Experimental superposition of orders of quantum gates

Abstract

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.

Causally nonseparable processes admitting a causal model

“…The relation between causally nonseparable processes and the violation of causal inequalities is not yet fully understood. On the one hand, there exist causally nonseparable processes that can be physically implemented [22] but have a causal model-they do not violate causal inequalities [7,8]. An example of such a process is the 'quantum switch' [6].…”

Quantum Neural Machine Learning: Backpropagation and Dynamics

“…While the framework, addressed in section 2, introduces a quantum neural learning scheme to adaptively solve specific computational problems, in section 3, the feedforward and backpropagation take on a role as building blocks for an unsupervised dynamical neural processing of an environment, with the conditional neural state transition taking place with respect to the different neural activation orders, thus extending the formalism of quantum computation with changing orders of gates (Procopio, et al, 2015;Brukner, 2014;Chiribella, et al, 2013;Aharonov, et al, 1990) to the context of quantum machine learning.…”

“…We now explore this later type of application of QuANNs, connecting it to networks with general architectures and to an approach to quantum computation where the ordering of quantum gates is not fixed (Procopio, et al, 2015;Brukner, 2014;Chiribella, et al, 2013;Aharonov, et al, 1990).…”

Functional quantum computing: An optical approach

“…It should be noted that [30] reports an experimental measurement of operator commutativity, but using spatial modes to control operator ordering. This is a simpler approach for performing a 2 − switch, because the con-trol information is encoded using a single beamsplitter and the experiment contains only passive components.…”