We study the implementation of quantum phase measurement in a superconducting circuit, where two Josephson phase qubits are coupled to the photon field inside a resonator. We show that the relative phase of the superposition of two Fock states can be imprinted in one of the qubits. The qubit can thus be used to probe and store the quantum coherence of two distinguishable Fock states of the single-mode photon field inside the resonator. The effects of dissipation of the photon field on the phase detection are investigated. We find that the visibilities can be greatly enhanced if the Kerr nonlinearity is exploited. We also show that the phase measurement method can be used to perform the Gauss sum factorization of numbers (${\geq} 10^4$) into a product of prime integers, as well as to precisely measure both the resonator's frequency and the nonlinear interaction strength. The largest factorizable number is mainly limited by the coherence time. If the relaxation time of the resonator were to be ${\sim} 10$ $μ$s (${\sim} 1$ ms), then the largest factorizable number can be ${\geq} 10^4N$ (${\geq} 10^{7}N$), where $N$ is the number of photons in the resonator.
New factorization algorithm based on a continuous representation of truncated Gauss sums
在本文中，我们将描述一个新的因式分解算法的基础上连续表示的高斯和，推广到阶j>2。这种算法首次允许在一次运行中找到数N的所有因子，而无需预先计算比率N/l，其中l是所有可能的试验因子。连续截尾指数和被证明是区分因子和非因子的有力工具（关于这个主题，我们还建议阅读S. Woelk et al.也发表在这个问题上[Woelk，Feiler，Schleich，J. Mod. Opt. in press]），并同时因式分解不同的数字。我们还将描述两种可能的M路光学干涉仪，它可以用来实验实现这种算法：液晶光栅和广义对称迈克耳孙干涉仪。
Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the assumption that noise obeys Gaussian statistics is commonly employed, noise is generically non-Gaussian in nature. In particular, the Gaussian approximation breaks down whenever a qubit is strongly coupled to discrete noise sources or has a non-linear response to the environmental degrees of freedom. Thus, in order to both scrutinize the applicability of the G…
Shor's algorithm has seriously challenged information security based on public key cryptosystems. However, to break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities. Here, we report a universal quantum algorithm for integer factorization by combining the classical lattice reduction with a quantum approximate optimization algorithm (QAOA). The number of qubits required is O(logN/loglog N), which is sublinear in the bit length of the integer $N$, making it the most qubit-saving factorization algorithm to date. We demonstra…
Factoring six-digit integers with superconducting quantum circuits
National Laboratory of Solid State Microstructures, School of Physics, Nanjing University（南京大学固体微结构物理学院）；Shishan Laboratory, Suzhou Campus of Nanjing University（南京大学苏州校区石湖实验室）；Jiangsu Key Laboratory of Quantum Information Science and Technology, Nanjing University（南京大学量子信息科学与技术江苏省重点实验室）；Hefei National Laboratory（合肥国家实验室）；Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学量子信息与量子科技创新研究院）
Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterises the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP),…
A challenge in the Gauss sums factorization scheme is the presence of ghost factors - non-factors that behave similarly to actual factors of an integer - which might lead to the misidentification of non-factors as factors or vice versa, especially in the presence of noise. We investigate Type II ghost factors, which are the class of ghost factors that cannot be suppressed with techniques previously laid out in the literature. The presence of Type II ghost factors and the coherence time of the qubit set an upper limit for the total experiment time, and hence the largest factorizable number with…
Bosonic modes have wide applications in various quantum technologies, such as optical photons for quantum communication, magnons in spin ensembles for quantum information storage and mechanical modes for reversible microwave-to-optical quantum transduction. There is emerging interest in utilizing bosonic modes for quantum information processing, with circuit quantum electrodynamics (circuit QED) as one of the leading architectures. Quantum information can be encoded into subspaces of a bosonic superconducting cavity mode with long coherence time. However, standard Gaussian operations (e.g., be…
