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Register a new userProjective measurement of energy on an ensemble of qubits with unknown frequencies
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In projective measurements of energy, a target system is projected to an eigenstate of the system Hamiltonian, and the measurement outcomes provide the information of corresponding eigen-energies. Recently, it has been shown that such a measurement can be in principle realized without detailed knowledge of the Hamiltonian by using probe qubits. However, in the previous approach for the energy measurement, the necessary size of the dimension for the probe increases as we increase the dimension of the target system, and also individual addresibility of every qubit is required, which may not be possible for many experimental settings with large systems. Here, we show that a single probe qubit is sufficient to perform such a projective measurement of energy if the target system is composed of non-interacting qubits whose resonant frequencies are unknown. Moreover, our scheme requires only global manipulations where every qubit is subjected to the same control fields. These results indicate the feasibility of our energy projection protocols.
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Superconducting flux qubits are a promising candidate for realizing quantum information processing and quantum simulations. Such devices behave like artificial atoms, with the advantage that one can easily tune the atoms internal properties. Here, by harnessing this flexibility, we propose a technique to minimize the inhomogeneous broadening of a large ensemble of flux qubits by tuning only the external flux. In addition, as an example of many-body physics in such an ensemble, we show how to observe superradiance, and its quadratic scaling with ensemble size, using a tailored microwave control pulse that takes advantage of the inhomogeneous broadening itself to excite only a sub-ensemble of the qubits. Our scheme opens up an approach to using superconducting circuits to explore the properties of quantum many-body systems.
The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown n-qubit pair-interaction Hamiltonian into a conditional one such that standard phase estimation can be applied to measure the energy. Our essential assumption is that the considered system can be brought into interaction with a quantum computer. For large n the algorithm could still be applicable for estimating the density of energy states and might therefore be useful for finding energy gaps in solid states.
We propose a quantum-enhanced iterative (with $K$ steps) measurement scheme based on an ensemble of $N$ two-level probes which asymptotically approaches the Heisenberg limit $delta_K propto R^{-K/(K+1)}$, $R$ the number of quantum resources. The protocol is inspired by Kitaevs phase estimation algorithm and involves only collective manipulation and measurement of the ensemble. The iterative procedure takes the shot-noise limited primary measurement with precision $delta_1propto N^{-1/2}$ to increasingly precise results $delta_Kpropto N^{-K/2}$. A straightforward implementation of the algorithm makes use of a two-component atomic cloud of Bosons in the precision measurement of a magnetic field.
The problem of combating de-coherence by weak measurements has already been studied for the amplitude damping channel and for specific input states. We generalize this to a large four-parameter family of qubit channels and for the average fidelity over all pure states. As a by-product we classify all the qubit channels which have one invariant pure state and show that the parameter manifold of these channels is isomorphic to $S^2times S^1times S^1$ and contains many interesting subclasses of channels. The figure of merit that we use is the average input-output fidelity which we show can be increased up to $30$ percents in some cases, by tuning of the weak measurement parameter.
We investigate how discrete internal degrees of freedom in a quasi-macroscopic system affect the violation of the Leggett--Garg inequality, a test of macroscopic-realism based on temporal correlation functions. As a specific example, we focus on an ensemble of qubits subject to collective and individual noise. This generic model can describe a range of physical systems, including atoms in cavities, electron or nuclear spins in NV centers in diamond, erbium in Y$_2$SiO$_5$, bismuth impurities in silicon, or arrays of superconducting circuits, to indicate but a few. Such large ensembles are potentially more macroscopic than other systems that have been used so far for testing the Leggett--Garg inequality, and open a route toward probing the boundaries of quantum mechanics at macroscopic scales. We find that, because of the non-trivial internal structure of such an ensemble, the behavior of different measurement schemes, under the influence of noise, can be surprising. We discuss which measurement schemes are optimal for flux qubits and NV centers, and some of the technological constraints and difficulties for observing such violations with present-day experiments.
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