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The group structure of dynamical transformations between quantum reference frames

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Angel Ballesteros1, Flaminia Giacomini2, and Giulia Gubitosi3

1Departamento de Física, Universidad de Burgos, 09001 Burgos, Spain
2Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L 2Y5, Canada
3Dipartimento di Fisica Ettore Pancini, Università di Napoli Federico II, and INFN, Sezione di Napoli, Complesso Univ. Monte S. Angelo, I-80126 Napoli, Italy

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Abstract

Recently, it was shown that when reference frames are associated to quantum systems, the transformation laws between such quantum reference frames need to be modified to take into account the quantum and dynamical features of the reference frames. This led to a relational description of the phase space variables of the quantum system of which the quantum reference frames are part of. While such transformations were shown to be symmetries of the system’s Hamiltonian, the question remained unanswered as to whether they enjoy a group structure, similar to that of the Galilei group relating classical reference frames in quantum mechanics. In this work, we identify the canonical transformations on the phase space of the quantum systems comprising the quantum reference frames, and show that these transformations close a group structure defined by a Lie algebra, which is different from the usual Galilei algebra of quantum mechanics. We further find that the elements of this new algebra are in fact the building blocks of the quantum reference frames transformations previously identified, which we recover. Finally, we show how the transformations between classical reference frames described by the standard Galilei group symmetries can be obtained from the group of transformations between quantum reference frames by taking the zero limit of the parameter that governs the additional noncommutativity introduced by the quantum nature of inertial transformations.

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Cited by

[1] Jianhao M. Yang, “Quantum Mechanics from Relational Properties, Part III: Path Integral Implementation”, arXiv:1807.01583.

[2] Philipp A. Hoehn, Maximilian P. E. Lock, Shadi Ali Ahmad, Alexander R. H. Smith, and Thomas D. Galley, “Quantum Relativity of Subsystems”, arXiv:2103.01232.

[3] Flaminia Giacomini, “Spacetime Quantum Reference Frames and superpositions of proper times”, arXiv:2101.11628.

[4] Marion Mikusch, Luis C. Barbado, and Časlav Brukner, “Transformation of Spin in Quantum Reference Frames”, arXiv:2103.05022.

[5] Ismael L. Paiva, Augusto C. Lobo, and Eliahu Cohen, “Flow of time during energy measurements and the resulting time-energy uncertainty relations”, arXiv:2106.00523.

The above citations are from SAO/NASA ADS (last updated successfully 2021-06-08 12:49:27). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2021-06-08 12:49:26: Could not fetch cited-by data for 10.22331/q-2021-06-08-470 from Crossref. This is normal if the DOI was registered recently.

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Source: https://quantum-journal.org/papers/q-2021-06-08-470/

Quantum

Graphene Superconductors May Be Less Exotic Than Physicists Hoped

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Three years ago, physicists discovered that two stacked sheets of carbon with a tiny, 1.1-degree twist between them could exhibit a dazzling array of behaviors. Most famously, when cooled to low temperatures, the material conducts electricity with zero resistance.

Researchers raced to figure out why twisted bilayer graphene (as it’s called) becomes a superconductor, with a form of superconductivity that seems unusually robust. Many theorists hoped the discovery would rewrite their understanding of superconductivity, and perhaps even allow researchers to engineer materials capable of sustaining the phenomenon at higher temperatures.

But the intense focus on that twist between the graphene sheets may have been a case of misdirection. A team of physicists announced today at an online conference that they’ve observed superconductivity in a triple-decker stack of graphene with no twists at all. The discovery, led by Andrea Young and Haoxin Zhou of the University of California, Santa Barbara, could reset discussions about superconductivity in graphene. It has led some theorists to suspect that graphene’s superconductivity is the vanilla variety after all.

“That’s a very important discovery showing that superconductivity [in graphene] is, in some sense, regular,” said Sankar Das Sarma, a theoretical condensed matter physicist at the University of Maryland who was not involved in the research.

But the evidence for conventional superconductivity is not conclusive. And researchers note that twisted graphene’s superconductivity could still be exotic even if untwisted graphene’s isn’t.

Albert Einstein, Richard Feynman and Werner Heisenberg are just a few of the titans of 20th-century physics who tried and failed to understand why many metals carry current without resistance at low temperatures. In 1957, nearly half a century after this standard kind of superconductivity was discovered, John Bardeen, Leon Cooper and John Robert Schrieffer finally explained the phenomenon, an achievement that earned them the Nobel Prize in Physics.

They determined that sound waves in metals — ripples where atoms bunch together, called phonons — create concentrations of positive charge that attract electrons, which are negatively charged. The phonons stick electrons together into “Cooper pairs.” Coupled off in this way, electrons play by different quantum mechanical rules, fusing into a quantum fluid whose flow is no longer gummed up by the atoms in the lattice. This phonon-mediated theory, known (after its authors’ initials) as BCS, matches almost all superconductivity experiments.

Alternative ways of gluing electrons together work on paper, and experimentalists have seen signs of puzzlingly strong “unconventional” glues in some superconductors, but such claims remain unsettled.

“It’s like if someone tells you in some very distant village on some island there are people with three heads,” Das Sarma said. “You should be very, very skeptical.”

In 2018, some researchers thought they might have stumbled upon just such a mythical island of exotic superconductivity, since twisted bilayer graphene appeared to somehow bind electrons much more tightly together than most superconductors do. Excitement rose earlier this year with the discovery of superconductivity in a similar system: three layers of graphene twisted at their own special angle. Both systems shared a rare, 180-degree rotational symmetry, which theorists argued could support an especially exotic form of superconductivity based on electron vortices known as skyrmions.

But the new incarnation of superconducting graphene appears strikingly plain.

ABC trilayer graphene, as Young and his colleagues call their graphene stack, is one of the cleanest and simplest materials they could make. The second and third layers are shifted rather than twisted, each nudged over by an additional half-honeycomb, so carbon atoms below fall in the center of lattices above.

Stacking graphene sheets is hard, with or without twists. Twisted devices are riddled with wrinkles that disrupt the magic angle in different zones, making each apparatus unique. Even when Young and colleagues manufactured their ABC trilayer devices, most attempts snapped back into an alternative stacking pattern. But — unlike the fussy twisted samples — the ones that stayed put were identical down to the last atom. The atoms “lock into place like Legos,” Young said.

Once the team had their first ABC device, they used an adjustable electric field to shuffle electrons between the pristine layers. As they tuned the electron distribution at cryogenic temperatures, they saw that the system behaved much as twisted graphene does, jumping between various types of magnetic behavior, as indicated by shifts in how the device slowed electric current. They posted their results in an April preprint.

When they examined the transitions in more detail, they identified brief flickers of zero electrical resistance — superconductivity — when the material was about one-tenth of a degree above absolute zero.

Although Young and his colleagues have no way to peep at the Cooper pairs of electrons directly, they found behavior that Bardeen, Cooper and Schrieffer would recognize: Moving electrons between the three layers increased the number of possible configurations the electrons could choose from, a quantity known as the system’s “density of states.” At high densities of states, electrons can more easily fraternize among themselves. BCS theory predicts that this electronic liberty aids the formation of Cooper pairs, and that’s what the researchers found: As the density of states rose, the material displayed two blips of superconductivity.

Since the BCS equation appears to hold, ordinary phonons might be responsible for the superconductivity.

“It’s quacking like a duck and walking like a duck,” Das Sarma said. “Phonons are natural to assume.”

Others are less convinced, noting that the evidence supporting phonons in ABC trilayer graphene remains rough. Superconductivity appears to track with the higher density of states, but that doesn’t mean the BCS equation is obeyed in detail, said Mike Zaletel, a condensed matter physicist at the University of California, Berkeley who consulted with Young during the research and helped develop the skyrmion theory of superconductivity.

In Young’s data, Zaletel sees hints of a mildly exotic sort of superconductivity — something like an island with a six-fingered population, rather than people with three heads. He explained that both flashes of superconductivity appeared immediately before the electrons organized into ferromagnetic states, where their spin directions became aligned. As regions of electrons started lining up, these fluctuating pockets of uniformity could have shepherded electrons into Cooper pairs much as phonons do.

Young’s group is already testing whether ferromagnetism is key to the onset of superconductivity in ABC trilayer graphene, or if it’s irrelevant — which would hint at conventional phonons.

Many physicists feel optimistic that Young’s new platform will help them figure out how electrons superconduct in graphene. The idiosyncrasies of each twisted graphene device made it impossible for even an individual lab to identically replicate its own results. ABC trilayer graphene, with its perfect layout, overcomes that challenge.

“Materials are complicated, and they have a way of lying to us,” said Steven Kivelson, a theoretical physicist at Stanford University. “What’s exciting about this development” is that it promises reproducible materials, “so that everybody can get the same answer.”

Since ABC graphene can become a superconductor and various types of magnet, all without twists or other obvious tricks, it also suggests that a much wider range of fairly ordinary materials might hold overlooked magic. This material versatility “may be hiding in plain sight much more ubiquitously than we thought,” Young said.

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Source: https://www.quantamagazine.org/graphene-superconductors-may-be-less-exotic-than-physicists-hoped-20210614/

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Visualizing the emission of a single photon with frequency and time resolved spectroscopy

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Aleksei Sharafiev1, Mathieu L. Juan2, Oscar Gargiulo1, Maximilian Zanner3, Stephanie Wögerer3, Juan José García-Ripoll4, and Gerhard Kirchmair1,3

1Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstrasse 21a, 6020 Innsbruck, Austria
2Institut quantique and Département de Physique, Université de Sherbrooke, Sherbrooke, Québec, J1K 2R1, Canada
3Institute for Experimental Physics, University of Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
4Instituto de Fisica Fundamental IFF-CSIC, 28006 Madrid, Spain

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Abstract

At the dawn of Quantum Physics, Wigner and Weisskopf obtained a full analytical description (a $textit{photon portrait}$) of the emission of a single photon by a two-level system, using the basis of frequency modes (Weisskopf and Wigner, “Zeitschrift für Physik”, 63, 1930). A direct experimental reconstruction of this portrait demands an accurate measurement of a time resolved fluorescence spectrum, with high sensitivity to the off-resonant frequencies and ultrafast dynamics describing the photon creation. In this work we demonstrate such an experimental technique in a superconducting waveguide Quantum Electrodynamics (wQED) platform, using single transmon qubit and two coupled transmon qubits as quantum emitters. In both scenarios, the photon portraits agree quantitatively with the predictions of the input-output theory and qualitatively with Wigner-Weisskopf theory. We believe that our technique allows not only for interesting visualization of fundamental principles, but may serve as a tool, e.g. to realize multi-dimensional spectroscopy in waveguide Quantum Electrodynamics.

We report on a direct measurement of a single photon “wave function” (electrical field amplitude distribution) in frequency and time domains. The “wavefunction” has been measured directly (without any post-processing) taking advantage of superconducting quantum circuits platform for the first time. We demonstrate the technique on a rather simple example of a two-level system emitting a single excitation into a waveguide – the situation with well known analytical description. This technique can be readily applied, for instance, to study near field radiation from an artificial atom or to realize a multi-dimensional spectroscopy of an artificial matter.

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Variational quantum solver employing the PDS energy functional

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Bo Peng and Karol Kowalski

Physical and Computational Science Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States of America

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Abstract

Recently a new class of quantum algorithms that are based on the quantum computation of the connected moment expansion has been reported to find the ground and excited state energies. In particular, the Peeters-Devreese-Soldatov (PDS) formulation is found variational and bearing the potential for further combining with the existing variational quantum infrastructure. Here we find that the PDS formulation can be considered as a new energy functional of which the PDS energy gradient can be employed in a conventional variational quantum solver. In comparison with the usual variational quantum eigensolver (VQE) and the original static PDS approach, this new variational quantum solver offers an effective approach to navigate the dynamics to be free from getting trapped in the local minima that refer to different states, and achieve high accuracy at finding the ground state and its energy through the rotation of the trial wave function of modest quality, thus improves the accuracy and efficiency of the quantum simulation. We demonstrate the performance of the proposed variational quantum solver for toy models, H$_2$ molecule, and strongly correlated planar H$_4$ system in some challenging situations. In all the case studies, the proposed variational quantum approach outperforms the usual VQE and static PDS calculations even at the lowest order. We also discuss the limitations of the proposed approach and its preliminary execution for model Hamiltonian on the NISQ device.

In this paper, we developed a new effective cost function for the variational quantum solver, which in principle can not only help avoid some Barren Plateaus, but also converge to ground state energies outside of the ansatz class, and thus outperforms the conventional one in some challenging cases.

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[1] Daniel Claudino, Bo Peng, Nicholas P. Bauman, Karol Kowalski, and Travis S. Humble, “Improving the accuracy and efficiency of quantum connected moments expansions”, arXiv:2103.09124.

[2] Edgar Andres Ruiz Guzman and Denis Lacroix, “Predicting ground state, excited states and long-time evolution of many-body systems from short-time evolution on a quantum computer”, arXiv:2104.08181.

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Quantum

Certifying dimension of quantum systems by sequential projective measurements

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on

Adel Sohbi1, Damian Markham2,3, Jaewan Kim1, and Marco Túlio Quintino4,5

1School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea
2LIP6, CNRS, Université Pierre et Marie Curie, Sorbonne Universités, 75005 Paris, France
3JFLI, CNRS, National Institute of Informatics, University of Tokyo, Tokyo, Japan
4Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria
5Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria

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Abstract

This work analyzes correlations arising from quantum systems subject to sequential projective measurements to certify that the system in question has a quantum dimension greater than some $d$. We refine previous known methods and show that dimension greater than two can be certified in scenarios which are considerably simpler than the ones presented before and, for the first time in this sequential projective scenario, we certify quantum systems with dimension strictly greater than three. We also perform a systematic numerical analysis in terms of robustness and conclude that performing random projective measurements on random pure qutrit states allows a robust certification of quantum dimensions with very high probability.

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Cited by

[1] Lucas B. Vieira and Costantino Budroni, “Temporal correlations in the simplest measurement sequences”, arXiv:2104.02467.

The above citations are from SAO/NASA ADS (last updated successfully 2021-06-10 14:40:07). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2021-06-10 14:40:05: Could not fetch cited-by data for 10.22331/q-2021-06-10-472 from Crossref. This is normal if the DOI was registered recently.

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