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Register a new userDetection of quantum critical points by a probe qubit
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Quantum phase transitions occur when the ground state of a quantum system undergoes a qualitative change when an external control parameter reaches a critical value. Here, we demonstrate a technique for studying quantum systems undergoing a phase transition by coupling the system to a probe qubit. It uses directly the increased sensibility of the quantum system to perturbations when it is close to a critical point. Using an NMR quantum simulator, we demonstrate this measurement technique for two different types of quantum phase transitions in an Ising spin chain.
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We study the protective measurement of a qubit by a second qubit acting as a probe. Consideration of this model is motivated by the possibility of its experimental implementation in multiqubit systems such as trapped ions. In our scheme, information about the expectation value of an arbitrary observable of the system qubit is encoded in the rotation of the state of the probe qubit. We describe the structure of the Hamiltonian that gives rise to this measurement and analyze the resulting dynamics under a variety of realistic conditions, such as noninfinitesimal measurement strengths, repeated measurements, non-negligible intrinsic dynamics of the probe, and interactions of the system and probe qubits with an environment. We propose an experimental realization of our model in an ion trap. The experiment may be performed with existing technology and makes use of established experimental methods for the engineering and control of Hamiltonians for quantum gates and quantum simulations of spin systems.
We propose a method to measure the quantum state of a single mode of the electromagnetic field. The method is based on the interaction of the field with a probe qubit. The qubit polarizations along coordinate axes are functions of the interaction time and from their Fourier transform we can in general fully reconstruct pure states of the field and obtain partial information in the case of mixed states. The method is illustrated by several examples, including the superposition of Fock states, coherent states, and exotic states generated by the dynamical Casimir effect.
In addition to their central role in quantum information processing, qubits have proven to be useful tools in a range of other applications such as enhanced quantum sensing and as spectrometers of quantum noise. Here we show that a superconducting qubit strongly coupled to a nonlinear resonator can act as a probe of quantum fluctuations of the intra-resonator field. Building on previous work [M. Boissoneault et al. Phys. Rev. A 85, 022305 (2012)], we derive an effective master equation for the qubit which takes into account squeezing of the resonator field. We show how sidebands in the qubit excitation spectrum that are predicted by this model can reveal information about squeezing and quantum heating. The main results of this paper have already been successfully compared to experimental data [F. R. Ong et al. Phys. Rev. Lett. 110, 047001 (2013)] and we present here the details of the derivations.
Calculations for open quantum systems are performed usually by taking into account their embedding into one common environment, which is mostly the common continuum of scattering wavefunctions. Realistic quantum systems are coupled however often to more than one continuum. For example, the conductance of an open cavity needs at least two environments, namely the input and the output channel. In the present paper, we study generic features of the transfer of particles through an open quantum system coupled to two channels. We compare the results with those characteristic of a one-channel system. Of special interest is the parameter range which is influenced by singular points. Here, the states of the system are mixed via the environment. In the one-channel case, the resonance structure of the cross section is independent of the existence of singular points. In the two-channel case, however, new effects appear caused by coherence. An example is the enhanced conductance of an open cavity in a certain finite parameter range. It is anti-correlated with the phase rigidity of the eigenfunctions of the non-Hermitian Hamilton operator.
One of the most important properties of classical neural networks is the clustering of local minima of the network near the global minimum, enabling efficient training. This has been observed not only numerically, but also has begun to be analytically understood through the lens of random matrix theory. Inspired by these results in classical machine learning, we show that a certain randomized class of variational quantum algorithms can be mapped to Wishart random fields on the hypertorus. Then, using the statistical properties of such random processes, we analytically find the expected distribution of critical points. Unlike the case for deep neural networks, we show the existence of a transition in the quality of local minima at a number of parameters exponentially large in the problem size. Below this transition, all local minima are concentrated far from the global minimum; above, all local minima are concentrated near the global minimum. This is consistent with previously observed numerical results on the landscape behavior of Hamiltonian agnostic variational quantum algorithms. We give a heuristic explanation as to why ansatzes that depend on the problem Hamiltonian might not suffer from these scaling issues. We also verify that our analytic results hold experimentally even at modest system sizes.
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