Estimation methods and applications in quantum sensing and quantum simulation

Abstract

Parameter estimation methods are necessary and commonly used in many fields. In this thesis, we study the basic tools of estimation theory and apply to practical physical systems. First, we investigate the use of twin-mode quantum states of light with symmet- ric statistical features in their photon number for improving intensity-sensitive sur- face plasmon resonance (SPR) sensors. For this purpose, one of the modes is sent into a prism setup where the Kretschmann configuration is employed as a sensing platform and the analyte to be measured influences the SPR excitation conditions. This influence modifies the output state of light that is subsequently analyzed by an intensity-difference measurement scheme. We show that quantum noise reduction is achieved not only as a result of the sub-Poissonian statistical nature of a single mode, but also as a result of the nonclassical correlation of the photon number between the two modes. When combined with the high sensitivity of the SPR sensor, we show that the use of twin-mode quantum states of light notably enhances the estimation precision of the refractive index of an analyte. With this we are able to identify a clear strategy to further boost the performance of SPR sensors, which are already a mature technology in biochemical and medical sensing applications. In the next work, we study the single-shot measurement learning which has been proved recently to be useful in various quantum informational tasks. In this study, we combine this method with the Maximum Likelihood Estimation, which is a well- known and widely used method, to learn unknown pure quantum states. Results show that the new method gives an improvement to the existed one with highly state learning accuracy and less resources. It is also shown that single-measurement scheme is the optimal scheme in the most cases over double-measurement and en- semble single-measurement schemes. The focus of our latest work is on the Variational Quantum Eigensolver, a popular algorithm that has captured the attention of the quantum information community over the past decade. Its primary function is to locate the ground state and ground energy of a Hermitian Hamiltonian matrix. Although it has demonstrated promis- ing results, the use of various types of measurements remains a significant obstacle. Recently, a new measurement scheme has been proposed to overcome this issue by introducing an additional ancilla system that is coupled to the primary system. By conducting measurements on this extra system, we can extract and infer the Hamil- tonian matrix’s information. In this study, we employ Nelder-Mead and Bayesian in- ference with von Mises-Fisher distribution methods to complete the task. Our results indicate that both methods can successfully locate solutions for random Hamiltonian matrices with finite quantum resources.