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We present the first polarized neutron transmission image of a model Ne\'el ferrimagnetic material, polycrystalline terbium iron garnet (Tb$_{3}$Fe$_{5}$O$_{12}$, TbIG for short), as it is taken through its compensation temperature $T_{comp}$ where, according to the theory of ferrimagnetism, the internal magnetization should vanish. Our polarized neutron imaging data and the additional supporting measurements using neutron spin echo spectroscopy and SQUID magnetometry are all consistent with a vanishing internal magnetization at $T_{comp}$., Comment: 15 pages, 15 figures

Minimizing both experimental effort and consumption of valuable quantum resources in state estimation is vital in practical quantum information processing. Here, we explore characterizing states as an additional benefit of the entanglement distillation protocols. We show that the Bell-diagonal parameters of any undistilled state can be efficiently estimated solely from the measurement statistics of probabilistic distillation protocols. We further introduce the state estimator `Disti-Mator' designed specifically for a realistic experimental setting, and exhibit its robustness through numerical simulations. Our results demonstrate that a separate estimation protocol can be circumvented whenever distillation is an indispensable communication-based task., Comment: 14+5 pages, 5 figures, comments are welcome, repository link updated

Quantum networks are expected to enhance distributed quantum computing and quantum communication over long distances while providing security dependent upon physical effects rather than mathematical assumptions. Through simulation, we show that a quantum network utilizing only entanglement purification or only quantum error correction as error management strategies cannot create Bell pairs with fidelity that exceeds the requirement for a secured quantum key distribution protocol for a broad range of hardware parameters. We propose hybrid strategies utilizing quantum error correction on top of purification and show that they can produce Bell pairs of sufficiently high fidelity. We identify the error parameter regime for gate and measurement errors in which these hybrid strategies are applicable., Comment: 8 pages, 3 figures, 1 table. This manuscript has been accepted for publication in the QCNC 2024 Conference Proceedings. The technical manuscript of this work is available at arXiv:2303.10295

The optical Bell State Analyzer (BSA) plays a key role in the optical generation of entanglement in quantum networks. The optical BSA is effective in controlling the timing of arriving photons to achieve interference. It is unclear whether timing synchronization is possible even in multi-hop and complex large-scale networks, and if so, how efficient it is. We investigate the scalability of BSA synchronization mechanisms over multiple hops for quantum networks both with and without memory in each node. We first focus on the exchange of entanglement between two network nodes via a BSA, especially effective methods of optical path coordination in achieving the simultaneous arrival of photons at the BSA. In optical memoryless quantum networks, including repeater graph state networks, we see that the quantum optical path coordination works well, though some possible timing coordination mechanisms have effects that cascade to adjacent links and beyond, some of which was not going to work well of timing coordination. We also discuss the effect of quantum memory, given that end-to-end extension of entangled states through multi-node entanglement exchange is essential for the practical application of quantum networks. Finally, cycles of all-optical links in the network topology are shown to may not be to synchronize, this property should be taken into account when considering synchronization in large networks., Comment: 7 pages, 9 figures. Submitted to the IEEE Quantum Week 2024

Quantum networking, heralded as the next frontier in communication networks, envisions a realm where quantum computers and devices collaborate to unlock capabilities beyond what is possible with the Internet. A critical component for realizing a long-distance quantum network, and ultimately, the Quantum Internet, is the quantum repeater. As with the race to build a scalable quantum computer with different technologies, various schemes exist for building quantum repeaters. This article offers a gentle introduction to the two-way ``all-photonic quantum repeaters,'' a recent addition to quantum repeater technologies. In contrast to conventional approaches, these repeaters eliminate the need for quantum memories, offering the dual benefits of higher repetition rates and intrinsic tolerance to both quantum operational errors and photon losses. Using visualization and simple rules for manipulating graph states, we describe how all-photonic quantum repeaters work. We discuss the problem of the increased volume of classical communication required by this scheme, which places a huge processing requirement on the end nodes. We address this problem by presenting a solution that decreases the amount of classical communication by three orders of magnitude. We conclude by highlighting other key open challenges in translating the theoretical all-photonic framework into real-world implementation, providing insights into the practical considerations and future research directions of all-photonic quantum repeater technology., Comment: 9 pages, 4 figures, 2 tables; comments welcome!

The heterogeneity of quantum link architectures is an essential theme in designing quantum networks for technological interoperability and possibly performance optimization. However, the performance of heterogeneously connected quantum links has not yet been addressed. Here, we investigate the integration of two inherently different technologies, with one link where the photons flow from the nodes toward a device in the middle of the link, and a different link where pairs of photons flow from a device in the middle towards the nodes. We utilize the quantum internet simulator QuISP to conduct simulations. We first optimize the existing photon pair protocol for a single link by taking the pulse rate into account. Here, we find that increasing the pulse rate can actually decrease the overall performance. Using our optimized links, we demonstrate that heterogeneous networks actually work. Their performance is highly dependent on link configuration, but we observe no significant decrease in generation rate compared to homogeneous networks. This work provides insights into the phenomena we likely will observe when introducing technological heterogeneity into quantum networks, which is crucial for creating a scalable and robust quantum internetwork., Comment: 10 pages, 10 figures

To scale quantum computers to useful levels, we must build networks of quantum computational nodes that can share entanglement for use in distributed forms of quantum algorithms. In one proposed architecture, node-to-node entanglement is created when nodes emit photons entangled with stationary memories, with the photons routed through a switched interconnect to a shared pool of Bell state analyzers (BSAs). Designs that optimize switching circuits will reduce loss and crosstalk, raising entanglement rates and fidelity. We present optimal designs for switched interconnects constrained to planar layouts, appropriate for silicon waveguides and Mach-Zehnder interferometer (MZI) $2 \times 2$ switch points. The architectures for the optimal designs are scalable and algorithmically structured to pair any arbitrary inputs in a rearrangeable, non-blocking way. For pairing $N$ inputs, $N(N - 2)/4$ switches are required, which is less than half of number of switches required for full permutation switching networks. An efficient routing algorithm is also presented for each architecture. These designs can also be employed in reverse for entanglement generation using a shared pool of entangled paired photon sources., Comment: 11 pages, 8 figures, 1 table

Quantum repeater networks play a crucial role in distributing entanglement. Various link architectures have been proposed to facilitate the creation of Bell pairs between distant nodes, with entangled photon sources emerging as a primary technology for building quantum networks. Our work advances the Memory-Source-Memory (MSM) link architecture, addressing the absence of practical implementation details. We conduct numerical simulations using the Quantum Internet Simulation Package (QuISP) to analyze the performance of the MSM link and contrast it with other link architectures. We observe a saturation effect in the MSM link, where additional quantum resources do not affect the Bell pair generation rate of the link. By introducing a theoretical model, we explain the origin of this effect and characterize the parameter region where it occurs. Our work bridges theoretical insights with practical implementation, which is crucial for robust and scalable quantum networks., Comment: 8 pages, 8 figures

In quantum kernel learning, the primary method involves using a quantum computer to calculate the inner product between feature vectors, thereby obtaining a Gram matrix used as a kernel in machine learning models such as support vector machines (SVMs). However, a method for consistently achieving high performance has not been established. In this study, we investigate the diagnostic accuracy using a commercial dataset of a network service fault diagnosis system used by telecommunications carriers, focusing on quantum kernel learning, and propose a method to stably achieve high performance.We show significant performance improvements and an efficient achievement of high performance over conventional methods can be attained by applying quantum entanglement in the portion of the general quantum circuit used to create the quantum kernel, through input data parameter mapping and parameter tuning related to relative phase angles. Furthermore, experimental validation of the quantum kernel was conducted using IBM' s superconducting quantum computer IBM-Kawasaki, and its practicality was verified while applying the error suppression feature of Q-CTRL' s Fire Opal., Comment: Submitted to the IEEE International Conference on Quantum Computing and Engineering 2024

Satellite quantum communication is a promising way to build long distance quantum links, making it an essential complement to optical fiber for quantum internetworking beyond metropolitan scales. A satellite point to point optical link differs from the more common fiber links in many ways, both quantitative (higher latency, strong losses) and qualitative (nonconstant parameter values during satellite passage, intermittency of the link, impossibility to set repeaters between the satellite and the ground station). We study here the performance of a quantum link between two ground stations, using a quantum-memory-equipped satellite as a quantum repeater. In contrast with quantum key distribution satellite links, the number of available quantum memory slots m, together with the unavoidable round-trip communication latency t of at least a few milliseconds, severely reduces the effective average repetition rate to m/t -- at most a few kilohertz for foreseeable quantum memories. Our study uses two approaches, which validate each other: 1) a simple analytical model of the effective rate of the quantum link; 2) an event-based simulation using the open source Quantum Internet Simulation Package (QuISP). The important differences between satellite and fiber links led us to modify QuISP itself. This work paves the way to the study of hybrid satellite- and fiber-based quantum repeater networks interconnecting different metropolitan areas., Comment: 7 pages, 6 figures. Accepted for presentation at the IEEE International Conference on Quantum Computing and Engineering 2024

Estimating noise processes is an essential step for practical quantum information processing. Standard estimation tools require consuming valuable quantum resources. Here we ask the question of whether the noise affecting entangled states can be learned solely from the measurement statistics obtained during a distillation protocol. As a first step, we consider states of the Werner form and find that the Werner parameter can be estimated efficiently from the measurement statistics of an idealized distillation protocol. Our proposed estimation method can find application in scenarios where distillation is an unavoidable step., Comment: 3 pages, 1 figures, Proceedings of Quantum Systems and Computation Workshop in conjunction with ACM Sigmetrics (2023)

This paper introduces a process framework for debugging quantum circuits, focusing on three distinct types of circuit blocks: Amplitude Permutation, Phase Modulation, and Amplitude Redistribution circuit blocks. Our research addresses the critical need for specialized debugging approaches tailored to the unique properties of each circuit type. For Amplitude Permutation Circuits, we propose techniques to correct amplitude permutations mimicking classical operations. In phase modulation circuits, our proposed strategy targets the precise calibration of phase alterations essential for quantum computations. The most complex Amplitude Redistribution Circuits demand advanced methods to adjust probability amplitudes. This research bridges a vital gap in current methodologies and lays the groundwork for future advancements in quantum circuit debugging. Our contributions are twofold: We present a comprehensive unit testing tool (Cirquo) and debugging approaches tailored to the unique demands of quantum computing, and we provide empirical evidence of its effectiveness in optimizing quantum circuit performance. This work is a crucial step toward realizing robust quantum computing systems and their applications in various domains.

Hydraulic geometry parameters describing river hydrogeomorphic is important for flood forecasting. Although well-established, power-law hydraulic geometry curves have been widely used to understand riverine systems and mapping flooding inundation worldwide for the past 70 years, we have become increasingly aware of the limitations of these approaches. In the present study, we have moved beyond these traditional power-law relationships for river geometry, testing the ability of machine-learning models to provide improved predictions of river width and depth. For this work, we have used an unprecedentedly large river measurement dataset (HYDRoSWOT) as well as a suite of watershed predictor data to develop novel data-driven approaches to better estimate river geometries over the contiguous United States (CONUS). Our Random Forest, XGBoost, and neural network models out-performed the traditional, regionalized power law-based hydraulic geometry equations for both width and depth, providing R-squared values of as high as 0.75 for width and as high as 0.67 for depth, compared with R-squared values of 0.57 for width and 0.18 for depth from the regional hydraulic geometry equations. Our results also show diverse performance outcomes across stream orders and geographical regions for the different machine-learning models, demonstrating the value of using multi-model approaches to maximize the predictability of river geometry. The developed models have been used to create the newly publicly available STREAM-geo dataset, which provides river width, depth, width/depth ratio, and river and stream surface area (%RSSA) for nearly 2.7 million NHDPlus stream reaches across the rivers and streams across the contiguous US., Comment: 30 pages, 10 figures

The second quantum revolution has been picking up momentum over the last decade. Quantum technologies are starting to attract more attention from governments, private companies, investors, and public. The ability to control individual quantum systems for the purpose of information processing and communication is no longer a theoretical dream, but is steadily becoming routine in laboratories and startups around the world. With this comes the need to educate the future generation of quantum engineers. This textbook is a companion to our video lectures on Overview of Quantum Communications from the Q-Leap Education project known as Quantum Academy of Science and Technology. It is a gentle introduction to quantum networks, and is suitable for use as a textbook for undergraduate students of diverse background. No prior knowledge of quantum physics or quantum information is assumed. Exercises are included in each chapter., Comment: 308 pages, still an early draft, all comments are welcome!

Recent work has identified cosmic ray events as an error source limiting the lifetime of quantum data. These errors are correlated and affect a large number of qubits, leading to the loss of data across a quantum chip. Previous works attempting to address the problem in hardware or by building distributed systems still have limitations. We approach the problem from a different perspective, developing a new hybrid hardware-software-based strategy based on the 2-D surface code, assuming the parallel development of a hardware strategy that limits the phonon propagation radius. We propose to flee the area: move the logical qubits far enough away from the strike's epicenter to maintain our logical information. Specifically, we: (1) establish the minimum hardware requirements needed for our approach; (2) propose a mapping for moving logical qubits; and (3) evaluate the possible choice of the code distance. Our analysis considers two possible cosmic ray events: those far from both ``holes'' in the surface code and those near or overlapping a hole. We show that the probability that the logical qubit will be destroyed can be reduced from 100% to the range 4% to 15% depending on the time required to move the logical qubit.

Graph states are useful computational resources in quantum computing, particularly in measurement-based quantum computing models. However, compiling arbitrary graph states into executable form for fault-tolerant surface code execution and accurately estimating the compilation cost and the run-time resource cost remains an open problem. We introduce the Substrate Scheduler, a compiler module designed for fault-tolerant graph state compilation. The Substrate Scheduler aims to minimize the space-time volume cost of generating graph states. We show that Substrate Scheduler can efficiently compile graph states with thousands of vertices for "A Game of Surface Codes"-style patch-based surface code systems. Our results show that our module generates graph states with the lowest execution time complexity to date, achieving graph state generation time complexity that is at or below linear in the number of vertices and demonstrating specific types of graphs to have constant generation time complexity. Moreover, it provides a solid foundation for developing compilers that can handle a larger number of vertices, up to the millions or billions needed to accommodate a wide range of post-classical quantum computing applications., Comment: 11 pages, 11 figures

The all-photonic quantum repeater scheme, utilizing a type of graph state called the repeater graph state (RGS), promises resilience to photon losses and operational errors, offering a fast Bell pair generation rate limited only by the RGS creation time (rather than enforced round-trip waits). While existing research has predominantly focused on RGS generation and secret key sharing rate analysis, there is a need to extend investigations to encompass broader applications, such as distributed computation and teleportation, the main tasks envisioned for the Quantum Internet. Here we propose a new emitter-photonic qubit building block and an RGS protocol that addresses several key considerations: end node involvement in connection establishment, decoding of logical qubits within the RGS, and computing the Pauli frame corrections at each participating node to ensure the desired correct end-to-end Bell pair state. Our proposed building block significantly reduces the total number of emissive quantum memories required for end nodes and seamlessly integrates all-photonic and memory-based repeaters under the same communication protocol. We also present an algorithm for decoding logical measurement results, employing graphical reasoning based on graph state manipulation rules., Comment: 11 pages, 7 figures, (improve protocol details); comments welcome!

We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Thus far, promising quantum algorithms have been proposed to simulate quantum dynamics in non-relativistic regimes efficiently. However, only some studies have attempted to simulate relativistic dynamics due to its theoretical and computational difficulty. By leveraging the convergence of discrete-time quantum walks to the Dirac equation, we develop a quantum spectral method that approximates smooth solutions with exponential convergence. This mitigates errors in implementing potential functions and reduces the overall gate complexity that depends on errors. We demonstrate that our approach does not require additional operations compared to the asymptotic gate complexity of non-relativistic real-space algorithms. Our findings indicate that simulating relativistic dynamics is achievable with quantum computers and can provide insights into relativistic quantum physics and chemistry., Comment: 11 pages, 5 figures

A quantum network is expected to enhance distributed quantum computing and quantum communication over a long distance while providing unconditional security. As quantum entanglement is essential for a quantum network, major issues from various types of noise and decoherence prevent it from being realized, and research has been intensively active to obtain optimal configurations for a quantum network. In this work, we address the performance of a quantum network capable of quantum error correction and entanglement purification. Our results show that one should distribute Bell pairs as fast as possible while balancing the deployment of fidelity enhancement. We also show suitable hybrid strategies in quantum cryptography tasks under some noise regimes that need to use purification and quantum error correction together. Our results suggest that using purification to distribute high fidelity Bell pairs and preserving them for application using quantum error correction is a promising way to achieve a near-term quantum network for secure communication., Comment: 22 pages, 7 figures

In the era of quantum computing without full fault-tolerance, it is essential to suppress noise effects via the quantum error mitigation techniques to enhance the computational power of the quantum devices. One of the most effective noise-agnostic error mitigation schemes is the generalized quantum subspace expansion (GSE) method, which unifies various mitigation algorithms under the framework of the quantum subspace expansion. Specifically, the fault-subspace method, a subclass of GSE method, constructs an error-mitigated quantum state with copies of quantum states with different noise levels. However, from the experimental aspect, it is nontrivial to determine how to reliably amplify the noise so that the error in the simulation result is efficiently suppressed. In this work, we explore the potential of the fault-subspace method by leveraging the hardware-oriented noise: intentional amplification of the decoherence, noise boost by insertion of identity, making use of crosstalk, and probabilistic implementation of noise channel. We demonstrate the validity of our proposals via both numerical simulations with the noise parameters reflecting those in quantum devices available via IBM Quantum, and also experiments performed therein., Comment: 11 pages, 10 figures

As the scale of quantum programs grows to match that of classical software, the nascent field of quantum software engineering must mature and tools such as debuggers will become increasingly important. However, developing a quantum debugger is challenging due to the nature of a quantum computer; sneaking a peek at the value of a quantum state will cause either partial or complete collapse of the superposition and may destroy the necessary entanglement. As a first step to developing a full quantum circuit debugger, we have designed and implemented a quantum circuit debugging tool. The tool allows the user to divide the circuit vertically or horizontally into smaller chunks known as slices, and manage their simulation or execution for either interactive debugging or automated testing. The tool also enables developers to track gates within the overall circuit and each chunk to understand their behavior better. Feedback on usefulness and usability from early users shows that using the tool to slice and test their circuits has helped make the debugging process more time-efficient for them.

We propose an algorithm using a modified variant of amplitude amplification to solve combinatorial optimization problems via the use of a subdivided phase oracle. Instead of dividing input states into two groups and shifting the phase equally for all states within the same group, the subdivided phase oracle changes the phase of each input state uniquely in proportion to their objective value. We provide visualization of how amplitudes change after each iteration of applying the subdivided phase oracle followed by conventional Grover diffusion in the complex plane. We then show via numerical simulation that for normal, skew normal, and exponential distribution of objective values, the algorithm can be used to amplify the probability of measuring the optimal solution to a significant degree independent of the search space size. In the case of skew normal and exponential distributions, this probability can be amplified to be close to unity, making our algorithm near deterministic. We then modify our algorithm in order to demonstrate how it can be extended to a broader set of objective value distributions. Finally, we discuss the speedup compared to classical schemes using the query complexity model, and show that our algorithm offers a significant advantage over these classical approaches., Comment: 9 pages, 7 figures, comments welcome

Quantum error correction holds the key to scaling up quantum computers. Cosmic ray events severely impact the operation of a quantum computer by causing chip-level catastrophic errors, essentially erasing the information encoded in a chip. Here, we present a distributed error correction scheme to combat the devastating effect of such events by introducing an additional layer of quantum erasure error correcting code across separate chips. We show that our scheme is fault tolerant against chip-level catastrophic errors and discuss its experimental implementation using superconducting qubits with microwave links. Our analysis shows that in state-of-the-art experiments, it is possible to suppress the rate of these errors from 1 per 10 seconds to less than 1 per month.

We present an event-driven simulation package called QuISP for large-scale quantum networks built on top of the OMNeT++ discrete event simulation framework. Although the behavior of quantum networking devices have been revealed by recent research, it is still an open question how they will work in networks of a practical size. QuISP is designed to simulate large-scale quantum networks to investigate their behavior under realistic, noisy and heterogeneous configurations. The protocol architecture we propose enables studies of different choices for error management and other key decisions. Our confidence in the simulator is supported by comparing its output to analytic results for a small network. A key reason for simulation is to look for emergent behavior when large numbers of individually characterized devices are combined. QuISP can handle thousands of qubits in dozens of nodes on a laptop computer, preparing for full Quantum Internet simulation. This simulator promotes the development of protocols for larger and more complex quantum networks., Comment: 17 pages, 12 figures

Entangled quantum communication is advancing rapidly, with laboratory and metropolitan testbeds under development, but to date there is no unifying Quantum Internet architecture. We propose a Quantum Internet architecture centered around the Quantum Recursive Network Architecture (QRNA), using RuleSet-based connections established using a two-pass connection setup. Scalability and internetworking (for both technological and administrative boundaries) are achieved using recursion in naming and connection control. In the near term, this architecture will support end-to-end, two-party entanglement on minimal hardware, and it will extend smoothly to multi-party entanglement and the use of quantum error correction on advanced hardware in the future. For a network internal gateway protocol, we recommend (but do not require) qDijkstra with seconds per Bell pair as link cost for routing; the external gateway protocol is designed to build recursively. The strength of our architecture is shown by assessing extensibility and demonstrating how robust protocol operation can be confirmed using the RuleSet paradigm., Comment: 17 pages, 7 numbered figures

In the NISQ era, multi-programming of quantum circuits (QC) helps to improve the throughput of quantum computation. Although the crosstalk, which is a major source of noise on NISQ processors, may cause performance degradation of concurrent execution of multiple QCs, its characterization cost grows quadratically in processor size. To address these challenges, we introduce palloq (parallel allocation of QCs) for improving the performance of quantum multi-programming on NISQ processors while paying attention to the combination of QCs in parallel execution and their layout on the quantum processor, and reducing unwanted interference between QCs caused by crosstalk. We also propose a software-based crosstalk detection protocol that efficiently and successfully characterizes the hardware's suitability for multi-programming. We found a trade-off between the success rate and execution time of the multi-programming. This would be attractive not only to quantum computer service but also to users around the world who want to run algorithms of suitable scale on NISQ processors that have recently attracted great attention and are being enthusiastically investigated., Comment: 10 pages, 10 figures

The discrete logarithm problem (DLP) is the basis for several cryptographic primitives. Since Shor's work, it has been known that the DLP can be solved by combining a polynomial-size quantum circuit and a polynomial-time classical post-processing algorithm. Evaluating and predicting the instance size that quantum devices can solve is an emerging research topic. In this paper, we propose a quantitative measure based on the success probability of the post-processing algorithm to determine whether an experiment on a quantum device (or a classical simulator) succeeded. We also propose a procedure to modify bit strings observed from a Shor circuit to increase the success probability of a lattice-based post-processing algorithm. We report preliminary experiments conducted on IBM-Quantum quantum computers and near-future predictions based on noisy-device simulations. We conducted our experiments with the ibm_kawasaki device and discovered that the simplest circuit (7 qubits) from a 2-bit DLP instance achieves a sufficiently high success probability to proclaim the experiment successful. Experiments on another circuit from a slightly harder 2-bit DLP instance, on the other hand, did not succeed, and we determined that reducing the noise level by half is required to achieve a successful experiment. Finally, we give a near-term prediction based on required noise levels to solve some selected small DLP and integer factoring instances.

An open problem of quantum information theory has been to determine under what conditions universal exchange-only computation is possible for qudits encoded on $d$-state systems for $d>2$. This problem can be posed in terms of representation theory by recognizing that each quantum mechanical swap, generated by exchange-interaction, can be identified with a transposition in a symmetric group, each $d$-state system can be identified with the fundamental representation of $SU(d)$, and each encoded qudit can be identified with an irreducible representation of a Lie algebra generated by transpositions. Towards this end we first give a mathematical definition of exchange-only universality in terms of a map from the special unitary algebra on the product of qudits into a representation of a Lie algebra generated by transpositions. We show that this definition is consistent with quantum computing requirements. We then proceed with the task of characterizing universal families of qudits, that is families of encoded qudits admitting exchange-only universality. This endeavor is aided by the fact that the irreducible representations corresponding to qudits are canonically labeled by partitions. In particular we derive necessary and sufficient conditions for universality on one or two such qudits, in terms of simple arithmetic conditions on the associated partitions. We also derive necessary and sufficient conditions for universality on arbitrarily many such qudits, in terms of Littlewood--Richardson coefficients. Among other results, we prove that universal families of multiple qudits are upward closed, that universality is guaranteed for sufficiently many qudits, and that any family that is not universal can be made so by simply adding at most five ancillae. We also obtain results for 2-state systems as a special case., Comment: PhD thesis in mathematics for the University of Colorado at Boulder

Control modular addition is a core arithmetic function, and we must consider the computational cost for actual quantum computers to realize efficient implementation. To achieve a low computational cost in a control modular adder, we focus on minimizing KQ, defined by the product of the number of qubits and the depth of the circuit. In this paper, we construct an efficient control modular adder with small KQ by using relative-phase Toffoli gates in two major types of quantum computers: Fault-Tolerant Quantum Computers (FTQ) on the Logical layer and Noisy Intermediate-Scale Quantum Computers (NISQ). We give a more efficient construction compared to Van Meter and Itoh's, based on a carry-lookahead adder. In FTQ, $T$ gates incur heavy cost due to distillation, which fabricates ancilla for running $T$ gates with high accuracy but consumes a lot of specially prepared ancilla qubits and a lot of time. Thus, we must reduce the number of $T$ gates. We propose a new control modular adder that uses only 20% of the number of $T$ gates of the original. Moreover, when we take distillation into consideration, we find that we minimize $\text{KQ}_{T}$ (the product of the number of qubits and $T$-depth) by running $\Theta\left(n / \sqrt{\log n} \right)$ $T$ gates simultaneously. In NISQ, CNOT gates are the major error source. We propose a new control modular adder that uses only 35% of the number of CNOT gates of the original. Moreover, we show that the $\text{KQ}_{\text{CX}}$ (the product of the number of qubits and CNOT-depth) of our circuit is 38% of the original. Thus, we realize an efficient control modular adder, improving prospects for the efficient execution of arithmetic in quantum computers.

Algorithms for triangle-finding, the smallest nontrivial instance of the k-clique problem, have been proposed for quantum computers. Still, those algorithms assume the use of fixed access time quantum RAM (QRAM). We present a practical gate-based approach to both the triangle-finding problem and its NP-hard k-clique generalization. We examine both constant factors for near-term implementation on a Noisy Intermediate Scale Quantum computer (NISQ) device, and the scaling of the problem to evaluate long-term use of quantum computers. We compare the time complexity and circuit practicality of the theoretical approach and actual implementation. We propose and apply two different strategies to the k-clique problem, examining the circuit size of Qiskit implementations. We analyze our implementations by simulating triangle finding with various error models, observing the effect on damping the amplitude of the correct answer, and compare to execution on six real IBMQ machines. Finally, we estimate the date when the methods proposed can run effectively on an actual device based on IBM's quantum volume exponential growth forecast and the results of our error analysis.

The main service provided by the coming Quantum Internet will be creating entanglement between any two quantum nodes. We discuss and classify attacks on quantum repeaters, which will serve roles similar to those of classical Internet routers. We have modeled the components for and structure of quantum repeater network nodes. With this model, we point out attack vectors, then analyze attacks in terms of confidentiality, integrity and availability. While we are reassured about the promises of quantum networks from the confidentiality point of view, integrity and availability present new vulnerabilities not present in classical networks and require care to handle properly. We observe that the requirements on the classical computing/networking elements affect the systems' overall security risks. This component-based analysis establishes a framework for further investigation of network-wide vulnerabilities., Comment: 16 pages, 5 figures

Because noisy, intermediate-scale quantum (NISQ) machines accumulate errors quickly, we need new approaches to designing NISQ-aware algorithms and assessing their performance. Algorithms with characteristics that appear less desirable under ideal circumstances, such as lower success probability, may in fact outperform their ideal counterparts on existing hardware. We propose an adaptation of Grover's algorithm, subdividing the phase flip into segments to replace a digital counter and complex phase flip decision logic. We applied this approach to obtaining the best solution of the MAX-CUT problem in sparse graphs, utilizing multi-control, Toffoli-like gates with residual phase shifts. We implemented this algorithm on IBM Q processors and succeeded in solving a 5-node MAX-CUT problem, demonstrating amplitude amplification on four qubits. This approach will be useful for a range of problems, and may shorten the time to reaching quantum advantage., Comment: 17 pages, 24 figures

Quantum network coding has been proposed to improve resource utilization to support distributed computation but has not yet been put in to practice. We investigate a particular implementation of quantum network coding using measurement-based quantum computation on IBM Q processors. We compare the performance of quantum network coding with entanglement swapping and entanglement distribution via linear cluster states. These protocols outperform quantum network coding in terms of the final Bell pair fidelities but are unsuitable for optimal resource utilization in complex networks with contention present. We demonstrate the suitability of noisy intermediate-scale quantum (NISQ) devices such as IBM Q for the study of quantum networks. We also identify the factors that limit the performance of quantum network coding on these processors and provide estimates or error rates required to boost the final Bell pair fidelities to a point where they can be used for generation of genuinely random cryptographic keys among other useful tasks. Surprisingly, the required error rates are only around a factor of 2 smaller than the current status and we expect they will be achieved in the near future., Comment: 10 pages, 8 figures