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The surface code is one of the leading quantum error correction codes for realizing large-scale fault-tolerant quantum computing (FTQC). One major challenge in realizing surface-code-based FTQC is the extremely large number of qubits…
Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone…
Programming a quantum device describes the usage of quantum logic gates, agnostic of hardware specifics, to perform a sequence of operations with (typically) a computing or sensing task in mind. Such programs have been executed on digital…
We describe a space-time optimized circuit for the table lookup subroutine from lattice-surgery surface code primitives respecting 2D grid connectivity. Table lookup circuits are ubiquitous in quantum computing, allowing the presented…
Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting…
Fault-tolerant logic gates will consume a large proportion of the resources of a two-dimensional quantum computing architecture. Here we show how to perform a fault-tolerant non-Clifford gate with the surface code; a quantum…
Unambiguous measurements play an important role in quantum information, with applications ranging from quantum key distribution to quantum state reconstruction. Recently, such measurements have also been used in quantum algorithms based on…
The implementation of fault-tolerant quantum gates on encoded logic qubits is considered. It is shown that transversal implementation of logic gates based on simple geometric control ideas is problematic for realistic physical systems…
Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…
A Bacon-Shor code is a subsystem quantum error-correcting code on an $L \times L$ lattice where the $2(L-1)$ weight-$2L$ stabilizers are usually inferred from the measurements of $(L-1)^2$ weight-2 gauge operators. Here we show that the…
The surface code is a spin-1/2 lattice system that can exhibit non-trivial topological order when defects are punctured in the lattice and thus can be used as a stabiliser code. The protocols developed to create defects in the system have…
Generalized code surgery is a versatile and low-overhead technique for performing fault-tolerant computation on quantum low-density parity-check (qLDPC) codes. In many settings, surgery exhibits practical space overheads, while its time…
Geometric quantum computation offers a practical strategy toward robust quantum computation due to its inherently error tolerance. However, the rigorous geometric conditions lead to complex and/or error-disturbed quantum controls,…
Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not the local geometry. I also introduce a…
Quantum computers herald the arrival of a new era in which previously intractable computational problems will be solved efficiently. However, quantum technology is held down by decoherence, a phenomenon that is omnipresent in the quantum…
Recently, it was realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties of realizing quantum…
The study of real-time evolution of lattice quantum field theories using classical computers is known to scale exponentially with the number of lattice sites. Due to a fundamentally different computational strategy, quantum computers hold…
We design flexible fault tolerant gate gadgets that allow the data and the ancilla to be encoded using different codes. By picking a stabilizer code for the ancilla we are able to perform both Clifford and non-Clifford gates fault…
Gauging is a general procedure for mapping a quantum many-body system with a global symmetry to one with a local gauge symmetry. We consider a generalized gauging map that does not enforce gauge symmetry at all lattice sites, and show that…
In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…