Connecting multiple processors via quantum interconnect technologies could help overcome scalability issues in single-processor quantum computers. Transmission via these interconnects can be performed more efficiently using quantum multiplexing, where information is encoded in high-dimensional photonic degrees of freedom. We explore the effects of multiplexing on logical error rates in surface codes and hypergraph product codes. We show that, although multiplexing makes loss errors more damaging, assigning qubits to photons in an intelligent manner can minimize these effects, and the ability to encode higher-distance codes in a smaller number of photons can result in overall lower logical error rates. This multiplexing technique can also be adapted to quantum communication and multimode quantum memory with high-dimensional qudit systems.

The quantum logic gates used in the design of a quantum computer should be both universal, meaning arbitrary quantum computations can be performed, and fault-tolerant, meaning the gates keep errors from cascading out of control. A number of no-go theorems constrain the ways in which a set of fault-tolerant logic gates can be universal. These theorems are very restrictive, and conventional wisdom holds that a universal fault-tolerant logic gate set cannot be implemented natively, requiring us to use costly distillation procedures for quantum computation. Here, we present a general framework for universal fault-tolerant logic with stabilizer codes, together with a no-go theorem that reveals the very broad conditions constraining such gate sets. Our theorem applies to a wide range of stabilizer code families, including concatenated codes and conventional topological stabilizer codes such as the surface code. The broad applicability of our no-go theorem provides a new perspective on how the constraints on universal fault-tolerant gate sets can be overcome. In particular, we show how nonunitary implementations of logic gates provide a general approach to circumvent the no-go theorem, and we present a rich landscape of constructions for logic gate sets that are both universal and fault-tolerant. That is, rather than restricting what is possible, our no-go theorem provides a signpost to guide us to new, efficient architectures for fault-tolerant quantum computing.

A powerful feature of stabiliser error correcting codes is the fact that stabiliser measurement projects arbitrary errors to Pauli errors, greatly simplifying the physical error correction process as well as classical simulations of code performance. However, logical non-Clifford operations can map Pauli errors to non-Pauli (Clifford) errors, and while subsequent stabiliser measurements will project the Clifford errors back to Pauli errors the resulting distributions will possess additional correlations that depend on both the nature of the logical operation and the structure of the code. Previous work has studied these effects when applying a transversal $T$ gate to the three-dimensional colour code and shown the existence of a non-local "linking charge" phenomenon between membranes of intersecting errors. In this work we generalise these results to the case of a $CCZ$ gate in the three-dimensional surface code and find that many aspects of the problem are much more easily understood in this setting. In particular, the emergence of linking charge is a local effect rather than a non-local one. We use the relative simplicity of Clifford errors in this setting to simulate their effect on the performance of a single-shot magic state preparation process (the first such simulation to account for the full effect of these errors) and find that their effect on the threshold is largely determined by probability of $X$ errors occurring immediately prior to the application of the gate, after the most recent stabiliser measurement.