the same density of TLFs. We further investigate the one- and two-qubit gate fidelities at different TLF densities. We find that given the small size of the quantum dots, sensitivity of a quantum gate to the distance between the noise sources and the quantum dot creates a strong variability in the quantum gate fidelities, which can compromise the device yields in scaled qubit technologies.
We consider one- and two-qubit operations on charge qubits that represent double quantum dots with one electron in each of them. The dots are formed inside a high-Q semiconductor cavity (disk, toroidal, or spherical) in the antinodes of one of its optical eigenmodes; the frequencies of the transitions between the ground (logic) and excited (auxiliary) states of the discrete electron spectrum in quantum dots are close to the frequency of this mode. The precise tuning of the transition frequency is performed by applying an electric potential on the qubit control gate. Within the model of qubits coherently interacting with a cavity quantum field, a few methods for controlling their states are developed. In particular, we propose different variants for implementing two-qubit CNOT and CZ gates and generating qubit entangled states. By the example of a micro-disk cavity, we calculate the operating characteristics that ensure a high rate of quantum gate implementation.
Since the mid-20th century it has been understood that a general-purpose quan- tum computer would be able to efficiently solve problems that will forever be out-of-reach for conventional computers. Since then, many quantum algorithms have been developed with applications in a wide range of domains including cryptography, simulations, machine learning and data analysis. While this has resulted in substantial attention being paid to the development of quantum com- puters, the best architectures to use in their fabrication is not yet clear. Semiconductor quantum dot devices are a particularly promising candidate for use in quantum computing architectures, as it is anticipated that once the funda- mental building blocks are implemented, they might be massively scalable using the existing lithography techniques of the semiconductor industry. So far, how- ever, it is not yet clear how best to implement the high-fidelity gates required for general-purpose quantum computation. In this thesis, we present and characterise novel theoretical proposals for fast, simple and high-fidelity two-qubit gates using magnetic (exchange) coupling for specific semiconductor quantum dot qubits; namely, the singlet-triplet and resonant-exchange qubits. These two-qubit operations are simple enough that it is feasible for them to be implemented in experiments of the near future. Success- ful implementations would significantly extend the experimentally demonstrable frontier of semi-conductor quantum dot devices as relevant to their use in uni- versal quantum computing architectures. We also develop simple parameter estimation schemes by which it is possible to substantially mitigate the dominant sources of error for our proposed gates; namely, low-frequency charge and magnetic noise. We develop the techniques in the context of pseudo-static magnetic field gradient fluctuations in singlet- triplet qubits, and demonstrate that these techniques lead to a several orders of magnitude improvement in single-qubit coherence times. With minimal effort this could be ported to other qubit architectures.