Magnetic noise from metal objects near qubit arrays

Jonathan Kenny, Hruday Mallubhotla, and Robert Joynt

Phys. Rev. A 103, 062401 – Published 1 June 2021

Abstract

All metal objects support fluctuating currents that are responsible for evanescent-wave Johnson noise in their vicinity due to both thermal and quantum effects. The noise fields can decohere qubits. It is quantified by the average value of $B (x, t) B (x^{'}, t^{'})$ and its time Fourier transform. We develop the formalism particularly for objects whose dimensions are small compared with the skin depth, which is the appropriate regime for nanoscale devices. This leads to a general and surprisingly simple formula for the two-point noise correlation function of an object of arbitrary shape. This formula has a clear physical interpretation in terms of induced currents in the object, and it can be the basis for straightforward numerical evaluation. We discuss its experimental implications. For a sphere, a solution is given in closed form in terms of a generalized multipole expansion. Plots of the solution illustrate the physical principles involved. We give examples of how the spatial pattern of noise can affect quantum information processing in nearby qubits. The theory implies that if the qubit system is miniaturized to a scale $D$ , then decoherence rates of qubits scale as $1 / D$ .

Received 29 November 2020
Accepted 27 April 2021

DOI:https://doi.org/10.1103/PhysRevA.103.062401

Physics Subject Headings (PhySH)

Fluctuation theorems Noise Quantum information architectures & platforms Quantum information processing Quantum memories

Quantum Information, Science & TechnologyStatistical Physics & Thermodynamics

Authors & Affiliations

Jonathan Kenny ^*

School of Physical and Mathematical Science, Nanyang Technological University, 21 Nanyang Link, 04-01, Singapore 637371

Hruday Mallubhotla and Robert Joynt ^†

Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706, USA

^*Also at the Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, WI 53706, USA.
^†rjjoynt@wisc.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 103, Iss. 6 — June 2021

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Basic noise pattern for qubits in the vicinity of a metallic sphere. The top plot is $F_{z z}^{(L = 5)} (\vec{x}, \vec{x}) \times {(r / a)}^{6}$ . It shows that noise is greatest when the separation vector of the qubit and the object is parallel to the noise field components considered. Here $\vec{x}$ is on the $x \times z$ plane. The unit of distance is $a$ , the radius of the sphere. The deep-blue color indicates regions of very small positive correlation, and the yellow color shows a region of high positive correlation. The bottom plot illustrates the rotation properties of the noise tensor. Plotted is $F_{x x}^{(L = 5)} (\vec{x}, \vec{x}) \times {(r / a)}^{6}$ . The two plots are related by a $π / 2$ rotation as follows from Eq. (31).
Reuse & Permissions
Figure 2
Convergence of the multipole expansion. Shown are the first five multipole approximations for the dimensionless one-point noise correlation function $F_{z z}^{(L)} (\vec{x}, \vec{x}) \times {(r / a)}^{6}$ for $L = 1$ to $L = 5$ , where $L$ is the number of multipoles included in the sum. The dipole approximation $F_{z z}^{(1)} (\vec{x}, \vec{x})$ gives qualitatively incorrect results. Rough convergence is achieved at $L = 5$ . The plot for $L = 5$ is a zoomed-out version of the top plot in Fig. 1.
Reuse & Permissions
Figure 3
Interqubit noise correlations. Shown is the two-point noise correlation function $F_{z z}^{(L = 5)} (\vec{x}, {\vec{x}}^{'})$ . Here the base point (qubit 1) is at ${\vec{x}}^{'} = (0, 0, 2 a)$ (red dot at the top center of the plot) and $\vec{x}$ , the position of qubit 2 is varied. The bottom plot is the same except that the base point is at ${\vec{x}}^{'} = (0, 0, 5 a)$ (off the plot). For the more distant base point the dipole approximation is excellent, and we see a dipole pattern, but when the base point is closer the up-down asymmetry is clear. Unlike the one-point NCF, the two-point NCF need not be positive.
Reuse & Permissions
Figure 4
Tensor character of interqubit noise correlations. The top panel is the dimensionless two-point noise correlation function $F_{x x}^{(L = 5)} (\vec{x}, {\vec{x}}^{'})$ with the base point at ${\vec{x}}^{'} = (0, 0, 2 a)$ . Is is indicated by a red dot. Here the separation vector (along $z$ ) is perpendicular to the noise vectors along $x$ . The up-down asymmetry is striking. It is nearly absent in the lower plot where the base point is at ${\vec{x}}^{'} = (0, 0, 5 a)$ (off the plot) because then the symmetric dipole term dominates.
Reuse & Permissions
Figure 5
Convergence of multipole expansion for two-point NCFs. Shown is $F_{x x}^{(L)} (\vec{x}, {\vec{x}}^{'})$ for a base point at $d = (0, 0, 2 a)$ (red dot). This is plotted for $L = 1 - 5$ to show the growth of the up-down asymmetry, which comes solely from the $ℓ = 2$ and $ℓ = 4$ terms. At $L = 5$ the plot is a zoomed-out version of the top plot in Fig. 4.
Reuse & Permissions
Figure 6
Off-diagonal noise correlations. Here the noise vectors in the NCF are perpendicular to one another. Top plot shows $F_{x z}^{(L)} (\vec{x}, {\vec{x}}^{'})$ . Here the base point is at ${\vec{x}}^{'} = (0, 0, 2 a)$ (red dot). In this case the dipole approximation is adequate, and this is confirmed by the fact that the function is little changed when the base point is moved to ${\vec{x}}^{'} = (0, 0, 5 a)$ (off the plot). This figure shows that the symmetry of the off-diagonal components is quite different from the diagonal components shown in earlier figures.
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information