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arXiv:2207.09441 · Physical Review Applied

Limits to Quantum Gate Fidelity from Near-Field Thermal and Vacuum Fluctuations

Wenbo Sun, Sathwik Bharadwaj, Li‐Ping Yang, Yu‐Ling Hsueh, Yifan Wang, Dan Jiao, Rajib Rahman, Zubin Jacob

Published Jun 12, 2023• 11 citations
arXivHTMLPDF

Abstract

High-fidelity quantum gate operations are essential for achieving scalable quantum circuits. In spin qubit quantum computing systems, metallic gates and antennas that are necessary for qubit operation, initialization, and readout, also cause detrimental effects by enhancing fluctuations of electromagnetic fields. Therefore, evanescent wave Johnson noise (EWJN) caused by near-field thermal and vacuum fluctuations becomes an important unmitigated noise, which induces the decoherence of spin qubits and limits the quantum gate operation fidelity. Here, we first develop a macroscopic quantum electrodynamics theory of EWJN to account for the dynamics of two spin qubits interacting with metallic circuitry. Then we propose a numerical technique based on volume integral equations to quantify EWJN strength in the vicinity of nanofabricated metallic gates with arbitrary geometry. We study the limits to two-spin-qubit gate fidelity from EWJN-induced relaxation processes in two experimentally relevant quantum computing platforms: (a) the silicon quantum dot system and (b) nitrogen-vacancy centers in diamond. Finally, we introduce a Lindbladian engineering method to optimize the control pulse sequence design and show its enhanced performance over Hamiltonian engineering in mitigating the influence of thermal and vacuum fluctuations. Our work leverages advances in computational electromagnetics, fluctuational electrodynamics, and open quantum systems to suppress the effects of near-field thermal and vacuum fluctuations and reach the limits of two-spin-qubit gate fidelity.

DOI
10.1103/physrevapplied.19.064038

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•Jul 22, 2013•0 citations
High-fidelity quantum gate operations are essential for achieving scalable quantum circuits. In spin qubit quantum computing systems, metallic gates and antennas that are necessary for qubit operation, initialization, and readout, also cause detrimental effects by enhancing fluctuations of electromagnetic fields. Therefore, evanescent wave Johnson noise (EWJN) caused by near-field thermal and vacuum fluctuations becomes an important unmitigated noise, which induces the decoherence of spin qubits and limits the quantum gate operation fidelity. Here, we first develop a macroscopic quantum electrodynamics theory of EWJN to account for the dynamics of two spin qubits interacting with metallic circuitry. Then we propose a numerical technique based on volume integral equations to quantify EWJN strength in the vicinity of nanofabricated metallic gates with arbitrary geometry. We study the limits to two-spin-qubit gate fidelity from EWJN-induced relaxation processes in two experimentally relevant quantum computing platforms: (a) the silicon quantum dot system and (b) nitrogen-vacancy centers in diamond. Finally, we introduce a Lindbladian engineering method to optimize the control pulse sequence design and show its enhanced performance over Hamiltonian engineering in mitigating the influence of thermal and vacuum fluctuations. Our work leverages advances in computational electromagnetics, fluctuational electrodynamics, and open quantum systems to suppress the effects of near-field thermal and vacuum fluctuations and reach the limits of two-spin-qubit gate fidelity.
We present our study of decoherence in charge (spin) qubits due to evanescent-wave Johnson noise (EWJN) in a laterally coupled double quantum dot (single quantum dot). The high density of evanescent modes in the vicinity of metallic gates causes energy relaxation and a loss of phase coherence of electrons trapped in quantum dots. We derive expressions for the resultant energy relaxation rates of charge and spin qubits in a variety of dot geometries, and EWJN is shown to be a dominant source of decoherence for spin qubits held at low magnetic fields. Previous studies in this field approximated the charge or spin qubit as a point dipole. Ignoring the finite size of the quantum dot in this way leads to a spurious divergence in the relaxation rate as the qubit approaches the metal. Our approach goes beyond the dipole approximation and remedies this unphysical divergence by taking into account the finite size of the quantum dot. Additionally, we derive an enhancement of EWJN that occurs outside a thin metallic film, relative to the field surrounding a conducting half-space.
In many quantum computer architectures, the qubits are in close proximity to metallic device elements. Metals have a high density of photon modes, and the fields spill out of the bulk metal because of the evanescent-wave component. Thus thermal and quantum electromagnetic Johnson-type noise from metallic device elements can decohere nearby qubits. In this Rapid Communication we use quantum electrodynamics to compute the strength of this evanescent-wave Johnson noise as a function of distance zzz from a metallic half space. Previous treatments have shown unphysical divergences at z=0z=0z=0. We remedy this by using a proper nonlocal dielectric function. Decoherence rates of local qubits are proportional to the magnitude of electric or magnetic correlation functions evaluated at the qubit position. We present formulas for the decoherence rates. These formulas serve as an important constraint on future device architectures. Comparison with single-electron spin relaxation measurements shows that evanescent-wave Johnson noise may constitute the dominant relaxation mechanism in experiments performed at low magnetic field.
Abstract : A key step in the construction of quantum computing technologies is the identification and elimination of unwanted sources of noise and its resulting quantum decoherence. In solid state devices, one important source of noise is the fluctuating electric and magnetic fields that come from the device elements themselves. The ultimate source of these fluctuations is the random electric currents that are strongest in the metallic electrodes and leads. This random motion has both thermal and quantum components, though in most devices presently under investigation, the thermal part dominates. In the past, this important physical effect has generally been modeled by picturing the device using an equivalent RC circuit and applying the Nyquist theorem to this circuit. This approach has limitations, since it depends on global quantities, rather than on the detailed geometry and the local electromagnetic properties of the components. Our aim in this research project was to compute the effect from first principles. We considered the underlying physical law (quantum electrodynamics) governing the devices in question. Given the position- and frequency-dependent dielectric function, the electromagnetic noise spectrum can be calculated, and the decohering effect can be deduced. Semiconducting quantum dot and superconducting flux qubits were investigated.
Abstract In many quantum computer architectures, the qubits are in close proximity to metallic device elements. The fluctuating currents in the metal give rise to noisy electromagnetic fields that leak out into the surrounding region. These fields are known as evanescent-wave Johnson noise. The noise can decohere the qubits. We review and update the general theory of this effect for charge qubits subject to electric noise and for spin and magnetic qubits subject to magnetic noise. A mapping of the quantum-mechanical problem onto a problem in classical electrodynamics simplifies the calculations. The focus is on relatively simple geometries in which analytical calculations can be done. Results are presented for the local noise spectral density in the vicinity of cylindrical conductors such as small antennae, noise from objects that can be treated as dipoles, and noise correlation functions for several geometries. We summarize the current state of the comparison of theory with experimental results on decoherence times of qubits. Emphasis is placed on qualitative understanding of the basic concepts and phenomena.
In semiconductor single-spin qubits, high-fidelity quantum gates have been demonstrated; however, achieving consistent performance remains challenging due to variations in driven qubit coherence, which is less explored than free-evolution coherence such as T2∗T_2^*T2∗​. Here, we report single-qubit gate fidelities above 99.999%, achieved by dramatically extending the driven-spin coherence time and suppressing off-resonant driving effects that are detrimental to accurate fidelity benchmarking. We demonstrate that removing proximal reservoirs significantly enhances the spin-locking coherence time (T1ρT_{1ρ}T1ρ​), a critical metric for qubits under microwave driving. Furthermore, we reveal that in typical spin qubit setups using parity readout and rectangular pulses, off-resonant excitation of neighboring qubits causes substantial benchmarking artifacts. By optimizing device conditions to mitigate microwave-induced degradation and implementing spectrally tailored pulse shaping, we achieve a π/2π/2π/2 gate fidelity of 99.99920(2)%, with remaining errors primarily limited by incoherent noise. These results showcase the mechanisms that bound fidelity benchmarking in state-of-the-art silicon spin qubits and provide practical guidelines for achieving and verifying high fidelities in these systems.
Abstract : This thesis addresses the origin and effect of noise and fluctuations in quantum devices that find applications in quantum information processing. In the first half of the thesis, we consider a phenomenological model of the noise and study its effect on the fidelity of quantum measurements and operations that are essential for quantum computing. We focus primarily on quantum gate operations in phase qubits, detection of microwave photons and the measurement of the Berry curvature. Specifically, we examine the effect of the Ohmic noise on optimally controlled flux-biased phase qubits for one- and two-quadrature microwave pulses and demonstrate that twoquadrature pulses with fixed driving frequency are as robust as variable driving frequency, in the presence of environment. Next, we present a model to analyze the quantum efficiency of a microwave photon detector based on a current-biased Josephson junction and study the effect of decoherence on the detection efficiency of the detector. We also present alternative set-ups for microwave photon detection and provide a systematic method to compute the power absorbed by the detector. We then consider the effect of decoherence on the Berry curvature measurement, which employs a novel non-adiabatic protocol, and show that the curvature is immune to decoherence. In the second half of the thesis, we go beyond the phenomenological models of the noises and perform a detailed study of the microscopic description of the Johnson noise. Here we focus primarily on quantum dot devices. We present a formalism to compute relaxation rates in charge and spin qubits due to evanescent wave Johnson noise (EWJN) from the metallic gates that are in proximity to quantum dots. The EWJN is analyzed for the metallic gates that are characterized by both local and nonlocal dielectric response functions.