Abstract
It is challenging to transform an arbitrary quantum circuit into a form protected by surface code quantum error correcting codes (a variant of topological quantum error correction), especially if the goal is to minimise overhead. One of the issues is the efficient placement of magic state distillation sub circuits, so-called distillation boxes, in the space-time volume that abstracts the computation’s required resources. This work presents a general, systematic, online method for the synthesis of such circuits. Distillation box placement is controlled by so-called schedulers. The work introduces a greedy scheduler generating compact box placements. The implemented software, whose source code is available at www.github.com/alexandrupaler/tqec, is used to illustrate and discuss synthesis examples. Synthesis and optimisation improvements are proposed.
Highlights
Arbitrary quantum computations are generally formulated as a quantum circuit consisting of quantum operations and quantum wires (e.g. Fig. 1)
The synthesis framework built according to the following requirements: (1) there is no general restriction on the placement of distillation boxes, as long they do not overlap with other circuit elements; (2) distillation box connections should be computed using a path finding algorithm instead of having a fixed structure like in ref. 1
Connection defects are more dense in the space-time volume occupied by the circuit, and this impacts the illustrations from this work as well as the existing simulation results: the improvement against the previous state of the art synthesis would be much higher, because the current work delivers more compact space-time volumes, but because the previous one was very naive
Summary
Arbitrary quantum computations are generally formulated as a quantum circuit consisting of quantum operations (initialisations, quantum gates, measurements) and quantum wires (e.g. Fig. 1). A time axis can be associated to the circuit’s execution, and time flows from left to right. A circuit is executed sequentially with regard to the ordering of operations on each quantum wire, so that preceding quantum operations are always on the left side of the currently executed operation. Quantum circuit wires cannot run backwards in time, because, quantum circuits have a two dimensional representation, the wires connecting the quantum operations have a temporal and not a hardware interpretation (classic circuit wires are mostly associated to hardware). Circuit execution depends on the availability of computational resources, which for a quantum computer are time and hardware: the time needed to operate the hardware in order to execute the entire computation. It can be assumed that hardware is arranged in a two dimensional lattice, so that the overall amount of available resources is abstracted by a metric similar to a space-time volume resulting after multiplying available hardware (strictly limited) with available time (faster is better)
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