Recently, Lloyd and Montangero have made a brief research proposal on universal quantum computation in integrable systems. The main idea is to encode qubits into quantum action variables and build up quantum gates by the method of resonant control. We study this proposal to argue quantum computation using action variables as fault-tolerant quantum computation, whose fault-tolerance is guaranteed by the quantum KAM theorem. Besides, we view the Birkhoff norm form as a mathematical framework of the extended harmonic oscillator quantum computation.
We apply a Gaussian state formalism to track fluctuating perturbations that act on the position and momentum quadrature variables of a harmonic oscillator. Following a seminal proposal by Tsang and Caves [Phys. Rev. Lett. 105, 123601 (2010)], Einstein-Podolsky-Rosen correlations with the quadrature variables of an ancillary harmonic oscillator are leveraged to significantly improve the estimates as relevant sensor variables can be arbitrarily squeezed while evading adverse effects from the conjugate, anti-squeezed variables. Our real-time analysis of the continuous monitoring of the system emp…
On Realization of Back-Action-Evading Measurements and Quantum Non-Demolition Variables via Linear Systems Engineering
School of Science, College of Frontier Sciences, Harbin Institute of Technology, Shenzhen（哈尔滨工业大学深圳前沿科学学院）；School of Automation Science and Engineering, Faculty of Electronic and Information Engineering, Xi’an Jiaotong University（西安交通大学电子与信息工程学院自动化系）；Department of Applied Mathematics, The Hong Kong Polytechnic University（香港理工大学应用数学系）；Research Institute for Quantum Technology, The Hong Kong Polytechnic University（香港理工大学量子技术研究院）
Measuring a quantum system can randomly perturb its state. The strength and nature of this back-action depends on the quantity which is measured. In a partial measurement performed by an ideal apparatus, quantum physics predicts that the system remains in a pure state whose evolution can be tracked perfectly from the measurement record. We demonstrate this property using a superconducting qubit dispersively coupled to a cavity traversed by a microwave signal. The back-action on the qubit state of a single measurement of both signal quadratures is observed and shown to produce a stochastic oper…
The additional information within a Hamilton-Jacobi representation of quantum mechanics is extra, in general, to the Schrödinger representation. This additional information specifies the microstate of $ψ$ that is incorporated into the quantum reduced action, $W$. Non-physical solutions of the quantum stationary Hamilton-Jacobi equation for energies that are not Hamiltonian eigenvalues are examined to establish Lipschitz continuity of the quantum reduced action and conjugate momentum. Milne quantization renders the eigenvalue $J$. Eigenvalues $J$ and $E$ mutually imply each other. Jacobi's theo…
In the framework quotient algebra partition, a general methodology is introduced to construct fault tolerant encodes for an arbitrary action in an error-correcting code.
