It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical Hoelder classes with d variables. The optimal orders for the complexity of deterministic and (general) randomized methods are known. We obtain the respective optimal orders for quantum algorithms and also for restricted Monte Carlo (only coin tossing instead of general random numbers). To summarize the results one can say that (1) there is an exponential speed-up of quantum algorithms over deterministic (classical) algorithms, if the smoothness is small; (2) there is a (roughly) quadratic speed-up of quantum algorithms over randomized classical methods, if the smoothness is small.
Monte Carlo integration approximates an integral of a black-box function by taking the average of many evaluations (i.e., samples) of the function (integrand). For $N$ queries of the integrand, Monte Carlo integration achieves the estimation error of $O(1/ \sqrt{N})$. Recently, Johnston introduced quantum supersampling (QSS) into rendering as a numerical integration method that can run on quantum computers. QSS breaks the fundamental limitation of the $O(1/ \sqrt{N})$ convergence rate of Monte Carlo integration and achieves the faster convergence rate. We introduce yet another quantum numerica…
This paper proposes a method of quantum Monte Carlo integration that retains the full quadratic quantum advantage, without requiring any arithmetic or quantum phase estimation to be performed on the quantum computer. No previous proposal for quantum Monte Carlo integration has achieved all of these at once. The heart of the proposed method is a Fourier series decomposition of the sum that approximates the expectation in Monte Carlo integration, with each component then estimated individually using quantum amplitude estimation. The main result is presented as theoretical statement of asymptotic…
Recently, Belhadi and al. (2014) developed a new approach to quantize classical soluble systems based on the calculation of brackets among fundamental variables using the constants of integration (CI method). In this paper, we will apply this approach in some exactly soluble constrained Hamiltonian systems. We will complete our work with some applications in quantum field theory : Majorana neutrino, the scalar field on the light-cone, the O(2) nonlinear sigma model and the chiral boson theory. Key words : Quantization, constrainted systems, field theory, soluble systems, integration constants.
We apply quantum integration to elementary particle-physics processes. In particular, we look at scattering processes such as ${\rm e}^+{\rm e}^- \to q \bar q$ and ${\rm e}^+{\rm e}^- \to q \bar q' {\rm W}$. The corresponding probability distributions can be first appropriately loaded on a quantum computer using either quantum Generative Adversarial Networks or an exact method. The distributions are then integrated sing the method of Quantum Amplitude Estimation which shows a quadratic speed-up with respect to classical techniques. In simulations of noiseless quantum computers, we obtain per-c…
We propose a minimally invasive optical overlay for time-interleaved QRNG operation in NG-PON2 transceivers. We experimentally demonstrate that random numbers can be generated at a 0.5 Gb/s rate and validate the randomness through statistical tests.
This paper addresses the practical aspects of quantum algorithms used in numerical integration, specifically their implementation on Noisy Intermediate-Scale Quantum (NISQ) devices. Quantum algorithms for numerical integration utilize Quantum Amplitude Estimation (QAE) (Brassard et al., 2002) in conjunction with Grovers algorithm. However, QAE is daunting to implement on NISQ devices since it typically relies on Quantum Phase Estimation (QPE), which requires many ancilla qubits and controlled operations. To mitigate these challenges, a recently published QAE algorithm (Suzuki et al., 2020), wh…
A heterogeneous III-V/silicon integration platform for on-chip quantum photonic circuits with single quantum dot devices
光子集成是光子量子科学的一项使能技术，提供比传统体光学更大的可扩展性、稳定性和功能性。在这里，我们描述了一个可扩展的，异构的III-V/硅集成平台，以生产硅$_3$ N $_4$光子电路，将GaAs基纳米光子器件含有自组装的InAs/GaAs量子点。我们证明了纯单光子发射从GaAs波导和腔中的单个量子点-其中观察到自发发射率的强控制-直接发射到Si $_3$ N $_4$波导中，通过倏逝波耦合效率> 90%。迄今为止，InAs/GaAs量子点构成了最有前途的固态触发单光子源，提供明亮、纯净且难以区分的发射，并且可以通过电学和光学控制。Si $_3$ N $_4$波导提供低损耗传播、可定制的色散和高克尔非线性，这对于线性和非线性光信号处理到量子水平是理想的。我们将这两者结合在一个集成平台中，这将使一类新的可扩展，高效和通用的集成量子光子器件成为可能。
Identifying computational tasks suitable for (future) quantum computers is an active field of research. Here we explore utilizing quantum computers for the purpose of solving differential equations. We consider two approaches: (i) basis encoding and fixed-point arithmetic on a digital quantum computer, and (ii) representing and solving high-order Runge-Kutta methods as optimization problems on quantum annealers. As realizations applied to two-dimensional linear ordinary differential equations, we devise and simulate corresponding digital quantum circuits, and implement and run a 6$^{\mathrm{th…
Hexagonal boron nitride (hBN) is gaining interest for potential applications in integrated quantum nanophotonics. Yet, to establish hBN as an integrated photonic platform several cornerstones must be established, including the integration and coupling of quantum emitters to photonic waveguides. Supported by simulations, we study the approach of monolithic integration, which is expected to have coupling efficiencies that are 4 times higher than those of a conventional hybrid stacking strategy. We then demonstrate the fabrication of such devices from hBN and showcase the successful integration o…
In this work, using the noncommutative integration method of linear differential equations, we obtain a complete set of solutions to the Schrodinger equation for a quantum asymmetric top in Euler angles. It is shown that the noncommutative reduction of the Schrodinger equation leads to the Lame equation. The resulting set of solutions is determined by the Lame polynomials in a complex parameter, which is related to the geometry of the orbits of the coadjoint representation of the rotation group. The spectrum of an asymmetric top is obtained from the condition that the solutions are invariant w…
The speedup of heavy numerical tasks by quantum computing is now actively investigated in various fields including data analysis in physics and astronomy. In this paper, we propose a new quantum algorithm for matched filtering in gravitational wave (GW) data analysis based on the previous work by Gao et al., Phys. Rev. Research 4, 023006 (2022) [arXiv:2109.01535]. Our approach uses the quantum algorithm for Monte Carlo integration for the signal-to-noise ratio (SNR) calculation instead of the fast Fourier transform used in Gao et al. and searches signal templates with high SNR by quantum ampli…
The goal of integrated quantum photonics is to combine components for the generation, manipulation, and detection of non-classical light in a phase stable and efficient platform. Solid-state quantum emitters have recently reached outstanding performance as single photon sources. In parallel, photonic integrated circuits have been advanced to the point that thousands of components can be controlled on a chip with high efficiency and phase stability. Consequently, researchers are now beginning to combine these leading quantum emitters and photonic integrated circuit platforms to realize the best…
Spins in semiconductor quantum dots are a candidate for cryogenic quantum processors due to their exceptionally long coherence times. One major challenge to scaling quantum dot spin qubits is the dense wiring requirements, making it difficult to envision fabricating large arrays of nearest-neighbor-coupled qubits necessary for error correction. We describe a method to solve this problem by spacing the qubits out using high-impedance superconducting resonators with a 2D grid unit cell area of $0.16~\text{mm}^2$ using 3D integration. To prove the viability of this approach, we demonstrate 3D int…
Integrated quantum photonic circuits (IQPCs) with deterministically integrated quantum emitters are critical elements for scalable quantum information applications and have attracted significant attention in recent years. However, scaling up them towards fully functional photonic circuits with multiple deterministically integrated quantum emitters to generate photonic input states remains a great challenge. In this work, we report on a monolithic prototype IQPC consisting of two pre-selected quantum dots deterministically integrated into nanobeam cavities at the input ports of a 2x2 multimode …
The realization of a functional quantum repeater is one of the major research goals in long-distance quantum communication. Among the different approaches that are being followed, the one relying on quantum memories interfaced with deterministic quantum emitters is considered as among one of the most promising solutions. In this work, we focus on memory-based quantum-repeater schemes that rely on semiconductor quantum dots for the generation of polarization entangled photons. Going through the most relevant figures of merit related to efficiency of the photon source, we select significant deve…
Thin film 4H-silicon carbide (4H-SiC) is emerging as a contender for realizing large-scale optical quantum circuits due to its high CMOS technology compatibility and large optical nonlinearities. Though, challenges remain in producing wafer-scale 4H-SiC thin film on insulator (4H-SiCOI) for dense integration of photonic circuits, and in efficient coupling of deterministic quantum emitters that are essential for scalable quantum photonics. Here we demonstrate hybrid integration of self-assembled InGaAs quantum dots (QDs) based single-photon sources (SPSs) with wafer-scale 4H-SiC photonic chips …
