Um protocolo para explorar a dina¢mica de emaranhamento via dualidade do Espaço-tempo
Algumas questões fundamentais na física de muitos corpos que antes seriam consideradas especulativas e fora do reino da exploraça£o experimental podem agora ser examinadas em ambientes de laboratório.
![](data:image/jpeg;base64,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)
Dualidade Espaço-tempo: a troca dos papanãis do espaço e do tempo na dina¢mica qua¢ntica simula o efeito do monitoramento por um observador externo. Crédito: Ippoliti e Khemani.
Nos últimos anos, houve avanços significativos no desenvolvimento de computadores e simuladores qua¢nticos digitais. Esses sistemas fasicos emergentes estãoabrindo possibilidades sem precedentes para controlar e medir uma variedade de dina¢micas qua¢nticas. Como resultado, algumas questões fundamentais na física de muitos corpos que antes seriam consideradas especulativas e fora do reino da exploração experimental podem agora ser examinadas em ambientes de laboratório.
Pesquisadores da Universidade de Stanford realizaram recentemente um estudo explorando o papel das medições qua¢nticas na dina¢mica de muitos corpos. Em seu artigo, publicado na Physical Review Letters , eles apresentaram especificamente um protocolo que pode ser usado para realizar dina¢micas que incluem medições qua¢nticas em computadores qua¢nticos e simuladores qua¢nticos, evitando uma etapa processual conhecida como pa³s-seleção.
"As medições tem um lugar especial na física qua¢ntica: elas fazem o sistema 'colapsar' abruptamente em um dos vários resultados de medição possaveis, escolhidos aleatoriamente", disse Matteo Ippoliti e Vedika Khemani, os dois pesquisadores que realizaram o estudo. org. "Por exemplo, pense no gato de Schraµdinger em uma 'superposição' de vivos e mortos em uma caixa - assim que a caixa éaberta, o estado do gato se transforma em vivo ou morto. Em contraste, sistemas qua¢nticos que são 'deixados em paz' evoluem de forma determinastica, também conhecida como dina¢mica 'unita¡ria'. "
Nos últimos anos, em parte motivados pelo progresso recente no desenvolvimento de dispositivos de computação qua¢ntica, muitos pesquisadores começam a estudar a interação entre as medições qua¢nticas e a dina¢mica unita¡ria de muitos corpos. Curiosamente, eles previram que os estados produzidos por esses dispositivos exibiriam um conjunto variado de novos fena´menos. Posteriormente, essas observações tornaram-se o foco de numerosos estudos teóricos.
"Do ponto de vista experimental, a aleatoriedade das medições qua¢nticas representa um grande problema: para fazer o mesmo estado de forma confia¡vel (necessa¡rio para medir suas propriedades ou para usa¡-lo em aplicações), deve-se replicar a mesma sequaªncia aleata³ria de resultados de medição ao longo de e mais ", explicaram Ippoliti e Khemani. "Esta éuma ocorraªncia exponencialmente rara, como jogar uma moeda várias vezes e obter uma sequaªncia direta de caras, e não éuma limitação técnica, mas sim uma consequaªncia das regras ba¡sicas da meca¢nica qua¢ntica. Esse éo problema da 'pa³s-seleção'."
Para medir o emaranhamento em dina¢mica não unita¡ria, os pesquisadores teriam que repetir um experimento várias vezes para satisfazer esse requisito de 'pa³s-seleção', o que seria proibitivamente difacil. O objetivo principal do estudo realizado por Ippoliti e Khemani foi trazr uma estratanãgia que possibilitasse a realização experimental dessas dina¢micas sem a necessidade de pa³s-seleção. Eles propuseram que isso poderia ser alcana§ado trocando os papanãis do espaço e do tempo, alavancando uma ideia conhecida como dualidade do Espaço-tempo .
Â
"Em termos simples, imagine ter um conjunto de bits qua¢nticos (qubits) em seu laboratório, dispostos em uma linha, nas posições um, dois, etc.", disseram Ippoliti e Khemani. "Eles podem ser feitos para interagir com seus vizinhos e, assim, evoluir no tempo, descrevendo uma computação qua¢ntica. Agora imagine um sistema 'virtual' que existe na direção do tempo do laboratório e evolui na direção do espaço - movendo-se do qubit um para dois no laboratório significa desenvolver este sistema virtual por uma unidade de tempo, etc. "
A 'evolução virtual' do sistema examinado pelos investigadores revelou-se não unita¡ria, o que significa essencialmente que inclui alguns elementos de medição. Esses elementos, no entanto, são totalmente determinasticos e podem ser reproduzidos de forma confia¡vel e repetida. Essa característica crucial permitiu que eles traduzissem sua ideia em um protocolo para realizar e estudar a dina¢mica de emaranhamento em simuladores qua¢nticos.
"As ideias por trás de nosso estudo podem parecer muito abstratas, mas nosas traduzimos em um protocolo especafico que pode ser executado nos atuais simuladores qua¢nticos digitais", disseram Ippoliti e Khemani. "Isso cria uma rota direta para estudar experimentalmente esses novos tipos de dina¢mica qua¢ntica envolvendo medições, ao mesmo tempo que traz algumas ideias tea³ricas empolgantes para mais perto da realização."
No futuro, o protocolo idealizado por Ippoliti e Khemani podera¡ abrir novas possibilidades para o estudo da dina¢mica de emaranhamento em sistemas qua¢nticos. Além disso, seu trabalho pode informar o desenvolvimento de novas estratanãgias para proteger as informações armazenadas em dispositivos qua¢nticos existentes e recentemente desenvolvidos. A ideia de 'dualidade do Espaço-tempo' introduzida por esses pesquisadores também poderia ser usada para estudar vários fena´menos fasicos e dina¢micos associados a sistemas qua¢nticos.
“No momento, estamos explorando os tipos de estados interessantes que podem ser preparados dessa forma e como eles podem se conectar a s fases da matéria qua¢ntica que conhecemosâ€, acrescentaram Ippoliti e Khemani. “De uma forma mais geral, a nossa investigação seráinformada por esta nova era da computação qua¢ntica e da simulação, com dois objectivos: por um lado, descobrir novos fena³menos fundamentais possibilitados por este progresso tecnola³gico; por outro, perseguir novas ideias fundamentais que podem ser impactantes para as próprias tecnologias, particularmente novas maneiras de armazenar e manipular informações qua¢nticas informadas por dina¢mica. "