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Gustavo Balvedi Pimentel

com apoio da Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brasil.Processos nº 2022/01421-9 e nº 2022/14069-1.Eu agradeço muito pelo suporte financeiro, que me permitiu atender eventos importantes do meu campo de pesquisa e a fazer um intercâmbio inesquecível.iv I would first like to thank my advisor, Bárbara Amaral.Her guidance over these almost four years of undergraduate and master's studies has been essential to my development as a student and researcher.Thank you for all your patience, for giving me so many incredible opportunities, and for showing me that it is possible to do physics without giving up on other important aspects of life.Thank you for being an incredible person, in whom I draw inspiration.I hope to continue learning a lot from you and gossiping over coffee breaks at conferences and IFQIFs.To my parents, Maria de Fátima and Jones, who are my foundation and the loves of my life.I am immensely grateful for all the support you have given me.This work is largely the result of your efforts.Mom, thank you for being strong, loving and for teaching me to believe in myself.Dad, thank you for supporting me, making awful jokes (which I laugh at from time to time), and for teaching me that life is too short not to enjoy the people we love.So thank you very much, I love you.To my siblings, Gabriela and Matheus, for being my biggest inspirations, even though I try hard not to admit it in front of you.Gabi, thank you for being the sweetest person I know (and the fiercest too!).You have the gift of making me feel welcome and comfortable.Being with you is easy.Math, thanks for getting excited about me studying something remotely close to quantum computing and genuinely believing that I'm going to get rich from it.If that happens, although it's highly unlikely, I'll dedicate part of the fortune to you.But beyond that, thank you for showing me that someone so serious and responsible can be so playful and kind.And to my brother and sister-in-law, Luc and Malu, thank you for making Gabi and Math so happy.I love you all.And Malu, thanks for Sosô.To my grandparents, Eunice, Jurandir, Victória and Olize.Abuela, know that the most important part of who I am today comes from you.Thank you for teaching me to laugh on difficult days and to look at life through the eyes of a child.Grandpa, I didn't have the privilege of knowing you, but thank you for raising this family with grandma.Vivitória, you're not here anymore either, but I'll never forget talking to you by the wood-burning stove on cold mornings in Caçador.And Grandpa, "Life is bitter enough already, isn't it?Barbarity."So I'll try to write happier things next.

Charles Day

Scott Aaronson

There are two ways to teach quantum mechanics. The first way – which for most physicists today is still the only way – follows the historical order in which the ideas were discovered. So, you start with classical mechanics and electrodynamics, solving lots of grueling differential equations at every step. Then, you learn about the “blackbody paradox” and various strange experimental results, and the great crisis these things posed for physics. Next, you learn a complicated patchwork of ideas that physicists invented between 1900 and 1926 to try to make the crisis go away. Then, if you're lucky, after years of study, you finally get around to the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes that can be positive, negative, or even complex. Look, obviously the physicists had their reasons for teaching quantum mechanics that way, and it works great for a certain kind of student. But the “historical” approach also has disadvantages, which in the quantum information age are becoming increasingly apparent. For example, I’ve had experts in quantum field theory – people who've spent years calculating path integrals of mind-boggling complexity – ask me to explain the Bell inequality to them , or other simple conceptual things like Grover's algorithm. I felt as if Andrew Wiles had asked me to explain the Pythagorean Theorem.

Sean M. Carroll

David Pogue