Connect with us

It’s “Extremely Unlikely” Ethereum Passes Its 2017 High Against Bitcoin: Here’s Why

Avatar

Published

on

From a price perspective, Ethereum’s golden age has long passed.

In 2017, the second-largest cryptocurrency saw a parabolic bull run that eclipsed that of most other top cryptocurrencies, Bitcoin included. There was a point in 2017 when one ETH was worth approximately 0.17 BTC (on Coinbase).

Ethereum rallied so far and so fast that for a few months near the peak of the mania, there were some expecting for its market capitalization to surpass that of Bitcoin.

But a long-time analyst and trader in the space doesn’t think that such strength will be seen again. And here’s why.

Will Ethereum Hit a New ATH Against Bitcoin? Top Investor Thinks Not

The expectations that Ethereum will rally strongly in the next market cycle has been sparked by Chris Burniske, a partner at Placeholder Capital.

On June 14th, the venture investor and top cryptocurrency analyst came out with a Twitter thread in which he explained the case for ETH to rally to $7,500 in the next (arguably ongoing) bull market cycle.

“If BTC goes > $50,000 in the next cycle, and ETHBTC returns to its former ATH, then expect to see ETH > $7,500. To the mainstream ETH will be the new kid on the block — expect a frenzy to go with that realization,” Burniske explained, showing how a 3,000% Ethereum rally in the coming years may be feasible.  

But according to a long-time pseudonymous cryptocurrency investor, this is unlikely to happen.

The commentator, part of the “Magical Crypto Friends” podcast with Charlie Lee, Samson Mow, and Riccardo Spagni, explained that ETH is “extremely unlikely to make a new ATH vs. Bitcoin.”

He cited two key factors:

  • The initial coin offering bubble has popped. This is important as the ICO craze is what drove Ethereum so high in 2017 and 2018.
  • There are “plenty of other smart contract platforms that are superior, have PoS, and that won’t do a complete rewrite of the code-breaking stuff.”

This strong assertion that Ethereum is unlikely to strongly rally against Bitcoin over the long run comes shortly after a fund manager said that there is no viable investment case for ETH.

In the Short-Term, a Rally Is Possible

While there are these long-term risk factors, that’s not to say that Ethereum can rally against Bitcoin in the short term.

Real Vision chief executive Raoul Pal noted earlier this month that ETH broke out against Bitcoin, moving above a symmetrical triangle that has confined price action over the past year:

“It even looks like Ether will outperform Bitcoin at some point (no position yet). Please remember: No tribal attacks about bitcoin vs ethereum. They are two different things and two different ecosystems.”

ETH/BTC

ETH/BTC chart from prominent Wall Street investor and analyst Raoul Pal (@RaoulGMI on Twitter).

Featured Image from Shutterstock
Price tags: ethusd, ethbtc
It's "Extremely Unlikely" Ethereum Passes Its 2017 High Against Bitcoin: Here's Why

Source: https://bitcoinist.com/its-extremely-unlikely-ethereum-passes-its-2017-high-against-bitcoin-heres-why/?utm_source=rss&utm_medium=rss&utm_campaign=its-extremely-unlikely-ethereum-passes-its-2017-high-against-bitcoin-heres-why

Quantum

Bell nonlocality with a single shot

Avatar

Published

on


Mateus Araújo1, Flavien Hirsch1, and Marco Túlio Quintino2,1,3

1Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
2Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
3Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

In order to reject the local hidden variables hypothesis, the usefulness of a Bell inequality can be quantified by how small a $p$-value it will give for a physical experiment. Here we show that to obtain a small expected $p$-value it is sufficient to have a large gap between the local and Tsirelson bounds of the Bell inequality, when it is formulated as a nonlocal game. We develop an algorithm for transforming an arbitrary Bell inequality into an equivalent nonlocal game with the largest possible gap, and show its results for the CGLMP and $I_{nn22}$ inequalities.

We present explicit examples of Bell inequalities with gap arbitrarily close to one, and show that this makes it possible to reject local hidden variables with arbitrarily small $p$-value in a single shot, without needing to collect statistics. We also develop an algorithm for calculating local bounds of general Bell inequalities which is significantly faster than the naïve approach, which may be of independent interest.

Nonlocal games are cooperative games between two parties, Alice and Bob, that are not allowed to communicate. The maximal probability with which Alice and Bob can win the game depends on how the world fundamentally works: if it respects classical ideas about locality and determinism, this maximal probability is given by the local bound. On the other hand, if the world works according to quantum mechanics, the maximal probability is given by the Tsirelson bound, which is larger than the local bound. This makes it possible to experimentally falsify the classical worldview: let Alice and Bob play a nonlocal game with quantum devices for many rounds, and if they win more often than the local bound predicts, that’s it.

The number of rounds it takes for a decisive rejection of the classical worldview depends on the statistical power of the nonlocal game: a more powerful game requires fewer rounds to reach a conclusion with the same degree of confidence. We show that in order to get a large statistical power, it is enough to have a large gap between the local bound and the Tsirelson bound of the nonlocal game. Moreover, we show that this gap depends on how precisely a nonlocal game is formulated, so we develop an algorithm to maximise the gap over all possible formulations of a nonlocal game. With this, we derive the most powerful version of several well-known nonlocal games, such as the CHSH game, the CGLMP games, and the Inn22 games.

A natural question to ask is how high can the statistical power of a nonlocal game get. We show that it can get arbitrarily high, by constructing two nonlocal games with gap between their local and Tsirelson bounds arbitrarily close to one. This makes it possible to conclusively falsify the classical worldview with a single round of the nonlocal game, without needing to collect statistics. Unfortunately, neither of these games is experimentally feasible, so the question of whether a single-shot falsification is possible in practice is still open.

► BibTeX data

► References

[1] J. S. Bell “On the Einstein-Poldolsky-Rosen paradox” Physics 1, 195-200 (1964).
https:/​/​doi.org/​10.1103/​PhysicsPhysiqueFizika.1.195

[2] John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt, “Proposed experiment to test local hidden-variable theories” Physical Review Letters 23, 880–884 (1969).
https:/​/​doi.org/​10.1103/​PhysRevLett.23.880

[3] John S Bell “The theory of local beables” (1975).
https:/​/​cds.cern.ch/​record/​980036/​files/​197508125.pdf

[4] David Deutschand Patrick Hayden “Information flow in entangled quantum systems” Proceedings of the Royal Society A 456, 1759–1774 (2000).
https:/​/​doi.org/​10.1098/​rspa.2000.0585
arXiv:quant-ph/9906007

[5] Harvey R. Brownand Christopher G. Timpson “Bell on Bell’s theorem: The changing face of nonlocality” Cambridge University Press (2016).
https:/​/​doi.org/​10.1017/​CBO9781316219393.008
arXiv:1501.03521

[6] Alain Aspect, Jean Dalibard, and Gérard Roger, “Experimental Test of Bell’s Inequalities Using Time-Varying Analyzers” Physical Review Letters 49, 1804–1807 (1982).
https:/​/​doi.org/​10.1103/​PhysRevLett.49.1804

[7] Gregor Weihs, Thomas Jennewein, Christoph Simon, Harald Weinfurter, and Anton Zeilinger, “Violation of Bell’s Inequality under Strict Einstein Locality Conditions” Physical Review Letters 81, 5039–5043 (1998).
https:/​/​doi.org/​10.1103/​physrevlett.81.5039
arXiv:quant-ph/9810080

[8] M. A. Rowe, D. Kielpinski, V. Meyer, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, “Experimental violation of a Bell’s inequality with efficient detection” Nature 409, 791–794 (2001).
https:/​/​doi.org/​10.1038/​35057215

[9] B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg, R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres” Nature 526, 682–686 (2015).
https:/​/​doi.org/​10.1038/​nature15759
arXiv:1508.05949

[10] Marissa Giustina, Marijn A. M. Versteegh, Sören Wengerowsky, Johannes Handsteiner, Armin Hochrainer, Kevin Phelan, Fabian Steinlechner, Johannes Kofler, Jan-à ke Larsson, Carlos Abellán, and al., “Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons” Physical Review Letters 115, 250401 (2015).
https:/​/​doi.org/​10.1103/​physrevlett.115.250401
arXiv:1511.03190

[11] Lynden K. Shalm, Evan Meyer-Scott, Bradley G. Christensen, Peter Bierhorst, Michael A. Wayne, Martin J. Stevens, Thomas Gerrits, Scott Glancy, Deny R. Hamel, Michael S. Allman, and al., “Strong Loophole-Free Test of Local Realism” Physical Review Letters 115, 250402 (2015).
https:/​/​doi.org/​10.1103/​physrevlett.115.250402
arXiv:1511.03189

[12] Richard Cleve, Peter Høyer, Ben Toner, and John Watrous, “Consequences and Limits of Nonlocal Strategies” (2004).
arXiv:quant-ph/0404076

[13] Jonathan Barrett, Daniel Collins, Lucien Hardy, Adrian Kent, and Sandu Popescu, “Quantum nonlocality, Bell inequalities, and the memory loophole” Physical Review A 66, 042111 (2002).
https:/​/​doi.org/​10.1103/​PhysRevA.66.042111
arXiv:quant-ph/0205016

[14] Richard D. Gilland Jan-Åke Larsson “Accardi Contra Bell (Cum Mundi): The Impossible Coupling” Lecture Notes-Monograph Series 42, 133–154 (2003).
arXiv:quant-ph/0110137

[15] Anup Rao “Parallel repetition in projection games and a concentration bound” SIAM Journal on Computing 40, 1871–1891 (2011).
https:/​/​doi.org/​10.1137/​080734042

[16] Julia Kempe, Oded Regev, and Ben Toner, “Unique Games with Entangled Provers are Easy” (2007).
arXiv:0710.0655

[17] M. Junge, C. Palazuelos, D. Pérez-García, I. Villanueva, and M. M. Wolf, “Unbounded Violations of Bipartite Bell Inequalities via Operator Space Theory” Communications in Mathematical Physics 300, 715–739 (2010).
https:/​/​doi.org/​10.1007/​s00220-010-1125-5
arXiv:0910.4228

[18] M. Junge, C. Palazuelos, D. Pérez-García, I. Villanueva, and M. M. Wolf, “Operator Space Theory: A Natural Framework for Bell Inequalities” Physical Review Letters 104, 170405 (2010).
https:/​/​doi.org/​10.1103/​physrevlett.104.170405
arXiv:0912.1941

[19] B. S. Cirel’son “Quantum generalizations of Bell’s inequality” Letters in Mathematical Physics 4, 93–100 (1980).
https:/​/​doi.org/​10.1007/​BF00417500

[20] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality” Reviews of Modern Physics 86, 419–478 (2014).
https:/​/​doi.org/​10.1103/​RevModPhys.86.419
arXiv:1303.2849

[21] Michael Ben-Or, Shafi Goldwasser, Joe Kilian, and Avi Wigderson, “Multi-Prover Interactive Proofs: How to Remove Intractability Assumptions” Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing 113–131 (1988).
https:/​/​doi.org/​10.1145/​62212.62223

[22] Boris Tsirelson “Quantum information processing – Lecture notes” (1997).
https:/​/​www.webcitation.org/​5fl2WZOMI

[23] Harry Buhrman, Oded Regev, Giannicola Scarpa, and Ronald de Wolf, “Near-Optimal and Explicit Bell Inequality Violations” 2011 IEEE 26th Annual Conference on Computational Complexity (2011).
https:/​/​doi.org/​10.1109/​ccc.2011.30
arXiv:1012.5043

[24] Carlos Palazuelosand Thomas Vidick “Survey on nonlocal games and operator space theory” Journal of Mathematical Physics 57, 015220 (2016).
https:/​/​doi.org/​10.1063/​1.4938052
arXiv:1512.00419

[25] Marcel Froissart “Constructive generalization of Bell’s inequalities” Il Nuovo Cimento B (1971-1996) 64, 241–251 (1981).
https:/​/​doi.org/​10.1007/​BF02903286

[26] Yanbao Zhang, Scott Glancy, and Emanuel Knill, “Asymptotically optimal data analysis for rejecting local realism” Physical Review A 84, 062118 (2011).
https:/​/​doi.org/​10.1103/​PhysRevA.84.062118
arXiv:1108.2468

[27] David Elkoussand Stephanie Wehner “(Nearly) optimal P-values for all Bell inequalities” npj Quantum Information 2 (2016).
https:/​/​doi.org/​10.1038/​npjqi.2016.26
arXiv:1510.07233

[28] Richard D. Gill “Time, Finite Statistics, and Bell’s Fifth Position” (2003).
arXiv:quant-ph/0301059

[29] Yanbao Zhang, Scott Glancy, and Emanuel Knill, “Efficient quantification of experimental evidence against local realism” Physical Review A 88, 052119 (2013).
https:/​/​doi.org/​10.1103/​PhysRevA.88.052119
arXiv:1303.7464

[30] Peter Bierhorst “A Rigorous Analysis of the Clauser–Horne–Shimony–Holt Inequality Experiment When Trials Need Not be Independent” Foundations of Physics 44, 736–761 (2014).
https:/​/​doi.org/​10.1007/​s10701-014-9811-3
arXiv:1311.3605

[31] Denis Rosset, Jean-Daniel Bancal, and Nicolas Gisin, “Classifying 50 years of Bell inequalities” Journal of Physics A Mathematical General 47, 424022 (2014).
https:/​/​doi.org/​10.1088/​1751-8113/​47/​42/​424022
arXiv:1404.1306

[32] M. O. Renou, D. Rosset, A. Martin, and N. Gisin, “On the inequivalence of the CH and CHSH inequalities due to finite statistics” Journal of Physics A Mathematical General 50, 255301 (2017).
https:/​/​doi.org/​10.1088/​1751-8121/​aa6f78
arXiv:1610.01833

[33] Steven Diamondand Stephen Boyd “CVXPY: A Python-embedded modeling language for convex optimization” Journal of Machine Learning Research 17, 1–5 (2016).
arXiv:1603.00943

[34] Akshay Agrawal, Robin Verschueren, Steven Diamond, and Stephen Boyd, “A rewriting system for convex optimization problems” Journal of Control and Decision 5, 42–60 (2018).
https:/​/​doi.org/​10.1080/​23307706.2017.1397554
arXiv:1709.04494

[35] Daniel Collins, Nicolas Gisin, Noah Linden, Serge Massar, and Sandu Popescu, “Bell Inequalities for Arbitrarily High-Dimensional Systems” Physical Review Letters 88, 040404 (2002).
https:/​/​doi.org/​10.1103/​PhysRevLett.88.040404
arXiv:quant-ph/0106024

[36] Antonio Acín, Richard Gill, and Nicolas Gisin, “Optimal Bell Tests Do Not Require Maximally Entangled States” Physical Review Letters 95, 210402 (2005).
https:/​/​doi.org/​10.1103/​PhysRevLett.95.210402
arXiv:quant-ph/0506225

[37] Stefan Zohrenand Richard D. Gill “Maximal Violation of the CGLMP Inequality for Infinite Dimensional States” Physical Review Letters 100 (2008).
https:/​/​doi.org/​10.1103/​physrevlett.100.120406
arXiv:quant-ph/0612020

[38] A. Acín, T. Durt, N. Gisin, and J. I. Latorre, “Quantum nonlocality in two three-level systems” Physical Review A 65 (2002).
https:/​/​doi.org/​10.1103/​physreva.65.052325
arXiv:quant-ph/0111143

[39] Miguel Navascués, Stefano Pironio, and Antonio Acín, “Bounding the Set of Quantum Correlations” Physical Review Letters 98 (2007).
https:/​/​doi.org/​10.1103/​physrevlett.98.010401
arXiv:quant-ph/0607119

[40] S. Zohren, P. Reska, R. D. Gill, and W. Westra, “A tight Tsirelson inequality for infinitely many outcomes” EPL (Europhysics Letters) 90, 10002 (2010).
https:/​/​doi.org/​10.1209/​0295-5075/​90/​10002
arXiv:1003.0616

[41] Daniel Collinsand Nicolas Gisin “A relevant two qubit Bell inequality inequivalent to the CHSH inequality” Journal of Physics A Mathematical General 37, 1775–1787 (2004).
https:/​/​doi.org/​10.1088/​0305-4470/​37/​5/​021
arXiv:quant-ph/0306129

[42] David Avisand Tsuyoshi Ito “New classes of facets of the cut polytope and tightness of $I_{mm22}$ Bell inequalities” Discrete Applied Mathematics 155, 1689 –1699 (2007).
https:/​/​doi.org/​10.1016/​j.dam.2007.03.005
arXiv:math/0505143

[43] Károly F. Páland Tamás Vértesi “Maximal violation of the I3322 inequality using infinite-dimensional quantum systems” Physical Review A 82 (2010).
https:/​/​doi.org/​10.1103/​physreva.82.022116
arXiv:1006.3032

[44] Péter Diviánszky, Erika Bene, and Tamás Vértesi, “Qutrit witness from the Grothendieck constant of order four” Physical Review A 96, 012113 (2017).
https:/​/​doi.org/​10.1103/​physreva.96.012113
arXiv:1707.04719

[45] Lance Fortnow “Complexity-theoretic aspects of interactive proof systems” thesis (1989).
http:/​/​people.cs.uchicago.edu/​~fortnow/​papers/​thesis.pdf

[46] Uriel Feigeand László Lovász “Two-Prover One-Round Proof Systems: Their Power and Their Problems (Extended Abstract)” Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing 733–744 (1992).
https:/​/​doi.org/​10.1145/​129712.129783

[47] Gilles Brassard, Anne Broadbent, and Alain Tapp, “Quantum Pseudo-Telepathy” Foundations of Physics 35, 1877–1907 (2005).
https:/​/​doi.org/​10.1007/​s10701-005-7353-4
arXiv:quant-ph/0407221

[48] P. K. Aravind “A simple demonstration of Bell’s theorem involving two observers and no probabilities or inequalities” American Journal of Physics 72, 1303 (2004).
https:/​/​doi.org/​10.1119/​1.1773173
arXiv:quant-ph/0206070

[49] Ran Raz “A Parallel Repetition Theorem” SIAM Journal on Computing 27, 763–803 (1998).
https:/​/​doi.org/​10.1137/​S0097539795280895

[50] Thomas Holenstein “Parallel repetition: simplifications and the no-signaling case” Theory of Computing 141–172 (2009).
https:/​/​doi.org/​10.4086/​toc.2009.v005a008
arXiv:cs/0607139

[51] S. A. Khotand N. K. Vishnoi “The unique games conjecture, integrality gap for cut problems and embeddability of negative type metrics into $ell_1$” 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS’05) 53–62 (2005).
https:/​/​doi.org/​10.1109/​SFCS.2005.74
arXiv:1305.4581

[52] Carlos Palazuelos “Superactivation of Quantum Nonlocality” Physical Review Letters 109, 190401 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.109.190401
arXiv:1205.3118

[53] Mafalda L. Almeida, Stefano Pironio, Jonathan Barrett, Géza Tóth, and Antonio Acín, “Noise Robustness of the Nonlocality of Entangled Quantum States” Physical Review Letters 99, 040403 (2007).
https:/​/​doi.org/​10.1103/​PhysRevLett.99.040403
arXiv:quant-ph/0703018

[54] Carlos Palazuelos “On the largest Bell violation attainable by a quantum state” Journal of Functional Analysis 267, 1959–1985 (2014).
https:/​/​doi.org/​10.1016/​j.jfa.2014.07.028
arXiv:1206.3695

[55] Boris Tsirelson “Quantum analogues of the Bell inequalities. The case of two spatially separated domains” Journal of Soviet Mathematics 36, 557–570 (1987).
https:/​/​doi.org/​10.1007/​BF01663472

[56] Antonio Acín, Nicolas Gisin, and Benjamin Toner, “Grothendieck’s constant and local models for noisy entangled quantum states” Physical Review A 73, 062105 (2006).
https:/​/​doi.org/​10.1103/​PhysRevA.73.062105
arXiv:quant-ph/0606138

[57] Flavien Hirsch, Marco Túlio Quintino, Tamás Vértesi, Miguel Navascués, and Nicolas Brunner, “Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$” Quantum 1, 3 (2017).
https:/​/​doi.org/​10.22331/​q-2017-04-25-3
arXiv:1609.06114

[58] Yeong-Cherng Liang, Chu-Wee Lim, and Dong-Ling Deng, “Reexamination of a multisetting Bell inequality for qudits” Physical Review A 80 (2009).
https:/​/​doi.org/​10.1103/​physreva.80.052116
arXiv:0903.4964

[59] Stephen Brierley, Miguel Navascués, and Tamas Vértesi, “Convex separation from convex optimization for large-scale problems” (2016).
arXiv:1609.05011

[60] H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox” Physical Review Letters 98, 140402 (2007).
https:/​/​doi.org/​10.1103/​PhysRevLett.98.140402
arXiv:quant-ph/0612147

[61] Marco Túlio Quintino, Tamás Vértesi, Daniel Cavalcanti, Remigiusz Augusiak, Maciej Demianowicz, Antonio Acín, and Nicolas Brunner, “Inequivalence of entanglement, steering, and Bell nonlocality for general measurements” Physical Review A 92, 032107 (2015).
https:/​/​doi.org/​10.1103/​PhysRevA.92.032107
arXiv:1501.03332

[62] L. Gurvitsand H. Barnum “Largest separable balls around the maximally mixed bipartite quantum state” Physical Review A 66, 062311 (2002).
https:/​/​doi.org/​10.1103/​PhysRevA.66.062311
arXiv:quant-ph/0204159

[63] Stephen Boydand Lieven Vandenberghe “Convex Optimization” Cambridge University Press (2004).
http:/​/​www.stanford.edu/​~boyd/​cvxbook/​

Cited by

Could not fetch Crossref cited-by data during last attempt 2020-10-28 12:01:59: Could not fetch cited-by data for 10.22331/q-2020-10-28-353 from Crossref. This is normal if the DOI was registered recently. On SAO/NASA ADS no data on citing works was found (last attempt 2020-10-28 12:01:59).

Source: https://quantum-journal.org/papers/q-2020-10-28-353/

Continue Reading

Quantum

Optimization of the surface code design for Majorana-based qubits

Avatar

Published

on


Rui Chao1, Michael E. Beverland2, Nicolas Delfosse2, and Jeongwan Haah2

1University of Southern California, Los Angeles, CA, USA
2Microsoft Quantum and Microsoft Research, Redmond, WA, USA

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

The surface code is a prominent topological error-correcting code exhibiting high fault-tolerance accuracy thresholds. Conventional schemes for error correction with the surface code place qubits on a planar grid and assume native CNOT gates between the data qubits with nearest-neighbor ancilla qubits.

Here, we present surface code error-correction schemes using $textit{only}$ Pauli measurements on single qubits and on pairs of nearest-neighbor qubits. In particular, we provide several qubit layouts that offer favorable trade-offs between qubit overhead, circuit depth and connectivity degree. We also develop minimized measurement sequences for syndrome extraction, enabling reduced logical error rates and improved fault-tolerance thresholds.

Our work applies to topologically protected qubits realized with Majorana zero modes and to similar systems in which multi-qubit Pauli measurements rather than CNOT gates are the native operations.

► BibTeX data

► References

[1] A. Y. Kitaev, Ann. Phys. 303, 2 (2003), quant-ph/​9707021.
https:/​/​doi.org/​10.1016/​S0003-4916(02)00018-0
arXiv:quant-ph/9707021

[2] E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, J. Math. Phys. 43, 4452 (2002), quant-ph/​0110143.
https:/​/​doi.org/​10.1063/​1.1499754
arXiv:quant-ph/0110143

[3] A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Phys. Rev. A 86, 032324 (2012), 1208.0928.
https:/​/​doi.org/​10.1103/​PhysRevA.86.032324
arXiv:1208.0928

[4] R. Raussendorf and J. Harrington, Phys. Rev. Lett. 98, 190504 (2007), quant-ph/​0610082.
https:/​/​doi.org/​10.1103/​PhysRevLett.98.190504
arXiv:quant-ph/0610082

[5] A. G. Fowler, A. M. Stephens, and P. Groszkowski, Phys. Rev. A 80, 052312 (2009), 0803.0272.
https:/​/​doi.org/​10.1103/​PhysRevA.80.052312
arXiv:0803.0272

[6] N. Delfosse and G. Zémor, Physical Review Research 2, 033042 (2020), 1703.01517.
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.033042
arXiv:1703.01517

[7] N. Delfosse and N. H. Nickerson, 2017, 1709.06218.
arXiv:1709.06218

[8] T. Karzig, C. Knapp, R. M. Lutchyn, P. Bonderson, M. B. Hastings, C. Nayak, J. Alicea, K. Flensberg, S. Plugge, Y. Oreg, C. M. Marcus, and M. H. Freedman, Phys. Rev. B 95, 235305 (2017), 1610.05289.
https:/​/​doi.org/​10.1103/​PhysRevB.95.235305
arXiv:1610.05289

[9] C. Knapp, M. Beverland, D. I. Pikulin, and T. Karzig, Quantum 2, 88 (2018), 1806.01275.
https:/​/​doi.org/​10.22331/​q-2018-09-03-88
arXiv:1806.01275

[10] Y. Li, Physical Review Letters 117, 120403 (2016), 1512.05089.
https:/​/​doi.org/​10.1103/​PhysRevLett.117.120403
arXiv:1512.05089

[11] S. Plugge, L. Landau, E. Sela, A. Altland, K. Flensberg, and R. Egger, Phys. Rev. B 94, 174514 (2016), 1606.08408.
https:/​/​doi.org/​10.1103/​PhysRevB.94.174514
arXiv:1606.08408

[12] D. Litinski, M. S. Kesselring, J. Eisert, and F. von Oppen, Phys. Rev. X 7, 031048 (2017), 1704.01589.
https:/​/​doi.org/​10.1103/​PhysRevX.7.031048
arXiv:1704.01589

[13] A. G. Fowler, D. S. Wang, and L. C. L. Hollenberg, Quant. Info. Comput. 11, 8 (2011), 1004.0255.
https:/​/​doi.org/​10.26421/​QIC11.1-2
arXiv:1004.0255

[14] M. Newman, L. A. de Castro, and K. R. Brown, Quantum 4, 295 (2020), 1909.11817.
https:/​/​doi.org/​10.22331/​q-2020-07-13-295
arXiv:1909.11817

[15] A. G. Fowler, 2013, 1310.0863.
arXiv:1310.0863

[16] N. Delfosse and J.-P. Tillich, in 2014 IEEE Int. Symp. Info. (IEEE, 2014) pp. 1071–1075, 1401.6975.
https:/​/​doi.org/​10.1109/​ISIT.2014.6874997
arXiv:1401.6975

[17] S. Huang and K. R. Brown, Phys. Rev. A 101, 042312 (2020), 1911.11317.
https:/​/​doi.org/​10.1103/​PhysRevA.101.042312
arXiv:1911.11317

[18] S. Huang, M. Newman, and K. R. Brown, Phys. Rev. A 102, 012419 (2020), 2004.04693.
https:/​/​doi.org/​10.1103/​PhysRevA.102.012419
arXiv:2004.04693

[19] J. MacWilliams, Bell Syst. Tech. J. 42, 79 (1963).
https:/​/​doi.org/​10.1002/​j.1538-7305.1963.tb04003.x

[20] S. Bravyi and A. Vargo, Phys. Rev. A 88, 062308 (2013), 1308.6270.
https:/​/​doi.org/​10.1103/​PhysRevA.88.062308
arXiv:1308.6270

Cited by

Could not fetch Crossref cited-by data during last attempt 2020-10-28 11:03:33: Could not fetch cited-by data for 10.22331/q-2020-10-28-352 from Crossref. This is normal if the DOI was registered recently. On SAO/NASA ADS no data on citing works was found (last attempt 2020-10-28 11:03:33).

Source: https://quantum-journal.org/papers/q-2020-10-28-352/

Continue Reading

Quantum

Classical Simulations of Quantum Field Theory in Curved Spacetime I: Fermionic Hawking-Hartle Vacua from a Staggered Lattice Scheme

Avatar

Published

on

Adam G. M. Lewis1 and Guifré Vidal1,2

1Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, Ontario, Canada, N2L 2Y5
2X, The Moonshot Factory, Mountain View, CA 94043

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

We numerically compute renormalized expectation values of quadratic operators in a quantum field theory (QFT) of free Dirac fermions in curved two-dimensional (Lorentzian) spacetime. First, we use a staggered-fermion discretization to generate a sequence of lattice theories yielding the desired QFT in the continuum limit. Numerically-computed lattice correlators are then used to approximate, through extrapolation, those in the continuum. Finally, we use so-called point-splitting regularization and Hadamard renormalization to remove divergences, and thus obtain finite, renormalized expectation values of quadratic operators in the continuum. As illustrative applications, we show how to recover the Unruh effect in flat spacetime and how to compute renormalized expectation values in the Hawking-Hartle vacuum of a Schwarzschild black hole and in the Bunch-Davies vacuum of an expanding universe described by de Sitter spacetime. Although here we address a non-interacting QFT using free fermion techniques, the framework described in this paper lays the groundwork for a series of subsequent studies involving simulation of interacting QFTs in curved spacetime by tensor network techniques.

► BibTeX data

► References

[1] Radiation damping in a gravitational field. Annals of Physics, 9 (2): 220 – 259, 1960. ISSN 0003-4916. https:/​/​doi.org/​10.1016/​0003-4916(60)90030-0.
https:/​/​doi.org/​https:/​/​doi.org/​10.1016/​0003-4916(60)90030-0

[2] Andreas Albrecht and Paul J. Steinhardt. Cosmology for grand unified theories with radiatively induced symmetry breaking. Phys. Rev. Lett., 48: 1220–1223, Apr 1982. 10.1103/​PhysRevLett.48.1220.
https:/​/​doi.org/​10.1103/​PhysRevLett.48.1220

[3] Miguel Alcubierre. Introduction to 3+1 Numerical Relativity. 10.1093/​acprof:oso/​9780199205677.001.0001.
https:/​/​doi.org/​10.1093/​acprof:oso/​9780199205677.001.0001

[4] Bruce Allen. Vacuum states in de Sitter space. Phys. Rev. D, 32: 3136–3149, Dec 1985. 10.1103/​PhysRevD.32.3136.
https:/​/​doi.org/​10.1103/​PhysRevD.32.3136

[5] Victor E. Ambruș and Elizabeth Winstanley. Renormalised fermion vacuum expectation values on anti-de Sitter space–time. Physics Letters B, 749: 597 – 602, 2015. ISSN 0370-2693. https:/​/​doi.org/​10.1016/​j.physletb.2015.08.045.
https:/​/​doi.org/​https:/​/​doi.org/​10.1016/​j.physletb.2015.08.045

[6] Richard Arnowitt, Stanley Deser, and Charles W. Misner. Republication of: The dynamics of general relativity. Gen. Relativ. Gravit., 40, 2008. 10.1007/​s10714-008-0661-1.
https:/​/​doi.org/​10.1007/​s10714-008-0661-1

[7] T. Banks, Leonard Susskind, and John Kogut. Strong-coupling calculations of lattice gauge theories: (1 + 1)-dimensional exercises. Phys. Rev. D, 13: 1043–1053, Feb 1976. 10.1103/​PhysRevD.13.1043.
https:/​/​doi.org/​10.1103/​PhysRevD.13.1043

[8] T.W. Baumgarte and S.L. Shapiro. Numerical Relativity: Solving Einstein’s Equations on the Computer. Cambridge University Press, 2010. ISBN 9780521514071. 10.1017/​CBO9781139193344.
https:/​/​doi.org/​10.1017/​CBO9781139193344

[9] N. D. Birrell and P. C. W. Davies. Quantum Fields in Curved Space. Cambridge University Press, Cambridge, 1982. 10.1017/​CBO9780511622632.
https:/​/​doi.org/​10.1017/​CBO9780511622632

[10] Elliot Blommaert. Hamiltonian simulation of free lattice fermions in curved spacetime. Master’s thesis, Ghent University, 2019.

[11] T. S. Bunch and P. C. W. Davies. Covariant point-splitting regularization for a scalar quantum field in a Robertson-Walker Universe with spatial curvature. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 357 (1690): 381–394, 1977. 10.1098/​rspa.1977.0174.
https:/​/​doi.org/​10.1098/​rspa.1977.0174

[12] Curtis G. Callan, Steven B. Giddings, Jeffrey A. Harvey, and Andrew Strominger. Evanescent black holes. Phys. Rev. D, 45: R1005–R1009, Feb 1992. 10.1103/​PhysRevD.45.R1005.
https:/​/​doi.org/​10.1103/​PhysRevD.45.R1005

[13] Sean M. Carroll. Spacetime and geometry: An introduction to general relativity. 2004. ISBN 0805387323, 9780805387322. 10.1017/​9781108770385.
https:/​/​doi.org/​10.1017/​9781108770385

[14] N. A. Chernikov and E. A. Tagirov. Quantum theory of scalar fields in de Sitter space-time. Annales de l’I.H.P. Physique théorique, 9 (2): 109–141, 1968. URL http:/​/​www.numdam.org/​item/​AIHPA_1968__9_2_109_0.
http:/​/​www.numdam.org/​item/​AIHPA_1968__9_2_109_0

[15] S. M. Christensen. Vacuum expectation value of the stress tensor in an arbitrary curved background: The covariant point-separation method. Phys. Rev. D, 14: 2490–2501, November 1976. 10.1103/​PhysRevD.14.2490.
https:/​/​doi.org/​10.1103/​PhysRevD.14.2490

[16] S. M. Christensen. Regularization, renormalization, and covariant geodesic point separation. Phys. Rev. D, 17: 946–963, February 1978. 10.1103/​PhysRevD.17.946.
https:/​/​doi.org/​10.1103/​PhysRevD.17.946

[17] A J Daley, C Kollath, U Schollwöck, and G Vidal. Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces. Journal of Statistical Mechanics: Theory and Experiment, 2004 (04): P04005, apr 2004. 10.1088/​1742-5468/​2004/​04/​p04005.
https:/​/​doi.org/​10.1088/​1742-5468/​2004/​04/​p04005

[18] Ashmita Das, Surojit Dalui, Chandramouli Chowdhury, and Bibhas Ranjan Majhi. Conformal vacuum and the fluctuation-dissipation theorem in a de Sitter universe and black hole spacetimes. Phys. Rev. D, 100: 085002, Oct 2019. 10.1103/​PhysRevD.100.085002.
https:/​/​doi.org/​10.1103/​PhysRevD.100.085002

[19] Yves Décanini and Antoine Folacci. Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension. Phys. Rev. D., 78 (4): 044025, 2008. ISSN 1550-7998. 10.1103/​physrevd.78.044025.
https:/​/​doi.org/​10.1103/​physrevd.78.044025

[20] Daniel Z. Freedman and Antoine Van Proeyen. Supergravity. Cambridge University Press, New York, 2012. 10.1017/​CBO9781139026833.
https:/​/​doi.org/​10.1017/​CBO9781139026833

[21] G. W. Gibbons and S. W. Hawking. Cosmological event horizons, thermodynamics, and particle creation. Phys. Rev. D, 15: 2738–2751, May 1977. 10.1103/​PhysRevD.15.2738.
https:/​/​doi.org/​10.1103/​PhysRevD.15.2738

[22] G. W. Gibbons and M. J. Perry. Black holes in thermal equilibrium. Phys. Rev. Lett., 36: 985–987, Apr 1976. 10.1103/​PhysRevLett.36.985.
https:/​/​doi.org/​10.1103/​PhysRevLett.36.985

[23] Brian R Greene, Maulik K Parikh, and Jan Pieter van der Schaar. Universal correction to the inflationary vacuum. Journal of High Energy Physics, 2006 (04): 057–057, apr 2006. 10.1088/​1126-6708/​2006/​04/​057.
https:/​/​doi.org/​10.1088/​1126-6708/​2006/​04/​057

[24] Alan H. Guth. Inflationary universe: A possible solution to the horizon and flatness problems. Phys. Rev. D, 23: 347–356, Jan 1981. 10.1103/​PhysRevD.23.347.
https:/​/​doi.org/​10.1103/​PhysRevD.23.347

[25] Jacques Hadamard. Lectures on Cauchy’s problem in linear partial differential equations. New Haven Yale University Press, 1923.

[26] J. B. Hartle and S. W. Hawking. Path-integral derivation of black-hole radiance. Phys. Rev. D, 13: 2188–2203, Apr 1976. 10.1103/​PhysRevD.13.2188.
https:/​/​doi.org/​10.1103/​PhysRevD.13.2188

[27] S. W. Hawking. Black hole explosions? Nature, 248: 379–423. 10.1038/​248030a0.
https:/​/​doi.org/​10.1038/​248030a0

[28] W. Israel. Thermo-field dynamics of black holes. Physics Letters A, 57 (2): 107 – 110, 1976. ISSN 0375-9601. https:/​/​doi.org/​10.1016/​0375-9601(76)90178-X.
https:/​/​doi.org/​https:/​/​doi.org/​10.1016/​0375-9601(76)90178-X

[29] Ted Jacobson. Note on Hartle-Hawking vacua. Phys. Rev. D, 50: R6031–R6032, Nov 1994. 10.1103/​PhysRevD.50.R6031.
https:/​/​doi.org/​10.1103/​PhysRevD.50.R6031

[30] P. Jordan and E. Wigner. Über das Paulische äquivalenzverbot. Zeitschrift fur Physik, 47: 631–651, 1928. 10.1007/​BF01331938.
https:/​/​doi.org/​10.1007/​BF01331938

[31] Bernard S. Kay and Robert M. Wald. Theorems on the uniqueness and thermal properties of stationary, nonsingular, quasifree states on spacetimes with a bifurcate Killing horizon. Physics Reports, 207 (2): 49 – 136, 1991. ISSN 0370-1573. https:/​/​doi.org/​10.1016/​0370-1573(91)90015-E.
https:/​/​doi.org/​https:/​/​doi.org/​10.1016/​0370-1573(91)90015-E

[32] John Kogut and Leonard Susskind. Hamiltonian formulation of Wilson’s lattice gauge theories. Phys. Rev. D, 11: 395–408, Jan 1975. 10.1103/​PhysRevD.11.395.
https:/​/​doi.org/​10.1103/​PhysRevD.11.395

[33] R. Laflamme. Geometry and thermofields. Nuclear Physics B, 324 (1): 233 – 252, 1989. ISSN 0550-3213. https:/​/​doi.org/​10.1016/​0550-3213(89)90191-0.
https:/​/​doi.org/​https:/​/​doi.org/​10.1016/​0550-3213(89)90191-0

[34] Adam G. M. Lewis. Hadamard renormalization of a two-dimensional dirac field. Phys. Rev. D, 101: 125019, Jun 2020. 10.1103/​PhysRevD.101.125019.
https:/​/​doi.org/​10.1103/​PhysRevD.101.125019

[35] Adam G.M. Lewis and Guifré Vidal. Matrix product state simulations of quantum fields in curved spacetime.

[36] A.D. Linde. A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems. Physics Letters B, 108 (6): 389 – 393, 1982. ISSN 0370-2693. https:/​/​doi.org/​10.1016/​0370-2693(82)91219-9.
https:/​/​doi.org/​https:/​/​doi.org/​10.1016/​0370-2693(82)91219-9

[37] Fannes M., Nachtergaele B., and R.F Werner. Finitely correlated states on quantum spin chains. Comm. Math. Phys., 144: 443490, 1992. 10.1007/​BF02099178.
https:/​/​doi.org/​10.1007/​BF02099178

[38] V. Moretti. Comments on the stress-energy operator in curved spacetime. Commun. Math. Phys., 232 (2): 189–221. 10.1007/​s00220-002-0702-7.
https:/​/​doi.org/​10.1007/​s00220-002-0702-7

[39] A.-H. Najmi and A. C. Ottewill. Quantum states and the Hadamard form. II. Energy minimization for spin- 1/​2 fields. Phys. Rev. D., 30: 2573–2578, December 1984. 10.1103/​PhysRevD.30.2573.
https:/​/​doi.org/​10.1103/​PhysRevD.30.2573

[40] Stellan Östlund and Stefan Rommer. Thermodynamic limit of density matrix renormalization. Phys. Rev. Lett., 75: 3537–3540, Nov 1995. 10.1103/​PhysRevLett.75.3537.
https:/​/​doi.org/​10.1103/​PhysRevLett.75.3537

[41] Leonard Parker and David Toms. Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity. Cambridge University Press, Cambridge, 2009. 10.1017/​CBO9780511813924.
https:/​/​doi.org/​10.1017/​CBO9780511813924

[42] D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac. Matrix product state representations. Quantum Info. Comput., 7 (5): 401–430, July 2007. ISSN 1533-7146. URL http:/​/​dl.acm.org/​citation.cfm?id=2011832.2011833.
http:/​/​dl.acm.org/​citation.cfm?id=2011832.2011833

[43] Michael E. Peskin and Daniel V. Schroeder. An Introduction to Quantum Field Theory. Westview Press, Boulder, Colarado, 1995. 10.1201/​9780429503559.
https:/​/​doi.org/​10.1201/​9780429503559

[44] Eric Poisson, Adam Pound, and Ian Vega. The motion of point particles in curved spacetime. Living Reviews in Relativity, 14 (1): 7, Sep 2011. ISSN 1433-8351. 10.12942/​lrr-2011-7.
https:/​/​doi.org/​10.12942/​lrr-2011-7

[45] Frans Pretorius. Evolution of binary black-hole spacetimes. Phys. Rev. Lett., 95 (12): 121101, 2005a. 10.1103/​PhysRevLett.95.121101.
https:/​/​doi.org/​10.1103/​PhysRevLett.95.121101

[46] Frans Pretorius. Numerical relativity using a generalized harmonic decomposition. Class. Quant. Grav., 22 (2): 425, 2005b. 10.1088/​0264-9381/​22/​2/​014.
https:/​/​doi.org/​10.1088/​0264-9381/​22/​2/​014

[47] Stefan Rommer and Stellan Östlund. Class of ansatz wave functions for one-dimensional spin systems and their relation to the density matrix renormalization group. Phys. Rev. B, 55: 2164–2181, Jan 1997. 10.1103/​PhysRevB.55.2164.
https:/​/​doi.org/​10.1103/​PhysRevB.55.2164

[48] Katsuhiko Sato. First-order phase transition of a vacuum and the expansion of the Universe. Monthly Notices of the Royal Astronomical Society, 195 (3): 467–479, 07 1981. ISSN 0035-8711. 10.1093/​mnras/​195.3.467.
https:/​/​doi.org/​10.1093/​mnras/​195.3.467

[49] U. Schollwöck. The density-matrix renormalization group. Rev. Mod. Phys., 77: 259–315, Apr 2005. 10.1103/​RevModPhys.77.259.
https:/​/​doi.org/​10.1103/​RevModPhys.77.259

[50] Ulrich Schollwöck. The density-matrix renormalization group in the age of matrix product states. Annals of Physics, 326 (1): 96 – 192, 2011. ISSN 0003-4916. https:/​/​doi.org/​10.1016/​j.aop.2010.09.012. URL http:/​/​www.sciencedirect.com/​science/​article/​pii/​S0003491610001752. January 2011 Special Issue.
https:/​/​doi.org/​https:/​/​doi.org/​10.1016/​j.aop.2010.09.012
http:/​/​www.sciencedirect.com/​science/​article/​pii/​S0003491610001752

[51] Leonard Susskind. Lattice fermions. Phys. Rev. D, 16 (10): 3031–3039, 1976. ISSN 1550-7998. 10.1103/​physrevd.16.3031.
https:/​/​doi.org/​10.1103/​physrevd.16.3031

[52] W. G. Unruh. Notes on black-hole evaporation. Phys. Rev. D, 14: 870–892, Aug 1976. 10.1103/​PhysRevD.14.870.
https:/​/​doi.org/​10.1103/​PhysRevD.14.870

[53] William G. Unruh and Nathan Weiss. Acceleration radiation in interacting field theories. Phys. Rev. D, 29: 1656–1662, Apr 1984. 10.1103/​PhysRevD.29.1656.
https:/​/​doi.org/​10.1103/​PhysRevD.29.1656

[54] Guifré Vidal. Efficient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett., 91 (14): 147902, 2003. ISSN 0031-9007. 10.1103/​physrevlett.91.147902.
https:/​/​doi.org/​10.1103/​physrevlett.91.147902

[55] Guifré Vidal. Efficient simulation of One-Dimensional quantum Many-Body systems. Phys. Rev. Lett., 93 (4): 040502, 2004. ISSN 0031-9007. 10.1103/​physrevlett.93.040502.
https:/​/​doi.org/​10.1103/​physrevlett.93.040502

[56] Robert M Wald. General Relativity. University of Chicago Press, 1984. ISBN 9780226870328. 10.7208/​chicago/​9780226870373.001.0001.
https:/​/​doi.org/​10.7208/​chicago/​9780226870373.001.0001

[57] Robert M Wald. Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. The University of Chicago Press, Chicago, 1994.

[58] Steven R. White. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett., 69: 2863–2866, Nov 1992. 10.1103/​PhysRevLett.69.2863.
https:/​/​doi.org/​10.1103/​PhysRevLett.69.2863

[59] Steven R. White. Density-matrix algorithms for quantum renormalization groups. Phys. Rev. B, 48: 10345–10356, Oct 1993. 10.1103/​PhysRevB.48.10345. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevB.48.10345.
https:/​/​doi.org/​10.1103/​PhysRevB.48.10345

[60] Steven R. White and Adrian E. Feiguin. Real-time evolution using the density matrix renormalization group. Phys. Rev. Lett., 93: 076401, Aug 2004. 10.1103/​PhysRevLett.93.076401.
https:/​/​doi.org/​10.1103/​PhysRevLett.93.076401

[61] Run-Qiu Yang, Hui Liu, Shining Zhu, Le Luo, and Rong-Gen Cai. Simulating quantum field theory in curved spacetime with quantum many-body systems. Phys. Rev. Research, 2: 023107, Apr 2020. 10.1103/​PhysRevResearch.2.023107.
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.023107

Cited by

[1] Adam G. M. Lewis, “Hadamard renormalization of a two-dimensional Dirac field”, Physical Review D 101 12, 125019 (2020).

[2] Yue-Zhou Li and Junyu Liu, “On Quantum Simulation Of Cosmic Inflation”, arXiv:2009.10921.

The above citations are from SAO/NASA ADS (last updated successfully 2020-10-28 10:51:27). 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 2020-10-28 10:51:25: Could not fetch cited-by data for 10.22331/q-2020-10-28-351 from Crossref. This is normal if the DOI was registered recently.

Source: https://quantum-journal.org/papers/q-2020-10-28-351/

Continue Reading
Quantum2 hours ago

Bell nonlocality with a single shot

Quantum3 hours ago

Optimization of the surface code design for Majorana-based qubits

Quantum3 hours ago

Classical Simulations of Quantum Field Theory in Curved Spacetime I: Fermionic Hawking-Hartle Vacua from a Staggered Lattice Scheme

Ecommerce6 hours ago

How Digital Transformation Will Change the Retail Industry

AR/VR17 hours ago

Win a Huge The Walking Dead Onslaught Merch Bundle Including the Game

AR/VR20 hours ago

Hold Your Nerve With These Scary VR Horror Titles

Blockchain News20 hours ago

Ethereum City Builder MCP3D Goes DeFi with $MEGA Token October 28

Blockchain News20 hours ago

Why Bitcoin’s Price Is Rising Despite Selling Pressure from Crypto Whales

AR/VR21 hours ago

AR For Remote Assistance: A True Game Changer

Blockchain News21 hours ago

Smart Contract 101: MetaMask

AR/VR21 hours ago

Yupitergrad Adding PlayStation VR & Oculus Quest Support Jan 2021

Blockchain News22 hours ago

New Darknet Markets Launch Despite Exit Scams as Demand Rises for Illicit Goods

Blockchain News22 hours ago

Bitcoin Millionaires at an All-Time High as Analysts Warn of a Pullback Before BTC Moves Higher

Fintech22 hours ago

The Impact of BPM On the Banking And Finance Sector

AR/VR23 hours ago

Samsung & Stanford University are Developing a 10,000 PPI OLED Display

Energy24 hours ago

New Found Intercepts 22.3 g/t Au over 41.35m and 31.2 g/t Au over 18.85m in Initial Step-Out Drilling at Keats Zone, Queensway Project, Newfoundland

Energy24 hours ago

Kennebec County Community Solar Garden Reaches Project Milestone

Energy24 hours ago

Kalaguard® SB Sodium Benzoate Registered Under EPA FIFRA

Energy24 hours ago

LF Energy Launches openLEADR to Streamline Integration of Green Energy for Demand Side Management

Energy24 hours ago

Thermal Barrier Coatings Market To Reach USD 25.82 Billion By 2027 | CAGR of 4.9%: Reports And Data

Blockchain News1 day ago

$1 Billion in Bitcoin Moved, Making It the Largest Dollar Value Crypto Transaction in History

AR/VR1 day ago

Digital Catapult’s Augmentor Programme Reveals 10 new XR Startups

Singapore
Esports1 day ago

erkaSt joins NG

AR/VR1 day ago

Hands-on: Impressive PS5 DualSense Haptics & Tracking Tech Bodes Well for Future PSVR Controllers

Blockchain News1 day ago

Alibaba Founder Jack Ma Criticizes Current Financial Regulations

EdTech1 day ago

Google Classroom Comments: All You Need to Know! – SULS086

Blockchain News1 day ago

Bank for International Settlements to Issue a PoC CBDC With the Swiss Central Bank Before the End of 2020

Blockchain News1 day ago

Ripple CEO Disagrees with Coinbase CEO’s Apolitical Work Policy, Considers Relocating Overseas

Cyber Security1 day ago

Smart Solutions to Screen Mirroring iPad to Samsung TV

Esports1 day ago

Video: TeSeS vs. Vitality

Big Data1 day ago

Seven Tools for Effective CDO Leadership

Big Data1 day ago

Key Considerations for Executing a Successful M&A Data Migration or Carve-Out

Cyber Security1 day ago

Best Powered Subwoofer Car Reviews and Buying Guide

AR/VR1 day ago

Jorjin Technologies announcing J7EF, the latest of its J-Reality

Big Data1 day ago

Parallel ways of Data Scientist and Machine Learning

Supply Chain1 day ago

The New Role of Agricultural Machinery to Work the Land

Energy1 day ago

LONGi fornece 101 MW em módulos bifaciais para uma usina de larga escala no Chile.

Energy1 day ago

LONGi suministra 101 MW en módulos bifaciales para una planta de energía ultra grande en Chile

Energy1 day ago

Unabhängige Test bestätigen, dass der neue flüssigkeitsgekühlte Brennstoffzellenstapel von HYZON Motors bei der Leistungsdichte weltweit führend ist

Cyber Security1 day ago

Francisco Partners to Buy Forcepoint from Raytheon Technologies

Trending