Signatures of a Quantum Griffiths Phase Close to an Electronic Nematic Quantum Phase Transition

Reiss, Pascal; Graf, David; Haghighirad, Amir A.; Vojta, Thomas; Coldea, Amalia I.

doi:10.1103/PhysRevLett.127.246402

Estimating a quantum phase is a necessary task in a wide range of fields of quantum science. To accomplish this task, two well-known methods have been developed in distinct contexts, namely, Ramsey interferometry (RI) in atomic and molecular physics and quantum phase estimation (QPE) in quantum computing. We demonstrate that these canonical examples are instances of a larger class of phase estimation protocols, which we call reductive quantum phase estimation (RQPE) circuits. Here, we present an explicit algorithm that allows one to create an RQPE circuit. This circuit distinguishes an arbitrary set of phases with a smaller number of qubits and unitary applications, thereby solving a general class of quantum hypothesis testing to which RI and QPE belong. We further demonstrate a tradeoff between measurement precision and phase distinguishability, which allows one to tune the circuit to be optimal for a specific application.

<supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10314567-phase-engineered-bosonic-quantum-codes" itemprop="url"> <span class='span-link' itemprop="name">Phase-engineered bosonic quantum codes</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevA.103.062427" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevA.103.062427 <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Li, Linshu</span> <span class="sep">; </span><span class="author" itemprop="author">Young, Dylan J.</span> <span class="sep">; </span><span class="author" itemprop="author">Albert, Victor V.</span> <span class="sep">; </span><span class="author" itemprop="author">Noh, Kyungjoo</span> <span class="sep">; </span><span class="author" itemprop="author">Zou, Chang-Ling</span> <span class="sep">; </span><span class="author" itemprop="author">Jiang, Liang</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2021-06-01">June 2021</time> , Physical Review A) </span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10014683-columnar-phase-quantum-dimer-models" itemprop="url"> <span class='span-link' itemprop="name">Columnar phase in quantum dimer models</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1088/1751-8113/48/23/235203" target="_blank" title="Link to document DOI">https://doi.org/10.1088/1751-8113/48/23/235203 <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Giuliani, Alessandro</span> <span class="sep">; </span><span class="author" itemprop="author">Lieb, Elliott H</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2015-06-10">June 2015</time> , Journal of Physics A: Mathematical and Theoretical) </span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10303333-statistical-approach-quantum-phase-estimation" itemprop="url"> <span class='span-link' itemprop="name">Statistical approach to quantum phase estimation</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1088/1367-2630/ac320d" target="_blank" title="Link to document DOI">https://doi.org/10.1088/1367-2630/ac320d <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Moore, Alexandria J.</span> <span class="sep">; </span><span class="author" itemprop="author">Wang, Yuchen</span> <span class="sep">; </span><span class="author" itemprop="author">Hu, Zixuan</span> <span class="sep">; </span><span class="author" itemprop="author">Kais, Sabre</span> <span class="sep">; </span><span class="author" itemprop="author">Weiner, Andrew M.</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2021-11-25">November 2021</time> , New Journal of Physics) </span> </div> <div style="cursor: pointer;-webkit-line-clamp: 5;" class="abstract" itemprop="description"> <title>Abstract

We introduce a new statistical and variational approach to the phase estimation algorithm (PEA). Unlike the traditional and iterative PEAs which return only an eigenphase estimate, the proposed method can determine any unknown eigenstate–eigenphase pair from a given unitary matrix utilizing a simplified version of the hardware intended for the iterative PEA (IPEA). This is achieved by treating the probabilistic output of an IPEA-like circuit as an eigenstate–eigenphase proximity metric, using this metric to estimate the proximity of the input state and input phase to the nearest eigenstate–eigenphase pair and approaching this pair via a variational process on the input state and phase. This method may search over the entire computational space, or can efficiently search for eigenphases (eigenstates) within some specified range (directions), allowing those with some prior knowledge of their system to search for particular solutions. We show the simulation results of the method with the Qiskit package on the IBM Q platform and on a local computer.

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