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Register a new userQuantum self-learning Monte Carlo with quantum Fourier transform sampler
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The self-learning Metropolis-Hastings algorithm is a powerful Monte Carlo method that, with the help of machine learning, adaptively generates an easy-to-sample probability distribution for approximating a given hard-to-sample distribution. This paper provides a new self-learning Monte Carlo method that utilizes a quantum computer to output a proposal distribution. In particular, we show a novel subclass of this general scheme based on the quantum Fourier transform circuit; this sampler is classically simulable while having a certain advantage over conventional methods. The performance of this quantum inspired algorithm is demonstrated by some numerical simulations.
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The Quantum Fourier Transformation ($QFT$) is a key building block for a whole wealth of quantum algorithms. Despite its proven efficiency, only a few proof-of-principle demonstrations have been reported. Here we utilize $QFT$ to enhance the performance of a quantum sensor. We implement the $QFT$ algorithm in a hybrid quantum register consisting of a nitrogen-vacancy (NV) center electron spin and three nuclear spins. The $QFT$ runs on the nuclear spins and serves to process the sensor - NV electron spin signal. We demonstrate $QFT$ for quantum (spins) and classical signals (radio frequency (RF) ) with near Heisenberg limited precision scaling. We further show the application of $QFT$ for demultiplexing the nuclear magnetic resonance (NMR) signal of two distinct target nuclear spins. Our results mark the application of a complex quantum algorithm in sensing which is of particular interest for high dynamic range quantum sensing and nanoscale NMR spectroscopy experiments.
Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms where a considerable amount of ancilla qubits and gates are often needed to form a Hilbert space large enough for high-precision results. Qubit recycling reduces the number of ancilla qubits to one but imposes the requirement of repeated measurements and feedforward within the coherence time of the qubits. Moreover, recycling only applies to certain cases where QFT can be carried out in a semi-classical way. Here, we report a novel approach based on two harmonic resonators which form a high-dimensional Hilbert space for the realization of QFT. By employing the all-resonant and perfect state-transfer methods, we develop a protocol that transfers an unknown multi-qubit state to one resonator. QFT is performed by the free evolution of the two resonators with a cross-Kerr interaction. Then, the fully-quantum result can be localized in the second resonator by a projective measurement. Qualitative analysis shows that a 2^10-dimensional QFT can be realized in current superconducting quantum circuits which paves the way for implementing various quantum algorithms in the noisy intermediate-scale quantum (NISQ) era.
Fourier transform spectroscopy with classical interferometry corresponds to the measurement of a single-photon intensity spectrum from the viewpoint of the particle nature of light. In contrast, the Fourier transform of two-photon quantum interference patterns provides the intensity spectrum of the two photons as a function of the sum or difference frequency of the constituent photons. This unique feature of quantum interferometric spectroscopy offers a different type of spectral information from the classical measurement and may prove useful for nonlinear spectroscopy with two-photon emission. Here, we report the first experimental demonstration of two-photon quantum interference of photon pairs emitted via biexcitons in the semiconductor CuCl. Besides applying Fourier transform to quantum interference patterns, we reconstruct the intensity spectrum of the biexciton luminescence in the two-photon sum or difference frequency. We discuss the connection between the reconstructed spectra and exciton states in CuCl as well as the capability of quantum interferometry in solid-state spectroscopy.
In this work, we introduce a definition of the Discrete Fourier Transform (DFT) on Euclidean lattices in $R^n$, that generalizes the $n$-th fold DFT of the integer lattice $Z^n$ to arbitrary lattices. This definition is not applicable for every lattice, but can be defined on lattices known as Systematic Normal Form (SysNF) introduced in cite{ES16}. Systematic Normal Form lattices are sets of integer vectors that satisfy a single homogeneous modular equation, which itself satisfies a certain number-theoretic property. Such lattices form a dense set in the space of $n$-dimensional lattices, and can be used to approximate efficiently any lattice. This implies that for every lattice $L$ a DFT can be computed efficiently on a lattice near $L$. Our proof of the statement above uses arguments from quantum computing, and as an application of our definition we show a quantum algorithm for sampling from discrete distributions on lattices, that extends our ability to sample efficiently from the discrete Gaussian distribution cite{GPV08} to any distribution that is sufficiently smooth. We conjecture that studying the eigenvectors of the newly-defined lattice DFT may provide new insights into the structure of lattices, especially regarding hard computational problems, like the shortest vector problem.
Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. We show that, under reasonable assumptions about noise models, the fidelity of the quantum Fourier transformation improves considerably using this approach when the number of qubits involved grows. This suggests that, in the Noisy Intermediate-Scale Quantum (NISQ) era, hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach useful quantum supremacy.
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