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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…
High-fidelity two-logical-qubit gates are essential for realizing fault-tolerant quantum computation with bosonic codes, yet experimentally reported fidelities have rarely exceeded 90\%. Here, we propose a geometric phase engineering…
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…
We simulate the implementation of a T-gate, or $\frac{\pi}{8}$-gate, for a [7,1,3] encoded logical qubit in a non-equiprobable error environment. We demonstrate that the use of certain non-fault tolerant methods in the implementation may…
The cat code is a promising encoding scheme for bosonic quantum error correction as it allows for correction against losses--the dominant error mechanism in most bosonic systems. However, for losses to be detected efficiently without…
To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the…
Bosonic cat qubits stabilized with a driven two-photon dissipation are systems with exponentially biased noise, opening the door to low-overhead, fault-tolerant and universal quantum computing. However, current gate proposals for such…
A scalable and programmable quantum computer holds the potential to solve computationally intensive tasks that classical computers cannot accomplish within a reasonable time frame, achieving quantum advantage. However, the vulnerability of…
Transversal gates play an important role in the theory of fault-tolerant quantum computation due to their simplicity and robustness to noise. By definition, transversal operators do not couple physical subsystems within the same code block.…
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…
Code switching is an established technique that facilitates a universal set of FT quantum gate operations by combining two QEC codes with complementary sets of gates, which each by themselves are easy to implement fault-tolerantly. In this…
Recent advances in quantum error correction (QEC) across hardware platforms have demonstrated operation near and beyond the fault-tolerance threshold, yet achieving exponential suppression of logical errors through code scaling remains a…
Bosonic codes constitute a promising route to fault-tolerant quantum computing. {Existing Floquet protocols enable analytical construction of bosonic codes but typically rely on slow adiabatic ramps with thousands of driving periods.} In…
Bosonic codes offer a hardware-efficient strategy for quantum error correction by redundantly encoding quantum information in the large Hilbert space of a harmonic oscillator. However, experimental realizations of these codes are often…
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the…
Quantum error correction (QEC) aims to mitigate the loss of quantum information to the environment, which is a critical requirement for practical quantum computing. Existing QEC implementations heavily rely on measurement-based feedback,…
We suggest a method to perform a quantum logic gate between distant qubits by off-resonant field-atom dispersive interactions. The scheme we present is shown to work ideally even in the presence of errors in the photon channels used for…
Bosonic quantum error correcting codes are primarily designed to protect against single-photon loss. To correct for this type of error, one can encode the logical qubit in code spaces with a definite photon parity, such as cat codes or…
High-quality-factor 3D cavities in superconducting circuits are ideal candidates for bosonic logical qubits as their fidelity is limited only by the low photon loss rate. However, the transmon qubits that are used to manipulate bosonic…
Quantum computing experiments are transitioning from running on physical qubits to using encoded, logical qubits. Fault-tolerant computation can identify and correct errors, and has the potential to enable the dramatically reduced logical…