Quantum mechanics has long been recognized as a counter-intuitive theory, with ideas such as wave-particle duality, quantum superposition and entanglement defying our natural way of thinking. In recent years, these sorts of uniquely quantum properties are being exploited to develop revolutionary technologies, such as quantum cryptography, quantum metrology and perhaps the most well-known example, quantum computation. In the field of quantum computation, the circuit model was used to show that universal quantum computation is possible1, and the circuit model has since been an incredibly successful tool, leading to important quantum algorithms which greatly outperform their classical counterparts2. The circuit model takes advantage of the fact that quantum mechanics allows for the superposition and interference of quantum bits (qubits) in different states to achieve a computational speed-up. However, in addition to the superpositions of states, quantum mechanics also allows for the superposition of quantum circuits3,4—a feature which is not used in the standard quantum circuit model. Nevertheless, such superpositions of quantum circuits are rapidly becoming central to several foundational research programs studying the role of time and causality in quantum theory5,6,7,8,9. These superpositions of quantum circuits (sometimes called a ‘superposition of causal orders’) give rise to new counter-intuitive quantum predictions, and it has recently been predicted that they could provide quantum computers with even further computational advantages8,10. In particular, superimposing quantum circuits, each with a different gate ordering, can allow one to accomplish a specific computational task with fewer quantum gate uses than a quantum computer which has a fixed-gate order10. Quantum computers achieve a speed-up by placing quantum bits (qubits) in superpositions of different states. However, it has recently been appreciated that quantum mechanics also allows one to ‘superimpose different operations’. Furthermore, it has been shown that using a qubit to coherently control the gate order allows one to accomplish a task—determining if two gates commute or anti-commute—with fewer gate uses than any known quantum algorithm. Here we experimentally demonstrate this advantage, in a photonic context, using a second qubit to control the order in which two gates are applied to a first qubit. We create the required superposition of gate orders by using additional degrees of freedom of the photons encoding our qubits. The new resource we exploit can be interpreted as a superposition of causal orders, and could allow quantum algorithms to be implemented with an efficiency unlikely to be achieved on a fixed-gate-order quantum computer.An in silico designed dosimetric autologous living vaccine consisting of with Multiple Wilms’ Tumor 1 WT1-ConSynthetic–Restricted Peptide mimotopic Epitopes RMFPNAPYLP pulsed dendritic cells on a personalized Active Network analysis for asymptomatic or minimally symptomatic metastatic Pancreatic Cancer.
Experimental superposition of orders of quantum gatesAn in silico designed dosimetric autologous living vaccine consisting of with Multiple Wilms’ Tumor 1 WT1-ConSynthetic–Restricted Peptide mimotopic Epitopes RMFPNAPYLP pulsed dendritic cells on a personalized Active Network analysis for asymptomatic or minimally symptomatic metastatic Pancreatic Cancer.