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Issues using equivalent circuit elements to describe trapped ions

Noah Van Horne, Manas Mukherjee

Published Aug 17, 2020• 0 citations
OpenAlex

Abstract

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.

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Issues using equivalent circuit elements to describe trapped charged particles

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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.

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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.

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Hybrid quantum systems with trapped charged particles

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Trapped charged particles have been at the forefront of quantum information processing (QIP) for a few decades now, with deterministic two-qubit logic gates reaching record fidelities of $99.9%$ and single-qubit operations of much higher fidelity. In a hybrid system involving trapped charges, quantum degrees of freedom of macroscopic objects such as bulk acoustic resonators, superconducting circuits, or nanomechanical membranes, couple to the trapped charges and ideally inherit the coherent properties of the charges. The hybrid system therefore implements a ``quantum transducer,'' where the quantum reality (i.e., superpositions and entanglement) of small objects is extended to include the larger object. Although a hybrid quantum system with trapped charges could be valuable both for fundamental research and for QIP applications, no such system exists today. Here we study theoretically the possibilities of coupling the quantum-mechanical motion of a trapped charged particle (e.g., an ion or electron) to the quantum degrees of freedom of superconducting devices, nanomechanical resonators, and quartz bulk acoustic wave resonators. For each case, we estimate the coupling rate between the charged particle and its macroscopic counterpart and compare it to the decoherence rate, i.e., the rate at which quantum superposition decays. A hybrid system can only be considered quantum if the coupling rate significantly exceeds all decoherence rates. Our approach is to examine specific examples by using parameters that are experimentally attainable in the foreseeable future. We conclude that hybrid quantum systems involving a single atomic ion are unfavorable compared with the use of a single electron because the coupling rates between the ion and its counterpart are slower than the expected decoherence rates. A system based on trapped electrons, on the other hand, might have coupling rates that significantly exceed decoherence rates. Moreover, it might have appealing properties such as fast entangling gates, long coherence, and flexible topology that is fully electronic in nature. Realizing such a system, however, is technologically challenging because it requires accommodating both a trapping technology and superconducting circuitry in a compatible manner. We review some of the challenges involved, such as the required trap parameters, electron sources, electrical circuitry, and cooling schemes in order to promote further investigations towards the realization of such a hybrid system.

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The ability to distribute entanglement across a quantum network may lead to new capabilities like teleporting information over a difficult-to-access quantum channel or higher resolution quantum sensors. However, there are many outstanding challenges to realizing such a quantum network. One of these challenges is how to interface disparate quantum technologies effectively and efficiently. Ultimately a quantum network will be used to connect different types of devices, much like the current internet does today, and this requires one to seamlessly connect qubit technologies operating in vastly different environments. This talk will present results on interfacing trapped ion qubits to quantum integrated photonic circuits and discuss challenges related to interfacing trapped ion qubits with superconducting qubits.

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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 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.
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.
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 have been at the forefront of quantum information processing (QIP) for a few decades now, with deterministic two-qubit logic gates reaching record fidelities of 99.999.9%99.9 and single-qubit operations of much higher fidelity. In a hybrid system involving trapped charges, quantum degrees of freedom of macroscopic objects such as bulk acoustic resonators, superconducting circuits, or nanomechanical membranes, couple to the trapped charges and ideally inherit the coherent properties of the charges. The hybrid system therefore implements a ``quantum transducer,'' where the quantum reality (i.e., superpositions and entanglement) of small objects is extended to include the larger object. Although a hybrid quantum system with trapped charges could be valuable both for fundamental research and for QIP applications, no such system exists today. Here we study theoretically the possibilities of coupling the quantum-mechanical motion of a trapped charged particle (e.g., an ion or electron) to the quantum degrees of freedom of superconducting devices, nanomechanical resonators, and quartz bulk acoustic wave resonators. For each case, we estimate the coupling rate between the charged particle and its macroscopic counterpart and compare it to the decoherence rate, i.e., the rate at which quantum superposition decays. A hybrid system can only be considered quantum if the coupling rate significantly exceeds all decoherence rates. Our approach is to examine specific examples by using parameters that are experimentally attainable in the foreseeable future. We conclude that hybrid quantum systems involving a single atomic ion are unfavorable compared with the use of a single electron because the coupling rates between the ion and its counterpart are slower than the expected decoherence rates. A system based on trapped electrons, on the other hand, might have coupling rates that significantly exceed decoherence rates. Moreover, it might have appealing properties such as fast entangling gates, long coherence, and flexible topology that is fully electronic in nature. Realizing such a system, however, is technologically challenging because it requires accommodating both a trapping technology and superconducting circuitry in a compatible manner. We review some of the challenges involved, such as the required trap parameters, electron sources, electrical circuitry, and cooling schemes in order to promote further investigations towards the realization of such a hybrid system.
The ability to distribute entanglement across a quantum network may lead to new capabilities like teleporting information over a difficult-to-access quantum channel or higher resolution quantum sensors. However, there are many outstanding challenges to realizing such a quantum network. One of these challenges is how to interface disparate quantum technologies effectively and efficiently. Ultimately a quantum network will be used to connect different types of devices, much like the current internet does today, and this requires one to seamlessly connect qubit technologies operating in vastly different environments. This talk will present results on interfacing trapped ion qubits to quantum integrated photonic circuits and discuss challenges related to interfacing trapped ion qubits with superconducting qubits.