Quantum computations without definite causal structure

TL;DR

This paper demonstrates that quantum theory permits transformations of black boxes with indefinite causal order, exemplified by the quantum switch, which cannot be realized in fixed causal circuits without additional resources.

Contribution

It introduces the quantum switch as a novel quantum transformation with indefinite causal order, expanding the understanding of quantum processes beyond fixed causal structures.

Findings

Quantum switch entangles order control qubit with circuit structure

Simulating quantum switch requires postselection or extra queries

Indefinite causal order cannot be realized in fixed causal circuits

Abstract

We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order. The simplest example of such a transformation is the classical switch of black boxes, where two input black boxes are arranged in two different orders conditionally on the value of a classical bit. The quantum version of this transformation-the quantum switch-produces an output circuit where the order of the connections is controlled by a quantum bit, which becomes entangled with the circuit structure. Simulating these transformations in a circuit with fixed causal structure requires either postselection, or an extra query to the input black boxes.