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Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple…
Quantum computing hardware has grown sufficiently complex that it often can no longer be simulated by classical computers, but its computational power remains limited by errors. These errors corrupt the results of quantum algorithms, and it…
The surface code is a promising candidate for fault-tolerant quantum computation, achieving a high threshold error rate with nearest-neighbor gates in two spatial dimensions. Here, through a series of numerical simulations, we investigate…
We present a method for quantum error mitigation on partially error-corrected quantum computers - i.e., computers with some logical qubits and some noisy qubits. Our method is inspired by the error cancellation method and is implemented via…
Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…
A quantum channel models the interaction between the system we are interested in and its environment. Such a model can capture the main features of the interaction but because of the complexity of the environment we can not assume that it…
One of the largest obstacles to building a quantum computer is gate error, where the physical evolution of the state of a qubit or group of qubits during a gate operation does not match the intended unitary transformation. Gate error stems…
We investigate the use of Quantum Neural Networks for discovering and implementing quantum error-correcting codes. Our research showcases the efficacy of Quantum Neural Networks through the successful implementation of the Bit-Flip quantum…
I give a pedagogical account of Shor's nine-bit code for correcting arbitrary errors on single qubits, and I review work that determines when it is possible to maintain quantum coherence by reversing the deleterious effects of open-system…
We compare failure distributions of quantum error correction circuits for stochastic errors and coherent errors. We utilize a fully coherent simulation of a fault tolerant quantum error correcting circuit for a $d=3$ Steane and surface…
Quantum error correction protocols have been developed to offset the high sensitivity to noise inherent in quantum systems. However, much is still unknown about the behaviour of a quantum error-correcting code under general noise, including…
The demonstration of quantum error correction (QEC) is one of the most important milestones in the realization of fully-fledged quantum computers. Toward this, QEC experiments using the surface codes have recently been actively conducted.…
The highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1 - exp [-n E(R)+ o(n)] for some function E(R) on noisy quantum channels that are subject to not necessarily independent errors.…
As quantum computing hardware steadily increases in qubit count and quality, one important question is how to allocate these resources to mitigate the effects of hardware noise. In a transitional era between noisy small-scale and fully…
We analyze quantum state preservation in open quantum systems using quantum error-correcting (QEC) codes explicitly embedded in microscopic system-bath models. Rather than assuming abstract quantum channels, we consider multi-qubit…
The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…
We demonstrate that continuous-variable quantum error correction based on Gaussian ancilla states and Gaussian operations (for encoding, syndrome extraction, and recovery) can be very useful to suppress the effect of non-Gaussian error…
Reliable quantum information processing in the face of errors is a major fundamental and technological challenge. Quantum error correction protects quantum states by encoding a logical quantum bit (qubit) in multiple physical qubits. To be…
In this paper, we place bounds on when it is impossible to purify a noisy two-qubit state if all the gates used in the purification protocol are subject to adversarial local, independent, noise. It is found that the gate operations must be…
Near-term hardware is constrained by high error rates, small qubit counts, and relatively low output fidelity, making the execution of large, high performance quantum circuits difficult. Circuit partitioning (or circuit cutting) has emerged…