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The group structure of dynamical transformations between quantum reference frames



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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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.

► BibTeX data

► References

[1] Jean-Marc Lévy-Leblond. Galilei group and Galilean invariance. In Group theory and its applications, pages 221–299. Elsevier, 1971.

[2] Jean-Marc Lévy-Leblond. The pedagogical role and epistemological significance of group theory in quantum mechanics. Riv. Nuovo Cim., 4: 99–143, 1974.

[3] Yakir Aharonov and Leonard Susskind. Charge superselection rule. Phys. Rev., 155: 1428–1431, 1967a.

[4] Yakir Aharonov and Leonard Susskind. Observability of the sign change of spinors under $2{pi}$ rotations. Phys. Rev., 158: 1237–1238, 1967b.

[5] Y. Aharonov and T. Kaufherr. Quantum frames of reference. Phys. Rev. D, 30: 368–385, 1984.

[6] Stephen D. Bartlett, Terry Rudolph, and Robert W. Spekkens. Reference frames, superselection rules, and quantum information. Rev. Mod. Phys., 79: 555–609, 2007.

[7] Stephen D Bartlett, Terry Rudolph, Robert W Spekkens, and Peter S Turner. Quantum communication using a bounded-size quantum reference frame. New J. Phys., 11 (6): 063013, 2009.

[8] Gilad Gour and Robert W Spekkens. The resource theory of quantum reference frames: manipulations and monotones. New J. Phys., 10 (3): 033023, 2008.

[9] Matthew C. Palmer, Florian Girelli, and Stephen D. Bartlett. Changing quantum reference frames. Phys. Rev. A, 89: 052121, 2014.

[10] Stephen D Bartlett, Terry Rudolph, Robert W Spekkens, and Peter S Turner. Degradation of a quantum reference frame. New J. Phys., 8 (4): 58, 2006.

[11] Alexander R. H. Smith, Marco Piani, and Robert B. Mann. Quantum reference frames associated with noncompact groups: The case of translations and boosts and the role of mass. Phys. Rev. A, 94: 012333, 2016.

[12] David Poulin and Jon Yard. Dynamics of a quantum reference frame. New J. Phys., 9 (5): 156, 2007.

[13] Michael Skotiniotis, Borzu Toloui, Ian T. Durham, and Barry C. Sanders. Quantum Frameness for $CPT$ Symmetry. Phys. Rev. Lett., 111: 020504, 2013.

[14] Renato M Angelo, Nicolas Brunner, Sandu Popescu, Anthony J Short, and Paul Skrzypczyk. Physics within a quantum reference frame. J. Phys. A, 44 (14): 145304, 2011.

[15] R M Angelo and A D Ribeiro. Kinematics and dynamics in noninertial quantum frames of reference. J. Phys. A, 45 (46): 465306, 2012.

[16] S. T. Pereira and R. M. Angelo. Galilei covariance and Einstein’s equivalence principle in quantum reference frames. Phys. Rev. A, 91: 022107, 2015.

[17] Bryce S DeWitt. Quantum theory of gravity. I. The canonical theory. Physical Review, 160 (5): 1113, 1967.

[18] Carlo Rovelli. Quantum reference systems. Class. Quant. Grav., 8 (2): 317, 1991.

[19] Florian Girelli and David Poulin. Quantum reference frames and deformed symmetries. Phys. Rev. D, 77: 104012, 2008.

[20] Lucien Hardy. The construction interpretation: a conceptual road to quantum gravity. arXiv preprint arXiv:1807.10980, 2018.

[21] Lucien Hardy. Implementation of the Quantum Equivalence Principle. In Progress and Visions in Quantum Theory in view of Gravity, pages 189–220. Springer, 2020.

[22] Flaminia Giacomini and Časlav Brukner. Einstein’s Equivalence principle for superpositions of gravitational fields. arXiv preprint arXiv:2012.13754, 2020.

[23] Carlo Rovelli. Relational quantum mechanics. Int. J. Theor. Phys., 35 (8): 1637–1678, 1996.

[24] Takayuki Miyadera, Leon Loveridge, and Paul Busch. Approximating relational observables by absolute quantities: a quantum accuracy-size trade-off. J. Phys. A, 49 (18): 185301, 2016.

[25] Leon Loveridge, Paul Busch, and Takayuki Miyadera. Relativity of quantum states and observables. EPL (Europhysics Letters), 117 (4): 40004, 2017.

[26] Leon Loveridge, Takayuki Miyadera, and Paul Busch. Symmetry, reference frames, and relational quantities in quantum mechanics. Found. Phys., 48 (2): 135–198, 2018.

[27] Jacques Pienaar. A relational approach to quantum reference frames for spins. arXiv preprint arXiv:1601.07320, 2016.

[28] Flaminia Giacomini, Esteban Castro-Ruiz, and Časlav Brukner. Quantum mechanics and the covariance of physical laws in quantum reference frames. Nat. Commun., 10 (1): 494, 2019a.

[29] Augustin Vanrietvelde, Philipp A Höhn, Flaminia Giacomini, and Esteban Castro-Ruiz. A change of perspective: switching quantum reference frames via a perspective-neutral framework. Quantum, 4: 225, 2020.

[30] Augustin Vanrietvelde, Philipp A Höhn, and Flaminia Giacomini. Switching quantum reference frames in the N-body problem and the absence of global relational perspectives. arXiv preprint arXiv:1809.05093, 2018.

[31] Jianhao M Yang. Switching Quantum Reference Frames for Quantum Measurement. Quantum, 4: 283, 2020.

[32] Flaminia Giacomini, Esteban Castro-Ruiz, and Časlav Brukner. Relativistic quantum reference frames: the operational meaning of spin. Phys. Rev. Lett., 123 (9): 090404, 2019b.

[33] Lucas F Streiter, Flaminia Giacomini, and Časlav Brukner. A Relativistic Bell Test within Quantum Reference Frames. arXiv preprint arXiv:2008.03317, 2020.

[34] Philipp A Höhn and Augustin Vanrietvelde. How to switch between relational quantum clocks. arXiv preprint arXiv:1810.04153, 2018.

[35] Philipp A Höhn, Alexander RH Smith, and Maximilian PE Lock. The trinity of relational quantum dynamics. arXiv preprint arXiv:1912.00033, 2019.

[36] Esteban Castro-Ruiz, Flaminia Giacomini, Alessio Belenchia, and Časlav Brukner. Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems. Nat. Commun., 11 (1): 1–12, 2020.

[37] Philipp A Höhn, Alexander RH Smith, and Maximilian PE Lock. Equivalence of approaches to relational quantum dynamics in relativistic settings. arXiv preprint arXiv:2007.00580, 2020.

[38] Philipp A Höhn. Switching internal times and a new perspective on the wave function of the universe. Universe, 5 (5): 116, 2019.

[39] Anne-Catherine de la Hamette and Thomas D. Galley. Quantum reference frames for general symmetry groups. Quantum, 4: 367, November 2020.

[40] Marius Krumm, Philipp A. Höhn, and Markus P. Müller. Quantum reference frame transformations as symmetries and the paradox of the third particle. arXiv preprint arXiv:2011.01951, 2020.

[41] Kurt Bernardo Wolf. Geometric Optics on Phase Space. Springer-Verlag, 2004.

[42] Vyjayanthi Chari and Andrew Pressley. A guide to quantum groups. Cambridge University Press, 1995.

[43] Robert Gilmore. Lie groups, Lie algebras and some of their applications. John Wiley & Sons, 1974.

[44] Marcos Moshinsky and Christiane Quesne. Linear canonical transformations and their unitary representations. J. Math. Phys., 12 (8): 1772–1780, 1971.

[45] Nathan Jacobson. Lie algebras. John Wiley & Sons, 1966.

[46] Robert H Dicke. Coherence in spontaneous radiation processes. Phys. Rev., 93 (1): 99, 1954.

[47] Andrei B Klimov and Sergei M Chumakov. A group-theoretical approach to quantum optics: models of atom-field interactions. John Wiley & Sons, 2009.

[48] Angel Ballesteros and Sergei M Chumakov. On the spectrum of a Hamiltonian defined on $su_q(2)$ and quantum optical models. J. Phys. A, 32 (35): 6261–6269, 1999.

[49] Angel Ballesteros, Giulia Gubitosi, and Francisco J. Herranz. Lorentzian Snyder spacetimes and their Galilei and Carroll limits from projective geometry. Class. Quant. Grav., 37 (19): 195021, 2020.

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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Graphene Superconductors May Be Less Exotic Than Physicists Hoped



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



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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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.

► BibTeX data

► References

[1] V. Weisskopf and E. Wigner. Berechnung der natürlichen Linienbreite auf Grund der Diracschen Lichttheorie. Zeitschrift für Physik, 63 (1): 54–73, January 1930. ISSN 0044-3328. 10.1007/​BF01336768.

[2] Marlan O. Scully and M. Suhail Zubairy. Quantum optics. Cambridge University Press, September 1997. 10.1017/​CBO9780511813993.

[3] J. E. Sipe. Photon wave functions. Physical Review A, 52 (3): 1875–1883, September 1995. 10.1103/​PhysRevA.52.1875.

[4] Iwo Bialynicki-Birula. On the wave function of the photon. Acta Physica Polonica A, 86 (1-2): 97–111, August 1994. 10.12693/​APHYSPOLA.86.97.

[5] Iwo Bialynicki-Birula. Progress in Optics, volume XXXVI, chapter Photon wave function, pages 245–294. Elsevier, Amsterdam, 1996. 10.1016/​S0079-6638(08)70316-0.

[6] Jeff S. Lundeen, Brandon Sutherland, Aabid Patel, Corey Stewart, and Charles Bamber. Direct measurement of the quantum wavefunction. Nature, 474 (7350): 188–191, June 2011. ISSN 1476-4687. 10.1038/​nature10120.

[7] Alex O. C. Davis, Valérian Thiel, Michał Karpiński, and Brian J. Smith. Measuring the Single-Photon Temporal-Spectral Wave Function. Physical Review Letters, 121 (8): 083602, August 2018. 10.1103/​PhysRevLett.121.083602.

[8] T. D. Newton and E. P. Wigner. Localized States for Elementary Systems. Reviews of Modern Physics, 21 (3): 400–406, July 1949. 10.1103/​RevModPhys.21.400.

[9] Srikanth J. Srinivasan, Neereja M. Sundaresan, Darius Sadri, Yanbing Liu, Jay M. Gambetta, Terri Yu, S. M. Girvin, and Andrew A. Houck. Time-reversal symmetrization of spontaneous emission for quantum state transfer. Physical Review A, 89 (3): 033857, March 2014. 10.1103/​PhysRevA.89.033857.

[10] M. Pechal, L. Huthmacher, C. Eichler, S. Zeytinoğlu, A. A. Abdumalikov, S. Berger, A. Wallraff, and S. Filipp. Microwave-Controlled Generation of Shaped Single Photons in Circuit Quantum Electrodynamics. Physical Review X, 4 (4): 041010, October 2014. 10.1103/​PhysRevX.4.041010.

[11] P. Forn-Díaz, J. J. García-Ripoll, B. Peropadre, M. A. Yurtalan, J.-L. Orgiazzi, R. Belyansky, C. M. Wilson, and A. Lupascu. Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime. Nature Physics, 13 (1): 39–43, October 2016. ISSN 1745-2473, 1745-2481. 10.1038/​nphys3905.

[12] N. K. Langford, R. Sagastizabal, M. Kounalakis, C. Dickel, A. Bruno, F. Luthi, D. J. Thoen, A. Endo, and L. DiCarlo. Experimentally simulating the dynamics of quantum light and matter at deep-strong coupling. Nature Communications, 8 (1): 1715, November 2017. ISSN 2041-1723. 10.1038/​s41467-017-01061-x.

[13] Jochen Braumüller, Michael Marthaler, Andre Schneider, Alexander Stehli, Hannes Rotzinger, Martin Weides, and Alexey V. Ustinov. Analog quantum simulation of the Rabi model in the ultra-strong coupling regime. Nature Communications, 8 (1): 779, October 2017. ISSN 2041-1723. 10.1038/​s41467-017-00894-w.

[14] Yanbing Liu and Andrew A. Houck. Quantum electrodynamics near a photonic bandgap. Nature Physics, 13 (1): 48–52, January 2017. ISSN 1745-2481. 10.1038/​nphys3834.

[15] Nicholas T. Bronn, Yanbing Liu, Jared B. Hertzberg, Antonio D. Córcoles, Andrew A. Houck, Jay M. Gambetta, and Jerry M. Chow. Broadband filters for abatement of spontaneous emission in circuit quantum electrodynamics. Applied Physics Letters, 107 (17): 172601, October 2015. ISSN 0003-6951. 10.1063/​1.4934867.

[16] I.-C. Hoi, A. F. Kockum, L. Tornberg, A. Pourkabirian, G. Johansson, P. Delsing, and C. M. Wilson. Probing the quantum vacuum with an artificial atom in front of a mirror. Nature Physics, 11 (12): 1045–1049, 2015. ISSN 1745-2481. 10.1038/​nphys3484.

[17] J. A. Mlynek, A. A. Abdumalikov, C. Eichler, and A. Wallraff. Observation of Dicke superradiance for two artificial atoms in a cavity with high decay rate. Nature Communications, 5: 5186, November 2014. ISSN 2041-1723. 10.1038/​ncomms6186.

[18] Mohammad Mirhosseini, Eunjong Kim, Xueyue Zhang, Alp Sipahigil, Paul B. Dieterle, Andrew J. Keller, Ana Asenjo-Garcia, Darrick E. Chang, and Oskar Painter. Cavity quantum electrodynamics with atom-like mirrors. Nature, 569 (7758): 692–697, May 2019. ISSN 1476-4687. 10.1038/​s41586-019-1196-1.

[19] G. Wendin. Quantum information processing with superconducting circuits: a review. Reports on Progress in Physics, 80 (10): 106001, September 2017. ISSN 0034-4885. 10.1088/​1361-6633/​aa7e1a.

[20] Carlton M. Caves. Quantum limits on noise in linear amplifiers. Physical Review D, 26 (8): 1817–1839, October 1982. 10.1103/​PhysRevD.26.1817.

[21] N. Bergeal, F. Schackert, M. Metcalfe, R. Vijay, V. E. Manucharyan, L. Frunzio, D. E. Prober, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret. Phase-preserving amplification near the quantum limit with a Josephson ring modulator. Nature, 465 (7294): 64–68, May 2010. ISSN 1476-4687. 10.1038/​nature09035.

[22] M. Dalmonte, S. I. Mirzaei, P. R. Muppalla, D. Marcos, P. Zoller, and G. Kirchmair. Realizing dipolar spin models with arrays of superconducting qubits. Physical Review B, 92 (17): 174507, November 2015. 10.1103/​PhysRevB.92.174507.

[23] Kevin Lalumière, Barry C. Sanders, A. F. van Loo, A. Fedorov, A. Wallraff, and A. Blais. Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms. Physical Review A, 88 (4): 043806, October 2013. 10.1103/​PhysRevA.88.043806.

[24] A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf. Generating single microwave photons in a circuit. Nature, 449 (7160): 328–331, September 2007. ISSN 1476-4687. 10.1038/​nature06126.

[25] A. A. Abdumalikov, O. V. Astafiev, Yu. A. Pashkin, Y. Nakamura, and J. S. Tsai. Dynamics of Coherent and Incoherent Emission from an Artificial Atom in a 1d Space. Physical Review Letters, 107 (4): 043604, July 2011. 10.1103/​PhysRevLett.107.043604.

[26] C. Eichler, D. Bozyigit, C. Lang, L. Steffen, J. Fink, and A. Wallraff. Experimental State Tomography of Itinerant Single Microwave Photons. Physical Review Letters, 106 (22): 220503, June 2011. 10.1103/​PhysRevLett.106.220503.

[27] F. Mallet, M. A. Castellanos-Beltran, H. S. Ku, S. Glancy, E. Knill, K. D. Irwin, G. C. Hilton, L. R. Vale, and K. W. Lehnert. Quantum State Tomography of an Itinerant Squeezed Microwave Field. Physical Review Letters, 106 (22): 220502, June 2011. 10.1103/​PhysRevLett.106.220502.

[28] Tomás Ramos and Juan José García-Ripoll. Multiphoton scattering tomography with coherent states. Phys. Rev. Lett., 119: 153601, Oct 2017. 10.1103/​PhysRevLett.119.153601.

[29] Peter C. Chen. An Introduction to Coherent Multidimensional Spectroscopy. Applied Spectroscopy, 70 (12): 1937–1951, December 2016. ISSN 0003-7028. 10.1177/​0003702816669730.

[30] A. Lukashenko and A. V. Ustinov. Improved powder filters for qubit measurements. Review of Scientific Instruments, 79 (1): 014701, January 2008. ISSN 0034-6748. 10.1063/​1.2827515.

[31] Florent Lecocq, Ioan M Pop, Zhihui Peng, Iulian Matei, Thierry Crozes, Thierry Fournier, Cécile Naud, Wiebke Guichard, and Olivier Buisson. Junction fabrication by shadow evaporation without a suspended bridge. Nanotechnology, 22 (31): 315302, August 2011. ISSN 0957-4484, 1361-6528. 10.1088/​0957-4484/​22/​31/​315302.

[32] J.R. Johansson, P.D. Nation, and Franco Nori. Qutip: An open-source python framework for the dynamics of open quantum systems. Computer Physics Communications, 183 (8): 1760–1772, 2012. ISSN 0010-4655. https:/​/​​10.1016/​j.cpc.2012.02.021.

[33] J.R. Johansson, P.D. Nation, and Franco Nori. Qutip 2: A python framework for the dynamics of open quantum systems. Computer Physics Communications, 184 (4): 1234–1240, 2013. ISSN 0010-4655. https:/​/​​10.1016/​j.cpc.2012.11.019.

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Variational quantum solver employing the PDS energy functional



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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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] S. Amari. Natural gradient works efficiently in learning. Neural Computation, 10 (2): 251–276, 1998. https:/​/​​10.1162/​089976698300017746.

[2] Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Rami Barends, Sergio Boixo, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Yu Chen, Zijun Chen, Benjamin Chiaro, Roberto Collins, William Courtney, Sean Demura, Andrew Dunsworth, Edward Farhi, Austin Fowler, Brooks Foxen, Craig Gidney, Marissa Giustina, Rob Graff, Steve Habegger, Matthew P. Harrigan, Alan Ho, Sabrina Hong, Trent Huang, William J. Huggins, Lev Ioffe, Sergei V. Isakov, Evan Jeffrey, Zhang Jiang, Cody Jones, Dvir Kafri, Kostyantyn Kechedzhi, Julian Kelly, Seon Kim, Paul V. Klimov, Alexander Korotkov, Fedor Kostritsa, David Landhuis, Pavel Laptev, Mike Lindmark, Erik Lucero, Orion Martin, John M. Martinis, Jarrod R. McClean, Matt McEwen, Anthony Megrant, Xiao Mi, Masoud Mohseni, Wojciech Mruczkiewicz, Josh Mutus, Ofer Naaman, Matthew Neeley, Charles Neill, Hartmut Neven, Murphy Yuezhen Niu, Thomas E. O’Brien, Eric Ostby, Andre Petukhov, Harald Putterman, Chris Quintana, Pedram Roushan, Nicholas C. Rubin, Daniel Sank, Kevin J. Satzinger, Vadim Smelyanskiy, Doug Strain, Kevin J. Sung, Marco Szalay, Tyler Y. Takeshita, Amit Vainsencher, Theodore White, Nathan Wiebe, Z. Jamie Yao, Ping Yeh, and Adam Zalcman. Hartree-fock on a superconducting qubit quantum computer. Science, 369 (6507): 1084–1089, 2020. https:/​/​​10.1126/​science.abb9811.

[3] Ryan Babbush, Nathan Wiebe, Jarrod McClean, James McClain, Hartmut Neven, and Garnet Kin-Lic Chan. Low-depth quantum simulation of materials. Phys. Rev. X, 8: 011044, 2018. https:/​/​​10.1103/​PhysRevX.8.011044.

[4] Rodney J. Bartlett, Stanisław A. Kucharski, and Jozef Noga. Alternative coupled-cluster ansätze II. the unitary coupled-cluster method. Chem. Phys. Lett., 155 (1): 133–140, 1989. https:/​/​​10.1016/​s0009-2614(89)87372-5.

[5] Dominic W Berry, Graeme Ahokas, Richard Cleve, and Barry C Sanders. Efficient quantum algorithms for simulating sparse hamiltonians. Comm. Math. Phys., 270 (2): 359–371, 2007. https:/​/​​10.1007/​s00220-006-0150-x.

[6] Dominic W. Berry, Andrew M. Childs, Richard Cleve, Robin Kothari, and Rolando D. Somma. Simulating hamiltonian dynamics with a truncated taylor series. Phys. Rev. Lett., 114: 090502, 2015. https:/​/​​10.1103/​PhysRevLett.114.090502.

[7] Tatiana A. Bespalova and Oleksandr Kyriienko. Hamiltonian operator approximation for energy measurement and ground state preparation. preprint, arXiv:2009.03351, 2020. URL https:/​/​​abs/​2009.03351.

[8] N. Bogolubov. On the theory of superfluidity. J. Phys., 11: 23–32, 1947. https:/​/​​10.1142/​9789814612524_0001.

[9] Sergey Bravyi, Jay M. Gambetta, Antonio Mezzacapo, and Kristan Temme. Tapering off qubits to simulate fermionic hamiltonians. preprint, arXiv:1701.08213, 2017. URL https:/​/​​abs/​1701.08213.

[10] M. Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, and Patrick J. Coles. Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nat. Commun., 12 (1), 2021. https:/​/​​10.1038/​s41467-021-21728-w.

[11] Marco Cerezo and Patrick J Coles. Impact of barren plateaus on the hessian and higher order derivatives. preprint, arXiv:2008.07454, 2020. URL https:/​/​​abs/​2008.07454. https:/​/​​10.1088/​2058-9565/​abf51a.

[12] Andrew M Childs. On the relationship between continuous-and discrete-time quantum walk. Comm. Math. Phys., 294 (2): 581–603, 2010. https:/​/​​10.1007/​s00220-009-0930-1.

[13] Andrew M. Childs and Nathan Wiebe. Hamiltonian simulation using linear combinations of unitary operations. Quantum Inf. Comput., 12 (11-12): 0901–0924, 2012. https:/​/​​10.26421/​qic12.11-12.

[14] Daniel Claudino, Bo Peng, Nicholas P. Bauman, Karol Kowalski, and Travis S. Humble. Improving the accuracy and efficiency of quantum connected moments expansions. Quantum Sci. Technol., accepted, 2021. https:/​/​​10.1088/​2058-9565/​ac0292.

[15] Richard Cleve, Artur Ekert, Chiara Macchiavello, and Michele Mosca. On quantum algorithms. Proc. R. Soc. Lond. A, 454 (1969): 339–354, 1998. https:/​/​​10.1002/​(SICI)1099-0526(199809/​10)4:1<33::AID-CPLX10>3.0.CO;2-U.

[16] J. I. Colless, V. V. Ramasesh, D. Dahlen, M. S. Blok, M. E. Kimchi-Schwartz, J. R. McClean, J. Carter, W. A. de Jong, and I. Siddiqi. Computation of molecular spectra on a quantum processor with an error-resilient algorithm. Phys. Rev. X, 8: 011021, 2018. https:/​/​​10.1103/​PhysRevX.8.011021.

[17] Francesco A Evangelista, Garnet Kin-Lic Chan, and Gustavo E Scuseria. Exact parameterization of fermionic wave functions via unitary coupled cluster theory. J. Chem. Phys., 151 (24): 244112, 2019. https:/​/​​10.1063/​1.5133059.

[18] Vassilios Fessatidis, Jay D Mancini, Robert Murawski, and Samuel P Bowen. A generalized moments expansion. Phys. Lett. A, 349 (5): 320–323, 2006. https:/​/​​10.1016/​j.physleta.2005.09.039.

[19] Vassilios Fessatidis, Frank A Corvino, Jay D Mancini, Robert K Murawski, and John Mikalopas. Analytic properties of moments matrices. Phys. Lett. A, 374 (28): 2890–2893, 2010. https:/​/​​10.1016/​j.physleta.2010.05.010.

[20] R. P. Feynman. Slow electrons in a polar crystal. Phys. Rev., 97: 660–665, 1955. https:/​/​​10.1103/​PhysRev.97.660.

[21] András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe. Quantum singular value transformation and beyond: Exponential improvements for quantum matrix arithmetics. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019, page 193–204, New York, NY, USA, 2019. Association for Computing Machinery. ISBN 9781450367059. https:/​/​​10.1145/​3313276.3316366.

[22] Pranav Gokhale, Olivia Angiuli, Yongshan Ding, Kaiwen Gui, Teague Tomesh, Martin Suchara, Margaret Martonosi, and Frederic T. Chong. $o(n^3)$ measurement cost for variational quantum eigensolver on molecular hamiltonians. IEEE Trans. Qunatum Eng., 1: 1–24, 2020. https:/​/​​10.1109/​TQE.2020.3035814.

[23] Jérôme F. Gonthier, Maxwell D. Radin, Corneliu Buda, Eric J. Doskocil, Clena M. Abuan, and Jhonathan Romero. Identifying challenges towards practical quantum advantage through resource estimation: the measurement roadblock in the variational quantum eigensolver. preprint, arXiv:2012.04001, 2020. URL https:/​/​​abs/​2012.04001.

[24] Harper R Grimsley, Sophia E Economou, Edwin Barnes, and Nicholas J Mayhall. An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nat. Commun., 10 (1): 1–9, 2019. https:/​/​​10.1038/​s41467-019-10988-2.

[25] Gian Giacomo Guerreschi and Mikhail Smelyanskiy. Practical optimization for hybrid quantum-classical algorithms. preprint, arXiv:1701.01450, 2017. URL https:/​/​​abs/​1701.01450.

[26] T. Häner, D. S. Steiger, M. Smelyanskiy, and M. Troyer. High performance emulation of quantum circuits. In SC ’16: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, pages 866–874, Nov 2016. https:/​/​​10.1109/​SC.2016.73.

[27] Mark R Hoffmann and Jack Simons. A unitary multiconfigurational coupled-cluster method: Theory and applications. J. Chem. Phys., 88 (2): 993–1002, 1988. https:/​/​​10.1063/​1.454125.

[28] William J. Huggins, Jarrod R. McClean, Nicholas C. Rubin, Zhang Jiang, Nathan Wiebe, K. Birgitta Whaley, and Ryan Babbush. Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers. npj Quantum Inf., 7 (1): 23, 2021. https:/​/​​10.1038/​s41534-020-00341-7.

[29] William James Huggins, Joonho Lee, Unpil Baek, Bryan O’Gorman, and K Birgitta Whaley. A non-orthogonal variational quantum eigensolver. New J. Phys., 22: 073009, 2020. https:/​/​​10.1088/​1367-2630/​ab867b.

[30] Artur F. Izmaylov, Tzu-Ching Yen, Robert A. Lang, and Vladyslav Verteletskyi. Unitary partitioning approach to the measurement problem in the variational quantum eigensolver method. J. Chem. Theory Comput., 16 (1): 190–195, 2020. https:/​/​​10.1021/​acs.jctc.9b00791.

[31] Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M. Chow, and Jay M. Gambetta. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549: 242–246, 2017. https:/​/​​10.1038/​nature23879.

[32] Abhinav Kandala, Kristan Temme, Antonio D Corcoles, Antonio Mezzacapo, Jerry M Chow, and Jay M Gambetta. Error mitigation extends the computational reach of a noisy quantum processor. Nature, 567: 491–495, 2019. https:/​/​​10.1038/​s41586-019-1040-7.

[33] Peter J Knowles. On the validity and applicability of the connected moments expansion. Chem. Phys. Lett., 134 (6): 512–518, 1987. https:/​/​​10.1016/​0009-2614(87)87184-1.

[34] Karol Kowalski and Bo Peng. Quantum simulations employing connected moments expansions. J. Chem. Phys., 153 (20): 201102, 2020. https:/​/​​10.1063/​5.0030688.

[35] Werner Kutzelnigg. Error analysis and improvements of coupled-cluster theory. Theor. Chim. Acta, 80 (4-5): 349–386, 1991. https:/​/​​10.1007/​BF01117418.

[36] Oleksandr Kyriienko. Quantum inverse iteration algorithm for programmable quantum simulators. npj Quantum Inf., 6 (1): 1–8, 2020. https:/​/​​10.1038/​s41534-019-0239-7.

[37] Joonho Lee, William J. Huggins, Martin Head-Gordon, and K. Birgitta Whaley. Generalized unitary coupled cluster wave functions for quantum computation. J. Chem. Theory Comput., 15 (1): 311–324, 2019. https:/​/​​10.1021/​acs.jctc.8b01004.

[38] A Luis and J Peřina. Optimum phase-shift estimation and the quantum description of the phase difference. Phys. Rev. A, 54 (5): 4564, 1996. https:/​/​​10.1103/​PhysRevA.54.4564.

[39] Jay D Mancini, Yu Zhou, and Peter F Meier. Analytic properties of connected moments expansions. Int. J. Quantum Chem., 50 (2): 101–107, 1994. https:/​/​​10.1002/​qua.560500203.

[40] Jay D Mancini, William J Massano, Janice D Prie, and Yu Zhuo. Avoidance of singularities in moments expansions: a numerical study. Phys. Lett. A, 209 (1-2): 107–112, 1995. https:/​/​​10.1016/​0375-9601(95)00757-2.

[41] Carlos Ortiz Marrero, Mária Kieferová, and Nathan Wiebe. Entanglement induced barren plateaus. preprint, arXiv:2010.15968, 2020. URL https:/​/​​abs/​2010.15968.

[42] Sam McArdle, Tyson Jones, Suguru Endo, Ying Li, Simon C Benjamin, and Xiao Yuan. Variational ansatz-based quantum simulation of imaginary time evolution. npj Quantum Inf., 5 (1): 1–6, 2019. https:/​/​​10.1038/​s41534-019-0187-2.

[43] Sam McArdle, Suguru Endo, Alan Aspuru-Guzik, Simon C Benjamin, and Xiao Yuan. Quantum computational chemistry. Rev. Mod. Phys., 92 (1): 015003, 2020. https:/​/​​10.1103/​RevModPhys.92.015003.

[44] Jarrod R McClean, Jonathan Romero, Ryan Babbush, and Alán Aspuru-Guzik. The theory of variational hybrid quantum-classical algorithms. New J. Phys., 18 (2): 023023, 2016. https:/​/​​10.1088/​1367-2630/​18/​2/​023023.

[45] Jarrod R McClean, Sergio Boixo, Vadim N Smelyanskiy, Ryan Babbush, and Hartmut Neven. Barren plateaus in quantum neural network training landscapes. Nat. Commun., 9 (1): 1–6, 2018. https:/​/​​10.1038/​s41467-018-07090-4.

[46] Mario Motta, Chong Sun, Adrian TK Tan, Matthew J O’Rourke, Erika Ye, Austin J Minnich, Fernando GSL Brandão, and Garnet Kin-Lic Chan. Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution. Nat. Phys., 16 (2): 205–210, 2020. https:/​/​​10.1038/​s41567-019-0704-4.

[47] Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, New York, NY, USA, 10th edition, 2011. ISBN 1107002176, 9781107002173. https:/​/​​10.1017/​CBO9780511976667.

[48] Robert M Parrish and Peter L McMahon. Quantum filter diagonalization: Quantum eigendecomposition without full quantum phase estimation. preprint, arXiv:1909.08925, 2019. URL https:/​/​​abs/​1909.08925.

[49] François M Peeters and Jozef T Devreese. Upper bounds for the free energy. a generalisation of the bogolubov inequality and the feynman inequality. J. Phys. A: Math. Gen., 17 (3): 625, 1984. https:/​/​​10.1088/​0305-4470/​17/​3/​024.

[50] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’brien. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun., 5: 4213, 2014. https:/​/​​10.1038/​ncomms5213.

[51] Arthur Pesah, M Cerezo, Samson Wang, Tyler Volkoff, Andrew T Sornborger, and Patrick J Coles. Absence of barren plateaus in quantum convolutional neural networks. preprint, arXiv:2011.02966, 2020. URL https:/​/​​abs/​2011.02966.

[52] David Poulin, Alexei Kitaev, Damian S. Steiger, Matthew B. Hastings, and Matthias Troyer. Quantum algorithm for spectral measurement with a lower gate count. Phys. Rev. Lett., 121: 010501, 2018. https:/​/​​10.1103/​PhysRevLett.121.010501.

[53] John Preskill. Quantum computing in the nisq era and beyond. Quantum, 2: 79, 2018. https:/​/​​10.22331/​q-2018-08-06-79.

[54] Janice D Prie, D Schwall, Jay D Mancini, D Kraus, and William J Massano. On the relation between the connected-moments expansion and the lanczos variational scheme. Nuov. Cim. D, 16 (5): 433–448, 1994. https:/​/​​10.1007/​BF02463732.

[55] Jonathan Romero, Ryan Babbush, Jarrod R McClean, Cornelius Hempel, Peter J Love, and Alán Aspuru-Guzik. Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz. Quantum Sci. Technol., 4 (1): 014008, 2018. https:/​/​​10.1088/​2058-9565/​aad3e4.

[56] Nicholas C Rubin, Ryan Babbush, and McClean Jarrod. Application of fermionic marginal constraints to hybrid quantum algorithms. New J. Phys., 20: 053020, 2018. https:/​/​​10.1088/​1367-2630/​aab919.

[57] Maria Schuld, Ville Bergholm, Christian Gogolin, Josh Izaac, and Nathan Killoran. Evaluating analytic gradients on quantum hardware. Phys. Rev. A, 99: 032331, 2019. https:/​/​​10.1103/​PhysRevA.99.032331.

[58] Jacob T. Seeley, Martin J. Richard, and Peter J. Love. The bravyi-kitaev transformation for quantum computation of electronic structure. J. Chem. Phys., 137 (22): 224109, 2012. https:/​/​​10.1063/​1.4768229.

[59] Kazuhiro Seki and Seiji Yunoki. Quantum power method by a superposition of time-evolved states. PRX Quantum, 2: 010333, 2021. https:/​/​​10.1103/​PRXQuantum.2.010333.

[60] Yangchao Shen, Xiang Zhang, Shuaining Zhang, Jing-Ning Zhang, Man-Hong Yung, and Kihwan Kim. Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure. Phys. Rev. A, 95: 020501, 2017. https:/​/​​10.1103/​PhysRevA.95.020501.

[61] Peter W Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev., 41 (2): 303–332, 1999. https:/​/​​10.1137/​S0036144598347011.

[62] Andrey V Soldatov. Generalized variational principle in quantum mechanics. Int. J. Mod. Phys. B, 9 (22): 2899–2936, 1995. https:/​/​​10.1142/​S0217979295001087.

[63] James Stokes, Josh Izaac, Nathan Killoran, and Giuseppe Carleo. Quantum Natural Gradient. Quantum, 4: 269, 2020. https:/​/​​10.22331/​q-2020-05-25-269.

[64] Andrew G Taube and Rodney J Bartlett. New perspectives on unitary coupled-cluster theory. Int. J. Quantum Chem., 106 (15): 3393–3401, 2006. https:/​/​​10.1002/​qua.21198.

[65] Nazakat Ullah. Removal of the singularity in the moment-expansion formalism. Phys. Rev. A, 51 (3): 1808, 1995. https:/​/​​10.1103/​PhysRevA.51.1808.

[66] Alexey Uvarov and Jacob Biamonte. On barren plateaus and cost function locality in variational quantum algorithms. J. Phys. A: Math. and Theo., 54: 245301, 2021. https:/​/​​10.1088/​1751-8121/​abfac7.

[67] Harish J. Vallury, Michael A. Jones, Charles D. Hill, and Lloyd C. L. Hollenberg. Quantum computed moments correction to variational estimates. Quantum, 4: 373, 2020. https:/​/​​10.22331/​q-2020-12-15-373.

[68] Samson Wang, Enrico Fontana, Marco Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, and Patrick J Coles. Noise-induced barren plateaus in variational quantum algorithms. preprint, arXiv:2007.14384, 2020. URL https:/​/​​abs/​2007.14384.

[69] Dave Wecker, Matthew B. Hastings, and Matthias Troyer. Progress towards practical quantum variational algorithms. Phys. Rev. A, 92: 042303, 2015. https:/​/​​10.1103/​PhysRevA.92.042303.

[70] David Wierichs, Christian Gogolin, and Michael Kastoryano. Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer. Phys. Rev. Research, 2: 043246, 2020. https:/​/​​10.1103/​PhysRevResearch.2.043246.

[71] Naoki Yamamoto. On the natural gradient for variational quantum eigensolver. preprint, arXiv:1909.05074, 2019. URL https:/​/​​abs/​1909.05074.

[72] Tzu-Ching Yen, Vladyslav Verteletskyi, and Artur F. Izmaylov. Measuring all compatible operators in one series of single-qubit measurements using unitary transformations. J. Chem. Theory Comput., 16 (4): 2400–2409, 2020. https:/​/​​10.1021/​acs.jctc.0c00008.

[73] Xiao Yuan, Suguru Endo, Qi Zhao, Ying Li, and Simon C. Benjamin. Theory of variational quantum simulation. Quantum, 3: 191, 2019. https:/​/​​10.22331/​q-2019-10-07-191.

Cited by

[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.

[3] Daniel Claudino, Alexander J. McCaskey, and Dmitry I. Lyakh, “A backend-agnostic, quantum-classical framework for simulations of chemistry in C++”, arXiv:2105.01619.

[4] Dmitry A. Fedorov, Bo Peng, Niranjan Govind, and Yuri Alexeev, “VQE Method: A Short Survey and Recent Developments”, arXiv:2103.08505.

The above citations are from SAO/NASA ADS (last updated successfully 2021-06-10 14:55:33). The list may be incomplete as not all publishers provide suitable and complete citation data.

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Certifying dimension of quantum systems by sequential projective measurements



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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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.

► BibTeX data

► References

[1] J. Eisert, D. Hangleiter, N. Walk, I. Roth, D. Markham, R. Parekh, U. Chabaud, and E. Kashefi, Nature Reviews Physics 2, 382 (2020).

[2] M. Kliesch and I. Roth, Theory of quantum system certification – a tutorial (2020), arXiv:2010.05925 [quant-ph].

[3] I. Šupić and J. Bowles, Quantum 4, 337 (2020).

[4] K. Bharti, M. Ray, A. Varvitsiotis, N. A. Warsi, A. Cabello, and L.-C. Kwek, Phys. Rev. Lett. 122, 250403 (2019).

[5] A. Tavakoli, J. m. k. Kaniewski, T. Vértesi, D. Rosset, and N. Brunner, Phys. Rev. A 98, 062307 (2018).

[6] A. Sohbi and J. Kim, Phys. Rev. A 100, 022117 (2019).

[7] D. Saha, R. Santos, and R. Augusiak, Quantum 4, 302 (2020).

[8] D. G. Marangon, G. Vallone, and P. Villoresi, Phys. Rev. Lett. 118, 060503 (2017).

[9] A. Acín and L. Masanes, Nature 540, 213 (2016).

[10] T. Lunghi, J. B. Brask, C. C. W. Lim, Q. Lavigne, J. Bowles, A. Martin, H. Zbinden, and N. Brunner, Phys. Rev. Lett. 114, 150501 (2015).

[11] N. Brunner, S. Pironio, A. Acin, N. Gisin, A. A. Méthot, and V. Scarani, Physical Review Letters 100, 10.1103/​physrevlett.100.210503 (2008).

[12] R. Gallego, N. Brunner, C. Hadley, and A. Acín, Phys. Rev. Lett. 105, 230501 (2010).

[13] N. Brunner, M. Navascués, and T. Vértesi, Phys. Rev. Lett. 110, 150501 (2013).

[14] O. Gühne, C. Budroni, A. Cabello, M. Kleinmann, and J.-A. Larsson, Phys. Rev. A 89, 062107 (2014).

[15] A. Sohbi, I. Zaquine, E. Diamanti, and D. Markham, Phys. Rev. A 94, 032114 (2016).

[16] Y. Cai, J.-D. Bancal, J. Romero, and V. Scarani, Journal of Physics A: Mathematical and Theoretical 49, 305301 (2016).

[17] H.-W. Li, Y.-S. Zhang, X.-B. An, Z.-F. Han, and G.-C. Guo, Communications Physics 1, 10 (2018).

[18] D. Saha, P. Horodecki, and M. Pawłowski, New Journal of Physics 21, 093057 (2019).

[19] E. T. Campbell, H. Anwar, and D. E. Browne, Phys. Rev. X 2, 041021 (2012).

[20] E. T. Campbell, Phys. Rev. Lett. 113, 230501 (2014).

[21] A. Krishna and J.-P. Tillich, Phys. Rev. Lett. 123, 070507 (2019).

[22] B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, Nature Physics 5, 134 (2009).

[23] H. S. Tonchev and N. V. Vitanov, Phys. Rev. A 94, 042307 (2016).

[24] A. Bocharov, M. Roetteler, and K. M. Svore, Phys. Rev. A 96, 012306 (2017).

[25] G. Duclos-Cianci and D. Poulin, Phys. Rev. A 87, 062338 (2013).

[26] M. H. Michael, M. Silveri, R. T. Brierley, V. V. Albert, J. Salmilehto, L. Jiang, and S. M. Girvin, Phys. Rev. X 6, 031006 (2016).

[27] M. Grassl, L. Kong, Z. Wei, Z. Yin, and B. Zeng, IEEE Transactions on Information Theory 64, 4674 (2018).

[28] M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, E. Lucero, A. D. O’Connell, D. Sank, H. Wang, J. Wenner, A. N. Cleland, M. R. Geller, and J. M. Martinis, Science 325, 722 (2009).

[29] M. Y. Niu, I. L. Chuang, and J. H. Shapiro, Phys. Rev. Lett. 120, 160502 (2018).

[30] D. Cozzolino, B. Da Lio, D. Bacco, and L. K. Oxenløwe, Advanced Quantum Technologies 2, 1900038 (2019).

[31] Y.-H. Luo, H.-S. Zhong, M. Erhard, X.-L. Wang, L.-C. Peng, M. Krenn, X. Jiang, L. Li, N.-L. Liu, C.-Y. Lu, A. Zeilinger, and J.-W. Pan, Phys. Rev. Lett. 123, 070505 (2019).

[32] A. Marin and D. Markham, Phys. Rev. A 88, 042332 (2013).

[33] J. Hoffmann, C. Spee, O. Gühne, and C. Budroni, New Journal of Physics 20, 102001 (2018).

[34] C. Spee, H. Siebeneich, T. F. Gloger, P. Kaufmann, M. Johanning, M. Kleinmann, C. Wunderlich, and O. Gühne, New Journal of Physics 22, 023028 (2020).

[35] Y. Mao, C. Spee, Z.-P. Xu, and O. Gühne, Structure of dimension-bounded temporal correlations (2020), arXiv:2005.13964 [quant-ph].

[36] A. Sohbi, R. Ohana, I. Zaquine, E. Diamanti, and D. Markham, Experimental approach to demonstrating contextuality for qudits (2020), arXiv:2010.13278 [quant-ph].

[37] M. Ray, N. G. Boddu, K. Bharti, L.-C. Kwek, and A. Cabello, Graph-theoretic approach to dimension witnessing (2020), arXiv:2007.10746 [quant-ph].

[38] M. Navascués, S. Pironio, and A. Acín, New Journal of Physics 10, 073013 (2008).

[39] S. Pironio, M. Navascués, and A. Acín, SIAM Journal on Optimization 20, 2157 (2010).

[40] M. Navascués and T. Vértesi, Phys. Rev. Lett. 115, 020501 (2015).

[41] M. Navascués, A. Feix, M. Araújo, and T. Vértesi, Phys. Rev. A 92, 042117 (2015).

[42] H. H. Jee, C. Sparaciari, O. Fawzi, and M. Berta, Characterising quantum correlations of fixed dimension (2020), arXiv:2005.08883 [quant-ph].

[43] G. Lüders, Annalen der Physik 15, 663–670 (2006).

[44] C. Budroni and C. Emary, Physical Review Letters 113, 10.1103/​physrevlett.113.050401 (2014).

[45] G. Schild and C. Emary, Physical Review A 92, 10.1103/​physreva.92.032101 (2015).

[46] Guth, Monatshefte für Mathematik und Physik 40, A31 (1933).

[47] A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985).

[48] C. Budroni, T. Moroder, M. Kleinmann, and O. Gühne, Phys. Rev. Lett. 111, 020403 (2013).

[49] N. D. Mermin, Phys. Rev. Lett. 65, 3373 (1990).

[50] A. Peres, Physics Letters A 151, 107 (1990).

[51] M. L. Almeida, J.-D. Bancal, N. Brunner, A. Acín, N. Gisin, and S. Pironio, Phys. Rev. Lett. 104, 230404 (2010).

[52] A. Sohbi, Online repository: Bounding the dimension of quantum systems via sequential measurements (2021).

[53] M. Navascués, G. de la Torre, and T. Vértesi, Phys. Rev. X 4, 011011 (2014).

[54] J. M. Donohue and E. Wolfe, Phys. Rev. A 92, 062120 (2015).

[55] G. Vidal and R. Tarrach, Phys. Rev. A 59, 141 (1999), arXiv:quant-ph/​9806094 [quant-ph].

[56] D. Cavalcanti and P. Skrzypczyk, Reports on Progress in Physics 80, 024001 (2017), arXiv:1604.00501 [quant-ph].

[57] J. Bavaresco, M. T. Quintino, L. Guerini, T. O. Maciel, D. Cavalcanti, and M. T. Cunha, Physical Review A 96, 10.1103/​physreva.96.022110 (2017).

[58] S. Designolle, M. Farkas, and J. Kaniewski, New Journal of Physics 21, 113053 (2019), arXiv:1906.00448 [quant-ph].

[59] M. Araújo, C. Branciard, F. Costa, A. Feix, C. Giarmatzi, and C. Brukner, New Journal of Physics 17, 102001 (2015).

[60] M. Oszmaniec and T. Biswas, Quantum 3, 133 (2019).

[61] K. Baek, A. Sohbi, J. Lee, J. Kim, and H. Nha, New Journal of Physics 22, 093019 (2020).

[62] S. Diamond and S. Boyd, Journal of Machine Learning Research 17, 1 (2016).

[63] A. Agrawal, R. Verschueren, S. Diamond, and S. Boyd, Journal of Control and Decision 5, 42 (2018).

[64] M. ApS, MOSEK Optimizer API for Python 9.2.28 (2020).

[65] J. Bertrand, Calcul des probabilités (Editions Jacques Gabay, 2006).

[66] I. Šupić and J. Bowles, Quantum 4, 337 (2020).

[67] A. A. Klyachko, M. A. Can, S. Binicioğlu, and A. S. Shumovsky, Phys. Rev. Lett. 101, 020403 (2008).

[68] F. Mezzadri, Notices of the American Mathematical Society 54, 592 (2007).

[69] M. Matsumoto and T. Nishimura, ACM Trans. Model. Comput. Simul. 8, 3–30 (1998).

[70] S. Boyd, S. P. Boyd, and L. Vandenberghe, Convex optimization (Cambridge university press, 2004).

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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