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DQRA: Deep Quantum Routing Agent for Entanglement Routing in Quantum Networks
DQRA: عامل مسیریابی کوانتومی عمیق برای مسیریابی درهم تنیده در شبکه های کوانتومی-2022 Quantum routing plays a key role in the development of the next-generation network system. In
particular, an entangled routing path can be constructed with the help of quantum entanglement and swapping
among particles (e.g., photons) associated with nodes in the network. From another side of computing,
machine learning has achieved numerous breakthrough successes in various application domains, including
networking. Despite its advantages and capabilities, machine learning is not as much utilized in quantum
networking as in other areas. To bridge this gap, in this article, we propose a novel quantum routing model
for quantum networks that employs machine learning architectures to construct the routing path for the
maximum number of demands (source–destination pairs) within a time window. Specifically, we present a
deep reinforcement routing scheme that is called Deep Quantum Routing Agent (DQRA). In short, DQRA
utilizes an empirically designed deep neural network that observes the current network states to accommodate
the network’s demands, which are then connected by a qubit-preserved shortest path algorithm. The training
process of DQRA is guided by a reward function that aims toward maximizing the number of accommodated
requests in each routing window. Our experiment study shows that, on average, DQRA is able to maintain a
rate of successfully routed requests at above 80% in a qubit-limited grid network and approximately 60% in
extreme conditions, i.e., each node can be repeater exactly once in a window. Furthermore, we show that the
model complexity and the computational time of DQRA are polynomial in terms of the sizes of the quantum
networks.
INDEX TERMS: Deep learning | deep reinforcement learning (DRL) | machine learning | next-generation network | quantum network routing | quantum networks. |
مقاله انگلیسی |
2 |
Efficient Floating Point Arithmetic for Quantum Computers
محاسبات ممیز شناور کارآمد برای کامپیوترهای کوانتومی-2022 One of the major promises of quantum computing is the realization of SIMD (single
instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the
state space grows exponentially with the number of qubits, we can easily reach situations where we pay less
than a single quantum gate per data point for data-processing instructions, which would be rather expensive
in classical computing. Formulating such instructions in terms of quantum gates, however, still remains
a challenging task. Laying out the foundational functions for more advanced data-processing is therefore a
subject of paramount importance for advancing the realm of quantum computing. In this paper, we introduce
the formalism of encoding so called-semi-boolean polynomials. As it turns out, arithmetic Z=2nZ ring
operations can be formulated as semi-boolean polynomial evaluations, which allows convenient generation
of unsigned integer arithmetic quantum circuits. For arithmetic evaluations, the resulting algorithm has been
known as Fourier-arithmetic. We extend this type of algorithm with additional features, such as ancillafree in-place multiplication and integer coefficient polynomial evaluation. Furthermore, we introduce a
tailor-made method for encoding signed integers succeeded by an encoding for arbitrary floating-point
numbers. This representation of floating-point numbers and their processing can be applied to any quantum algorithm that performs unsigned modular integer arithmetic. We discuss some further performance
enhancements of the semi boolean polynomial encoder and finally supply a complexity estimation. The
application of our methods to a 32-bit unsigned integer multiplication demonstrated a 90% circuit depth
reduction compared to carry-ripple approaches.
INDEX TERMS: Quantum arithmetic | quantum computing | floating point arithmetic. |
مقاله انگلیسی |
3 |
Efficient Hardware Implementation of Finite Field Arithmetic AB + C for Binary Ring-LWE Based Post-Quantum Cryptography
اجرای سخت افزار کارآمد محاسبات میدان محدود AB + C برای رمزنگاری پس کوانتومی مبتنی بر حلقه باینری-LWE-2022 Post-quantum cryptography (PQC) has gained significant attention from the community
recently as it is proven that the existing public-key cryptosystems are vulnerable to the attacks launched from
the well-developed quantum computers. The finite field arithmetic AB þ C, where A and C are integer polynomials and B is a binary polynomial, is the key component for the binary Ring-learning-with-errors (BRLWE)-
based encryption scheme (a low-complexity PQC suitable for emerging lightweight applications). In this paper,
we propose a novel hardware implementation of the finite field arithmetic AB þ C through three stages of interdependent efforts: (i) a rigorous mathematical formulation process is presented first; (ii) an efficient hardware
architecture is then presented with detailed description; (iii) a thorough implementation has also been given
along with the comparison. Overall, (i) the proposed basic structure (u ¼ 1) outperforms the existing designs,
e.g., it involves 55.9% less area-delay product (ADP) than [13] for n ¼ 512; (ii) the proposed design also offers
very efficient performance in time-complexity and can be used in many future applications.
INDEX TERMS: Binary ring-learning-with-errors | finite field arithmetic | FPGA platform | hardware design | post-quantum cryptography |
مقاله انگلیسی |
4 |
Efficient Quantum State Preparation for the Cauchy Distribution Based on Piecewise Arithmetic
آماده سازی حالت کوانتومی کارآمد برای توزیع کوشی بر اساس حساب تکه ای-2022 The benefits of the quantum Monte Carlo algorithm heavily rely on the efficiency of the
superposition state preparation. So far, most reported Monte Carlo algorithms use the Grover–Rudolph state
preparation method, which is suitable for efficiently integrable distribution functions. Consequently, most reported works are based on log-concave distributions, such as normal distributions. However, non-log-concave
distributions still have many uses, such as in financial modeling. Recently, a new method was proposed
that does not need integration to calculate the rotation angle for state preparation. However, performing
efficient state preparation is still difficult due to the high cost associated with high precision and low error
in the calculation for the rotation angle. Many methods of quantum state preparation use polynomial Taylor
approximations to reduce the computation cost. However, Taylor approximations do not work well with
heavy-tailed distribution functions that are not bounded exponentially. In this article, we present a method
of efficient state preparation for heavy-tailed distribution functions. Specifically, we present a quantum
gate-level algorithm to prepare quantum superposition states based on the Cauchy distribution, which is a
non-log-concave heavy-tailed distribution. Our procedure relies on a piecewise polynomial function instead
of a single Taylor approximation to reduce computational cost and increase accuracy. The Cauchy distribution is an even function, so the proposed piecewise polynomial contains only a quadratic term and a constant
term to maintain the simplest approximation of an even function. Numerical analysis shows that the required
number of subdomains increases linearly as the approximation error decreases exponentially. Furthermore,
the computation complexity of the proposed algorithm is independent of the number of subdomains in the
quantum implementation of the piecewise function due to quantum parallelism. An example of the proposed
algorithm based on a simulation conducted in Qiskit is presented to demonstrate its capability to perform
state preparation based on the Cauchy distribution.
INDEX TERMS: Algorithms | gate operations | quantum computing. |
مقاله انگلیسی |
5 |
Epsilon-Nets, Unitary Designs, and Random Quantum Circuits
شبکه های اپسیلون، طرح های واحد و مدارهای کوانتومی تصادفی-2022 Epsilon-nets and approximate unitary t-designs are
natural notions that capture properties of unitary operations
relevant for numerous applications in quantum information
and quantum computing. In this work we study quantitative
connections between these two notions. Specifically, we prove
that, for d dimensional Hilbert space, unitaries constituting
δ-approximate t-expanders form -nets for t d5/2 and δ
3d/2 d2. We also show that for arbitrary t, -nets can be used
to construct δ-approximate unitary t-designs for δ t, where
the notion of approximation is based on the diamond norm.
Finally, we prove that the degree of an exact unitary t design
necessary to obtain an -net must grow at least as fast as 1 (for
fixed dimension) and not slower than d2 (for fixed ). This shows
near optimality of our result connecting t-designs and nets.
We apply our findings in the context of quantum computing.
First, we show that that approximate t-designs can be generated
by shallow random circuits formed from a set of universal twoqudit gates in the parallel and sequential local architectures
considered in (Brandão et al., 2016). Importantly, our gate sets
need not to be symmetric (i.e., contains gates together with
their inverses) or consist of gates with algebraic entries. Second,
we consider compilation of quantum gates and prove a nonconstructive Solovay-Kitaev theorem for general universal gate
sets. Our main technical contribution is a new construction of
efficient polynomial approximations to the Dirac delta in the
space of quantum channels, which can be of independent interest.]
Index Terms: Unitary designs, epsilon nets | random quantum circuits | compilation of quantum gates | unitary channels. |
مقاله انگلیسی |
6 |
Learning Quantum Drift-Diffusion Phenomenon by Physics-Constraint Machine Learning
یادگیری پدیده رانش کوانتومی- انتشار با یادگیری ماشین محدودیت فیزیک-2022 Recently, deep learning (DL) is widely used to
detect physical phenomena and has obtained encouraging results.
Several works have shown that it can learn quantum phenomenon. Subsequently, quantum machine learning (QML) has
been paid more attention by academia and industry. Quantum
drift-diffusion (QDD) is a commonplace physical phenomenon,
which is a macroscopic description of electrons and holes in
a semiconductor. They are commonly used to attain an understanding of the property of semiconductor devices in physics
and engineering. We are motivated by the relaxation-time limit
from the quantum-Navier-Stokes-Poisson system (QNSP) to the
QDD equation and the existence of finite energy weak solutions
to the QDD equation has been proved. Therefore, in this work,
the quantum drift-diffusion learning neural network (QDDLNN)
is proposed to investigate the quantum drift phenomena from
limited observations. Furthermore, a piece of numerical evidence
is found that the NNs can describe quantum transport phenomena by simulating the quantum confinement transport equationquantum Navier-Stokes equation.
Index Terms: Quantum machine learning | quantum drift diffusion | physical-information learning | quantum transport | quantum fluid model. |
مقاله انگلیسی |
7 |
Quantum Algorithm for Fidelity Estimation
الگوریتم کوانتومی برای برآورد وفاداری-2022 For two unknown mixed quantum states ρ and σ in
an N-dimensional Hilbert space, computing their fidelity F (ρ, σ)
is a basic problem with many important applications in quantum
computing and quantum information, for example verification
and characterization of the outputs of a quantum computer,
and design and analysis of quantum algorithms. In this paper,
we propose a quantum algorithm that solves this problem in
poly(log(N ), r, 1/ε) time, where r is the lower rank of ρ and
σ, and ε is the desired precision, provided that the purifications
of ρ and σ are prepared by quantum oracles. This algorithm
exhibits an exponential speedup over the best known algorithm
(based on quantum state tomography) which has time complexity
polynomial in N. keywords: Quantum computing | quantum algorithms | quantum fidelity | quantum states. |
مقاله انگلیسی |
8 |
Quantum Cryptanalysis on a Multivariate Cryptosystem Based on Clipped Hopfield Neural Network
رمزگذاری کوانتومی بر روی یک سیستم رمزنگاری چند متغیره بر اساس شبکه عصبی هاپفیلد بریده شده-2022 Shor’s quantum algorithm and other efficient quantum
algorithms can break many public-key cryptographic schemes in polynomial time on a quantum computer. In response, researchers proposed
postquantum cryptography to resist quantum computers. The multivariate cryptosystem (MVC) is one of a few options of postquantum
cryptography. It is based on the NP-hardness of the computational
problem to solve nonlinear equations over a finite field. Recently,
Wang et al. (2018) proposed a MVC based on extended clipped hopfield
neural networks (eCHNN). Its main security assumption is backed by the
discrete logarithm (DL) problem over Matrics. In this brief, we present
quantum cryptanalysis of Wang et al.’s eCHNN-based MVC. We first
show that Shor’s quantum algorithm can be modified to solve the DL
problem over Matrics. Then we show that Wang et al.’s construction
of eCHNN-based MVC is not secure against quantum computers; this
against the original intention of that multivariate cryptography is one of
a few options of postquantum cryptography.
keywords: Clipped Hopfiled neural network | Diffie-Hellman key exchange scheme | discrete logarithm (DL) problem | multivariate cryptography | quantum algorithm. |
مقاله انگلیسی |
9 |
Quantum Radon Transforms and Their Applications
تبدیل کوانتومی رادون و کاربردهای آنها-2022 This article extends the Radon transform, a classical image-processing tool for fast tomography
and denoising, to the quantum computing platform. A new kind of periodic discrete Radon transform
(PDRT), called the quantum periodic discrete Radon transform (QPRT), is proposed. The quantum imple-
mentation of QPRT based on the amplitude encoding method is exponentially faster than the classical PDRT.
We design an efficient quantum image denoising algorithm using QPRT. The simulation results show that
QPRT preserves good denoising capability as in the classical PDRT. Also, a quantum algorithm for IDRT
is proposed, which can be used for fast line detection. Both the quantum extension of IDRT and the line
detection algorithm can provide polynomial speedups over the classical counterparts in certain cases. keywords: Quantum computing | radon transform. |
مقاله انگلیسی |
10 |
The Present and Future of Discrete Logarithm Problems on Noisy Quantum Computers
حال و آینده مسائل لگاریتم گسسته در کامپیوترهای کوانتومی پر سر و صدا-2022 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 postprocessing algorithm. The theoretical result corresponds the situation
where a quantum device working with a medium number of qubits of very small errors can solve the DLP.
However, all the quantum devices that we can use have a limited number of noisy qubits, as of the noisy
intermediate-scale quantum (NISQ) era. Thus, evaluating the instance size that the latest quantum device can
solve and giving a future prediction of the size along the progress of quantum devices are emerging research
topics. This article contains two proposals to discuss the performance of quantum devices against the DLP in
the NISQ era: 1) a quantitative measure based on the success probability of the postprocessing algorithm to
determine whether an experiment on a quantum device (or a classical simulator) succeeded; and 2) a procedure to modify bit strings observed from a Shor’s circuit to increase the success probability of a lattice-based
postprocessing algorithm. In this article, 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 DLPs and integer factoring instances.
INDEX TERMS: Discrete logarithm problem (DLP) | IBM quantum | lattice | postprocessing method | Shor’s algorithm. |
مقاله انگلیسی |