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arXiv:2304.12673 · IEEE Transactions on Quantum Engineering

Tools for the Analysis of Quantum Protocols Requiring State Generation Within a Time Window

Bethany Davies, Thomas Beauchamp, Gayane Vardoyan, Stephanie Wehner

Published Jan 1, 2024• 11 citations
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Abstract

Quantum protocols commonly require a certain number of quantum resource states to be available simultaneously. An important class of examples is quantum network protocols that require a certain number of entangled pairs. Here, we consider a setting in which a process generates a quantum resource state with some probability$p$in each time step, and stores it in a quantum memory that is subject to time-dependent noise. To maintain sufficient quality for an application, each resource state is discarded from the memory after$w$time steps. Let$s$be the number of desired resource states required by a protocol. We characterise the probability distribution$X_{(w,s)}$of the ages of the quantum resource states, once$s$states have been generated in a window$w$. Combined with a time-dependent noise model, knowledge of this distribution allows for the calculation of fidelity statistics of the$s$quantum resources. We also give exact solutions for the first and second moments of the waiting time$\tau _{(w,s)}$until$s$resources are produced within a window$w$, which provides information about the rate of the protocol. Since it is difficult to obtain general closed-form expressions for statistical quantities describing the expected waiting time$\mathbb {E}(\tau _{(w,s)})$and the distribution$X_{(w,s)}$, we present two novel results that aid their computation in certain parameter regimes. The methods presented in this work can be used to analyse and optimise the execution of quantum protocols. Specifically, with an example of a Blind Quantum Computing (BQC) protocol, we illustrate how they may be used to infer$w$and$p$to optimise the rate of successful protocol execution.

DOI
10.1109/tqe.2024.3358674

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Quantum protocols commonly require a certain number of quantum resource states to be available simultaneously. An important class of examples is quantum network protocols that require a certain number of entangled pairs. Here, we consider a setting in which a process generates a quantum resource state with some probabilitypppin each time step, and stores it in a quantum memory that is subject to time-dependent noise. To maintain sufficient quality for an application, each resource state is discarded from the memory afterwwwtime steps. Letsssbe the number of desired resource states required by a protocol. We characterise the probability distributionX(w,s)X_{(w,s)}X(w,s)​of the ages of the quantum resource states, oncesssstates have been generated in a windowwww. Combined with a time-dependent noise model, knowledge of this distribution allows for the calculation of fidelity statistics of thesssquantum resources. We also give exact solutions for the first and second moments of the waiting timeτ(w,s)\tau _{(w,s)}τ(w,s)​untilsssresources are produced within a windowwww, which provides information about the rate of the protocol. Since it is difficult to obtain general closed-form expressions for statistical quantities describing the expected waiting timeE(τ(w,s))\mathbb {E}(\tau _{(w,s)})E(τ(w,s)​)and the distributionX(w,s)X_{(w,s)}X(w,s)​, we present two novel results that aid their computation in certain parameter regimes. The methods presented in this work can be used to analyse and optimise the execution of quantum protocols. Specifically, with an example of a Blind Quantum Computing (BQC) protocol, we illustrate how they may be used to inferwwwandpppto optimise the rate of successful protocol execution.
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Distributed quantum applications impose requirements on the quality of the quantum states that they consume. When analyzing architecture implementations of quantum hardware, characterizing this quality forms an important factor in understanding their performance. Fundamental characteristics of quantum hardware lead to inherent tradeoffs between the quality of states and traditional performance metrics such as throughput. Furthermore, any real-world implementation of quantum hardware exhibits time-dependent noise that degrades the quality of quantum states over time. Here, we study the performance of two possible architectures for interfacing a quantum processor with a quantum network. The first corresponds to the current experimental state of the art in which the same device functions both as a processor and a network device. The second corresponds to a future architecture that separates these two functions over two distinct devices. We model these architectures as continuous-time Markov chains and compare their quality of executing quantum operations and producing entangled quantum states as functions of their memory lifetimes, as well as the time that it takes to perform various operations within each architecture. As an illustrative example, we apply our analysis to architectures based on Nitrogen-Vacancy centers in diamond, where we find that for present-day device parameters one architecture is more suited to computation-heavy applications, and the other for network-heavy ones. We validate our analysis with the quantum network simulator NetSquid. Besides the detailed study of these architectures, a novel contribution of our work are several formulas that connect an understanding of waiting time distributions to the decay of quantum quality over time for the most common noise models employed in quantum technologies. This provides a valuable new tool for performance evaluation experts, and its applications extend beyond the two architectures studied in this work.
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