Demonstrating efficient and robust bosonic state reconstruction via optimized excitation counting
Tanjung Krisnanda, Clara Yun Fontaine, Adrian Copetudo, Pengtao Song, Kai Xiang Lee, Ni-Ni Huang, Fernando Valadares, Timothy C. H. Liew, Yvonne Y. Gao
备注：
Main text (7 pages with 4 figures) and Appendices (12 pages with 8 figures and 4 tables)
Quantum state reconstruction is an essential element in quantum information processing. However, efficient and reliable reconstruction of non-trivial quantum states in the presence of hardware imperfections can be challenging. This task is particularly demanding for high-dimensional states encoded in continuous-variable (CV) systems, where a large number of grid-based measurements are often used to adequately sample relevant regions of phase space. In this work, we introduce an efficient and robust technique of Optimized Reconstruction with Excitation Number Sampling (ORENS) based on the idea of generalized Q-function. We use a standard bosonic circuit quantum electrodynamics (cQED) setup to experimentally demonstrate effective state reconstruction using the theoretically minimum number of measurements. Our investigation highlights that ORENS is naturally free of parasitic system dynamics and resilient to decoherence effects in the hardware, enabling it to outperform the conventional reconstruction techniques in cQED such as Wigner tomography. Finally, ORENS relies only on the ability to accurately measure the excitation number of a given CV state, making it a versatile and accessible tool for a wide range of CV platforms and readily scalable to multimode systems. Thus, our work provides a crucial and valuable primitive for practical quantum information processing using bosonic modes.
Detecting the spatial quantum uncertainty of bosonic systems
本文提出了用多象素探测器测量玻色子的量子理论。为了清楚起见，我们专门研究光子束。我们研究了不同的空间光束特性的测量，如位置和宽度。这些测量的极限由光场的量子性质决定。我们调查如何，探测器的缺陷和有限的像素大小影响光子计数分布。离散化测量方案的分析理论推导。我们讨论了结果，并将其与Chille等人在“Quantum uncertainty in the beam width of spatial optical modes，”Opt.Express 23，32777（2015）中提出的理论进行了比较，该理论研究了独立于测量系统的光束宽度噪声。最后，我们提出了数值模拟，为可能的实验研究提供现实和有前途的预测。
We show that detection of single photons is not subject to the fundamental limitations that accompany quantum linear amplification of bosonic mode amplitudes, even though a photodetector does amplify a few-photon input signal to a macroscopic output signal. Alternative limits are derived for \emph{nonlinear} photon-number amplification schemes with optimistic implications for single-photon detection. Four commutator-preserving transformations are presented: one idealized (which is optimal) and three more realistic (less than optimal). Our description makes clear that nonlinear amplification ta…
The achievable rate of information transfer in optical communications is determined by the physical properties of the communication channel, such as the intrinsic channel noise. Bosonic phase-noise channels, a class of non-Gaussian channels, have emerged as a relevant noise model in quantum information and optical communication. However, while the fundamental limits for communication over Gaussian channels have been extensively studied, the properties of communication over Bosonic phase-noise channels are not well understood. Here we propose and demonstrate experimentally the concept of optimi…
We investigate cat codes that can correct multiple excitation losses and identify two types of logical errors: bit-flip errors due to excessive excitation loss and dephasing errors due to quantum back-action from the environment. We show that selected choices of logical subspace and coherent amplitude can efficiently reduce dephasing errors. The trade-off between the two major errors enables optimized performance of cat codes in terms of minimized decoherence. With high coupling efficiency, we show that one-way quantum repeaters with cat codes feature drastically boosted secure communication r…
Direct estimation of arbitrary observables of an oscillator
National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Horizon Quantum Computing, Singapore（新加坡地平线量子计算）；Palacký University（帕拉茨基大学）；Department of Optics, Palacký University（帕拉茨基大学光学系）；Department of Physics, National University of Singapore（新加坡国立大学物理系）
In continuous-variable quantum computing with qubits encoded in the infinite-dimensional Hilbert space of bosonic modes, it is a difficult task to realize strong and on-demand interactions between the qubits. One option is to engineer a beamsplitter interaction for photons in two superconducting cavities by driving an intermediate superconducting circuit with two continuous-wave drives, as demonstrated in a recent experiment. Here, we show how quantum optimal control theory (OCT) can be used in a systematic way to improve the beamsplitter interaction between the two cavities. We find that repl…
Bosonic quantum error-correcting codes with finite stellar rank
Chalmers University of Technology（查尔姆斯理工大学）；The University of Sydney（悉尼大学）；École Normale Supérieure, PSL University（巴黎高等师范学院，PSL大学）；Università degli Studi di Milano（米兰大学）
We introduce a unary coding of bosonic occupation states based on the famous "balls and walls" counting for the number of configurations of $N$ indistinguishable particles on $L$ distinguishable sites. Each state is represented by an integer with a human readable bit string that has a compositional structure allowing for the efficient application of operators that locally modify the number of bosons. By exploiting translational and inversion symmetries, we identify a speedup factor of order $L$ over current methods when generating the basis states of bosonic lattice models. The unary coding is…
We study the computational complexity of quantum-mechanical expectation values of single-particle operators in bosonic and fermionic multi-particle product states. Such expectation values appear, in particular, in full-counting-statistics problems. Depending on the initial multi-particle product state, the expectation values may be either easy to compute (the required number of operations scales polynomially with the particle number) or hard to compute (at least as hard as a permanent of a matrix). However, if we only consider full counting statistics in a finite number of final single-particl…
The development of microwave photon detectors is paving the way for a wide range of quantum technologies and fundamental discoveries involving single photons. Here, we investigate the photon emission from a microwave cavity and find that distribution of photon waiting times contains information about few-photon processes, which cannot easily be extracted from standard correlation measurements. The factorial cumulants of the photon counting statistics are positive at all times, which may be intimately linked with the bosonic quantum nature of the photons. We obtain a simple expression for the r…
Physical realizations of the canonical phase measurement for the optical phase are unknown. Single-shot phase estimation, which aims to determine the phase of an optical field in a single shot, is critical in quantum information processing and metrology. Here we present a family of strategies for single-shot phase estimation of coherent states based on adaptive non-Gaussian, photon counting, measurements with coherent displacements that maximize information gain as the measurement progresses, which have higher sensitivities over the best known adaptive Gaussian strategies. To gain understandin…
Quantum error correction is essential for robust quantum information processing with noisy devices. As bosonic quantum systems play a crucial role in quantum sensing, communication, and computation, it is important to design error correction codes suitable for these systems against various different types of noises. While most efforts aim at protecting qubits encoded into the infinite dimensional Hilbert space of a bosonic mode, [Phys. Rev. Lett. 125, 080503 (2020)] proposed an error correction code to maintain the infinite-dimensional-Hilbert-space nature of bosonic systems by encoding a sing…
We show that the Franck-Condon Factor (FCF) associated to a transition between initial and final vibrational states in two different potential energy surfaces, having $N$ and $M$ vibrational quanta, respectively, is equivalent to calculating the number of perfect matchings of a weighted graph with loops that has $P = N+M$ vertices. This last quantity is the loop hafnian of the (symmetric) adjacency matrix of the graph which can be calculated in $O(P^3 2^{P/2})$ steps. In the limit of small numbers of vibrational quanta per normal mode our loop hafnian formula significantly improves the speed a…
Quantum antiferromagnets are of broad interest in condensed matter physics as they provide a platform for studying exotic many-body states including spin liquids and high-temperature superconductors. Here, we report on the creation of a one-dimensional Heisenberg antiferromagnet with ultracold bosons. In a two-component Bose-Hubbard system, we switch the sign of the spin-exchange interaction and realize the isotropic antiferromagnetic Heisenberg model in an extended 70-site chain. Starting from a low-entropy Néel-ordered state, we use optimized adiabatic passage to approach the bosonic antifer…
The final goal of quantum hypothesis testing is to achieve quantum advantage over all possible classical strategies. In the protocol of quantum reading this advantage is achieved for information retrieval from an optical memory, whose generic cell stores a bit of information in two possible lossy channels. For this protocol, we show, theoretically and experimentally, that quantum advantage is obtained by practical photon-counting measurements combined with a simple maximum-likelihood decision. In particular, we show that this receiver combined with an entangled two-mode squeezed vacuum source …
We show how series expansions of functions of bosonic number operators are naturally derived from finite-difference calculus. The scheme employs Newton series rather than Taylor series known from differential calculus, and also works in cases where the Taylor expansion fails. For a function of number operators, such an expansion is automatically normal ordered. Applied to the Holstein-Primakoff representation of spins, the scheme yields an exact series expansion with a finite number of terms and, in addition, allows for a systematic expansion of the spin operators that respects the spin commut…
Atominstitut, Technische Universität Wien（原子研究所，维也纳工业大学）；Vienna Center for Quantum Science and Technology, Technische Universität Wien（量子科学与技术维也纳中心，维也纳工业大学）；Institut für theoretische Physik, Technische Universität Wien（理论物理研究所，维也纳工业大学）；Department of Physics “E. Fermi”, University of Pisa（“E. 费米”物理学系，比萨大学）
Scuola Normale Superiore（比萨高等师范学院）；NEST-CNR（国家研究委员会纳米科学与技术创新研究所）；Inria（法国国家数字科学研究所）；Institut Polytechnique de Paris（巴黎理工学院）；Università di Bologna（博洛尼亚大学）
A method for the systematic construction of few-body damped harmonic oscillator networks accurately reproducing the effect of general bosonic environments in open quantum systems is presented. Under the sole assumptions of a Gaussian environment and regardless of the system coupled to it, an algorithm to determine the parameters of an equivalent set of interacting damped oscillators obeying a Markovian quantum master equation is introduced. By choosing a suitable coupling to the system and minimizing an appropriate distance between the two-time correlation function of this effective bath and t…
Quantum work statistics and coherence effects in quenched bosonic Josephson junctions
Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家光学研究所）；European Laboratory for Non-linear Spectroscopy, Università di Firenze（佛罗伦萨大学欧洲非线性光谱学实验室）；Department of Physics and Astronomy, University of Florence（佛罗伦萨大学物理与天文学系）
We study super-resolution imaging theoretically using a distant n-mode interferometer in the microwave regime for passive remote sensing, used e.g., for satellites like the "soil moisture and ocean salinity (SMOS)" mission to observe the surface of the Earth. We give a complete quantum mechanical analysis of multiparameter estimation of the temperatures on the source plane. We find the optimal detection modes by combining incoming modes with an optimized unitary that enables the most informative measurement based on photon counting in the detection modes and saturates the quantum Cramér-Rao bo…
Unveiling Topological Fusion in Quantum Hall Systems from Microscopic Principles
Jagiellonian University（雅盖隆大学）；Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与工程中心）；Princeton University（普林斯顿大学）；Karlstads Universitet（卡尔斯特大学）；Institute for Advanced Study, Princeton（普林斯顿高等研究院）；Indiana University（印第安纳大学）
