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Register a new userQuantum Langevin equations for optomechanical systems
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We provide a fully quantum description of a mechanical oscillator in the presence of thermal environmental noise by means of a quantum Langevin formulation based on quantum stochastic calculus. The system dynamics is determined by symmetry requirements and equipartition at equilibrium, while the environment is described by quantum Bose fields in a suitable non-Fock representation which allows for the introduction of temperature. A generic spectral density of the environment can be described by introducing its state trough a suitable P-representation. Including interaction of the mechanical oscillator with a cavity mode via radiation pressure we obtain a description of a simple optomechanical system in which, besides the Langevin equations for the system, one has the exact input-output relations for the quantum noises. The whole theory is valid at arbitrarily low temperature. This allows the exact calculation of the stationary value of the mean energy of the mechanical oscillator, as well as both homodyne and heterodyne spectra. The present analysis allows in particular to study possible cooling scenarios and to obtain the exact connection between observed spectra and fluctuation spectra of the position of the mechanical oscillator.
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We address the out-of-equilibrium thermodynamics of an isolated quantum system consisting of a cavity optomechanical device. We explore the dynamical response of the system when driven out of equilibrium by a sudden quench of the coupling parameter and compute analytically the full distribution of the work generated by the process. We consider linear and quadratic optomechanical coupling, where the cavity field is parametrically coupled to either the position or the square of the position of a mechanical oscillator, respectively. In the former case we find that the average work generated by the quench is zero, whilst the latter leads to a non-zero average value. Through fluctuations theorems we access the most relevant thermodynamical figures of merit, such as the free energy difference and the amount of irreversible work generated. We thus provide a full characterization of the out-of-equilibrium thermodynamics in the quantum regime for nonlinearly coupled bosonic modes. Our study is the first due step towards the construction and full quantum analysis of an optomechanical machine working fully out of equilibrium.
Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct matrix inversion or iteratively with judicious preconditioning. However, the convergence of iterative algorithms is highly variable and depends, in part, on the condition number. We present a direct method for solving general systems of polynomial equations based on quantum annealing, and we validate this method using a system of second-order polynomial equations solved on a commercially available quantum annealer. We then demonstrate applications for linear regression, and discuss in more detail the scaling behavior for general systems of linear equations with respect to problem size, condition number, and search precision. Finally, we define an iterative annealing process and demonstrate its efficacy in solving a linear system to a tolerance of $10^{-8}$.
We present a novel discrete-variable quantum teleportation scheme using pulsed optomechanics. In our proposal, we demonstrate how an unknown optical input state can be transferred onto the joint state of a pair of mechanical oscillators, without physically interacting with one another. We further analyze how experimental imperfections will affect the fidelity of the teleportation and highlight how our scheme can be realized in current state-of-the-art optomechanical systems.
Quantum teleportation, the faithful transfer of an unknown input state onto a remote quantum system, is a key component in long distance quantum communication protocols and distributed quantum computing. At the same time, high frequency nano-optomechanical systems hold great promise as nodes in a future quantum network, operating on-chip at low-loss optical telecom wavelengths with long mechanical lifetimes. Recent demonstrations include entanglement between two resonators, a quantum memory and microwave to optics transduction. Despite these successes, quantum teleportation of an optical input state onto a long-lived optomechanical memory is an outstanding challenge. Here we demonstrate quantum teleportation of a polarization-encoded optical input state onto the joint state of a pair of nanomechanical resonators. Our protocol also allows for the first time to store and retrieve an arbitrary qubit state onto a dual-rail encoded optomechanical quantum memory. This work demonstrates the full functionality of a single quantum repeater node, and presents a key milestone towards applications of optomechanical systems as quantum network nodes.
Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum resources are not immediately available on near-term quantum devices. In this work, we study near-term quantum algorithms for linear systems of equations of the form $Ax = b$. We investigate the use of variational algorithms and analyze their optimization landscapes. There exist types of linear systems for which variational algorithms designed to avoid barren plateaus, such as properly-initialized imaginary time evolution and adiabatic-inspired optimization, suffer from a different plateau problem. To circumvent this issue, we design near-term algorithms based on a core idea: the classical combination of variational quantum states (CQS). We exhibit several provable guarantees for these algorithms, supported by the representation of the linear system on a so-called Ansatz tree. The CQS approach and the Ansatz tree also admit the systematic application of heuristic approaches, including a gradient-based search. We have conducted numerical experiments solving linear systems as large as $2^{300} times 2^{300}$ by considering cases where we can simulate the quantum algorithm efficiently on a classical computer. These experiments demonstrate the algorithms ability to scale to system sizes within reach in near-term quantum devices of about $100$-$300$ qubits.
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