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Quantum error correction methods use processing power to combat noise. The noise level which can be tolerated in a fault-tolerant method is therefore a function of the computational resources available, especially the size of computer and…
Quantum computing promises to provide exponential speed-ups to certain classes of problems. In many such algorithms, a classical vector $\mathbf{b}$ is encoded in the amplitudes of a quantum state $\left |b \right >$. However, efficiently…
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction…
Debugging quantum states transformations is an important task of modern quantum computing. The use of quantum tomography for these purposes significantly expands the range of possibilities. However, the presence of preparation and…
Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…
Realizing universal fault-tolerant quantum computation is a key goal in quantum information science. By encoding quantum information into logical qubits utilizing quantum error correcting codes, physical errors can be detected and…
Quantum state preparation is an important subroutine for quantum computing. We show that any $n$-qubit quantum state can be prepared with a $\Theta(n)$-depth circuit using only single- and two-qubit gates, although with a cost of an…
Quantum state preparation is an important subroutine in many quantum algorithms. The goal is to encode classical information directly to the quantum state so that it is possible to leverage quantum algorithms for data processing. However,…
Quantum computing is entering a period in which progress will be shaped as much by advances in computer science as by improvements in hardware. The central thesis of this report is that early fault-tolerant quantum computing shifts many of…
Quantum error correction is a cornerstone of reliable quantum computing, with surface codes emerging as a prominent method for protecting quantum information. Surface codes are efficient for Clifford gates but require magic state…
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…
The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects…
Most previous efforts of quantum error correction focused on either extending classical error correction schemes to the quantum regime by performing a perfect correction on a subset of errors, or seeking a recovery operation to maximize the…
The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the…
Quantum computation can be performed by encoding logical qubits into the states of two or more physical qubits, and controlling a single effective exchange interaction and possibly a global magnetic field. This "encoded universality"…
A major milestone of quantum error correction is to achieve the fault-tolerance threshold beyond which quantum computers can be made arbitrarily accurate. This requires extraordinary resources and engineering efforts. We show that even…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…
Resource estimation is a significant challenge in evaluating fault tolerant quantum computers. Existing approaches often rely on either fixed architectural assumptions or coarse analytical models that fail to capture the interaction between…
Despite significant progress in quantum computing in recent years, executing quantum circuits for practical problems remains challenging due to error-prone quantum hardware. Hence, quantum error correction becomes essential but induces…