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Quantum hardware rarely suffers equal amounts of bit-flip ($X$) and phase-flip ($Z$) errors; one type is often much more common than the other. A code that is ``bias-tailored'' can exploit this imbalance, lowering the fault-tolerance…
Proving threshold theorems for fault-tolerant quantum computation is a burdensome endeavor with many moving parts that come together in relatively formulaic but lengthy ways. It is difficult and rare to combine elements from multiple papers…
Cat qubits have emerged as a promising candidate for quantum computation due to their higher error-correction thresholds and low resource overheads. In existing literature, the detuning of the two-photon drive is assumed to be zero for…
Quantum computation promises significant computational advantages over classical computation for some problems. However, quantum hardware suffers from much higher error rates than in classical hardware. As a result, extensive quantum error…
In recent years, there has been a significant progress in the development of digital quantum processors. The state-of-the-art quantum devices are imperfect, and fully-algorithmic fault-tolerant quantum computing is a matter of future. Until…
Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault tolerant schemes. Recently, error mitigation has been…
Quantum noise in real-world devices poses a significant challenge in achieving practical quantum advantage, since accurately compiled and executed circuits are typically deep and highly susceptible to decoherence. To facilitate the…
The ability to execute a large number of quantum gates in parallel is a fundamental requirement for quantum error correction, allowing an error threshold to exist under the finite coherence time of physical qubits. Recently, two-dimensional…
Overcoming the influence of noise and imperfections is a major challenge in quantum computing. Here, we present an approach based on applying a desired unitary computation in superposition between the system of interest and some auxiliary…
Universal quantum computation is striking for its unprecedented capability in processing information, but its scalability is challenging in practice because of the inevitable environment noise. Although quantum error correction (QEC)…
Quantum computers will require encoding of quantum information to protect them from noise. Fault-tolerant quantum computing architectures illustrate how this might be done but have not yet shown a conclusive practical advantage. Here we…
Fault-tolerant quantum computing demands many qubits with long lifetimes to conduct accurate quantum gate operations. However, external noise limits the computing time of physical qubits. Quantum error correction codes may extend such…
We propose a scalable trapped-ion quantum-computing architecture that efficiently incorporates quantum error correction. The chip design exploits orthogonal qubit connectivity by assigning horizontal trap regions to transversal logical…
For useful quantum computation, error-corrected machines are required that can dramatically reduce the inevitable errors experienced by physical qubits. While significant progress has been made in approaching and exceeding the surface-code…
Quantum error mitigation (QEM) is vital for noisy intermediate-scale quantum (NISQ) devices. While most conventional QEM schemes assume discrete gate-based circuits with noise appearing either before or after each gate, the assumptions are…
The promise of quantum computing is closer to reality today than ever before, thanks to rapid progress in the development of quantum hardware. Even as qubit lifetimes and gate fidelities continue to improve, realizing robust, fault-tolerant…
These are the lecture notes from the 2019 Les Houches Summer School on "Quantum Information Machines". After a brief introduction to quantum error correction and bosonic codes, we focus on the case of cat qubits stabilized by a nonlinear…
The central challenge in building a quantum computer is error correction. Unlike classical bits, which are susceptible to only one type of error, quantum bits ("qubits") are susceptible to two types of error, corresponding to flips of the…
Quantum error correction and fault-tolerance make it possible to perform quantum computations in the presence of imprecision and imperfections of realistic devices. An important question is to find the noise rate at which errors can be…
Quantum computing with qudits is an emerging approach that exploits a larger, more-connected computational space, providing advantages for many applications, including quantum simulation and quantum error correction. Nonetheless, qudits are…