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arXiv:2111.14957

A semi-classical analysis of the coupling strength $γ$ between motional quantum states of spatially distant trapped ions interacting via a conducting wire

Noah Van Horne, Manas Mukherjee

Published Nov 29, 2021• 1 citation
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Abstract

Interfacing ion qubits in separate traps is among the challenges towards scaling up trapped ion quantum computing. This theoretical study focuses on using a conducting wire to couple the motional quantum states of ions in separate planar traps. The approach of interfacing ion traps provides an alternative to coupling distant qubits with lasers or via ion shuttling. We develop a detailed model for the coupling strength $γ$, which in turn allows us to calculate the time required to exchange motional quantum states between two ions, $t_{\mathrm{ex.}}$. To maximize the coupling strength $γ$, a rule of thumb is developed to relate the distance $d_{\mathrm{eq.}}$ between a trapped ion and a nearby pickup disk, to the optimal radius $r_{\mathrm{opt.}}$ of the disk, $d_{\mathrm{eq.}} / \sqrt{2} \le r_{\mathrm{opt.}} \le d_{\mathrm{eq.}}$. We include a coefficient $ζ$ which describes three self-capacitances connected in series, relating the capacitances of each part of the coupling system, which corrects an oversight common to several previous works. Our analytical model for the coupling strength is then compared with other existing analytical models in the literature. This requires a standardization of the coupling systems and mapping them to a common set of parameter values. Similarities, differences and limitations of the various models are discussed. This study's focus on the coupling strength $γ$ and $t_{\mathrm{ex.}}$ provides a foundational pillar for exchanging quantum information between trapped ions via a wire. In addition, many insights are general and apply broadly to hybrid systems interfacing trapped ions with nearby conductors.

DOI
10.48550/arxiv.2111.14957

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A semi-classical analysis of the coupling strength γγγ between motional quantum states of spatially distant trapped ions interacting via a conducting wire
Interfacing ion qubits in separate traps is among the challenges towards scaling up trapped ion quantum computing. This theoretical study focuses on using a conducting wire to couple the motional quantum states of ions in separate planar traps. The approach of interfacing ion traps provides an alternative to coupling distant qubits with lasers or via ion shuttling. We develop a detailed model for the coupling strength γγγ, which in turn allows us to calculate the time required to exchange motional quantum states between two ions, tex.t_{\mathrm{ex.}}tex.​. To maximize the coupling strength γγγ, a rule of thumb is developed to relate the distance deq.d_{\mathrm{eq.}}deq.​ between a trapped ion and a nearby pickup disk, to the optimal radius ropt.r_{\mathrm{opt.}}ropt.​ of the disk, deq./2≤ropt.≤deq.d_{\mathrm{eq.}} / \sqrt{2} \le r_{\mathrm{opt.}} \le d_{\mathrm{eq.}}deq.​/2​≤ropt.​≤deq.​. We include a coefficient ζζζ which describes three self-capacitances connected in series, relating the capacitances of each part of the coupling system, which corrects an oversight common to several previous works. Our analytical model for the coupling strength is then compared with other existing analytical models in the literature. This requires a standardization of the coupling systems and mapping them to a common set of parameter values. Similarities, differences and limitations of the various models are discussed. This study's focus on the coupling strength γγγ and tex.t_{\mathrm{ex.}}tex.​ provides a foundational pillar for exchanging quantum information between trapped ions via a wire. In addition, many insights are general and apply broadly to hybrid systems interfacing trapped ions with nearby conductors.
Trapped charged particles, and in particular trapped ions, are among the leading candidates for quantum computing technologies. However, our ability to interconnect arrays of ions in different traps is a significant hurdle in scaling trapped ion quantum computing. One approach to overcome this problem is using a solid state conducting wire to mediate the Coulomb interaction between particles in different traps. Additionally, there is strong interest in interfacing trapped ion qubits with solid state superconducting qubits to develop hybrid systems which benefit from the complementary strengths of the two technologies. For studies related to these fields, a trapped charged particle inducing charge on a conductor has long been modeled using equivalent circuit elements. The equivalent circuit element approach is popular partly due to the appeal of a model for analyzing systems using simple electronic components. As a result, a body of theoretical work is founded on this approach. However, careful consideration of the model leads to inconsistencies. Here, we identify the origin of the inconsistencies and their implications. Our result removes a potential road-block for future studies aiming to use conductors to connect independent arrays of ions, or to interface charged particles with solid-state qubit technologies. In addition, for the specific case of two trapped ions interacting via a conducting coupling system, we introduce an alternative way to use linear relationships, which reproduces results from other works that are not based on the circuit element model. This method is useful in trouble-shooting real experimental designs and assessing the accuracy of different theoretical models.
Trapped ions are among the leading candidates for quantum computing technologies. Interfacing ion qubits in separate traps and interfacing ion qubits with superconducting qubits are two of the many challenges to scale up quantum computers. One approach to overcome both problems is to use a conducting wire to mediate the Coulomb interaction between ions in different traps or between ions and superconducting qubits. To this end, a trapped charged particle inducing charge on a conductor has long been modeled as a system of equivalent lumped element electronic components. Our careful consideration reveals two assumptions in the derivation of this model, which are generally unjustified. We explain how these assumptions undermine the model’s validity, and then introduce an improved way to use linear relationships to describe the interaction of trapped ions with nearby conductors. The new method reproduces results equivalent to those of other works that are not based on the circuit element model. This method is targeted for trouble-shooting experimental designs and allows experiments to test and compare the accuracy of different theoretical models.
Trapped charged particles are among the leading qubit candidates for quantum computing technologies. However, our ability to interconnect arrays of particles in different traps is a significant hurdle in scaling trapped charged particle quantum computing. One approach explored to overcome this problem is to use a solid state conducting wire to mediate the Coulomb interaction between particles in different traps. Additionally, there is strong interest in interfacing trapped charged particle qubits with solid state superconducting qubits to develop hybrid systems which benefit from the complementary strengths of the two technologies. For studies related to these fields, a trapped charged particle inducing charge on a conductor has long been modeled using equivalent circuit elements. The equivalent circuit element approach is popular partly due to the appeal of a model for analyzing systems using simple electronic components. As a result, a body of theoretical work is founded on this approach. However, careful consideration of the model leads to inconsistencies. We show that this suggests many studies based on the model should be reviewed. Our result removes a potential road-block for future studies aiming to use conductors to connect independent arrays of charged particles, or to interface charged particles with solid-state qubit technologies. In addition, for the specific case of two trapped charges interacting via a conducting coupling system, we introduce an alternative way to use linear relationships, which reproduces results from other works that are not based on the circuit-element model. This method may be useful in trouble-shooting real experimental designs and assessing the accuracy of different theoretical models.
There has been much interest in developing methods for transferring quantum information. We discuss a way to transfer quantum information between two trapped ions through a wire. The motion of a trapped ion induces oscillating charges in the trap electrodes. By sending this current to the electrodes of a nearby second trap, the motions of ions in the two traps are coupled. We investigate the electrostatics of a setup where two separately trapped ions are coupled through an electrically floating wire. We also discuss experimental issues, including possible sources of decoherence.
We demonstrate coupling between the motions of two independently trapped ions with a separation distance of 620 μm. The ion-ion interaction is enhanced via a room-temperature electrically floating metallic wire which connects two surface traps. Tuning the motion of both ions into resonance, we show flow of energy with a coupling rate of 11 Hz. Quantum-coherent coupling is hindered by strong surface electric-field noise in our device. Our ion-wire-ion system demonstrates that room-temperature conductors can be used to mediate and tune interactions between independently trapped charges over distances beyond those achievable with free-space dipole-dipole coupling. This technology may be used to sympathetically cool or entangle remotely trapped charges and enable coupling between disparate physical systems.
Ion trap quantum computers are based on modulating the Coulomb interaction between atomic ion qubits using external forces. However, the spectral crowding of collective motional modes could pose a challenge to the control of such interactions for large numbers of qubits. Here, we show that high-fidelity quantum gate operations are still possible with very large trapped ion crystals by using a small and fixed number of motional modes, simplifying the scaling of ion trap quantum computers. We present analytical work that shows that gate operations need not couple to the motion of distant ions, allowing parallel entangling gates with a crosstalk error that falls off as the inverse cube of the distance between the pairs. We also experimentally demonstrate high-fidelity entangling gates on a fully connected set of seventeen 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ qubits using simple laser pulse shapes that primarily couple to just a few modes.