Related papers: Fault Tolerance in Parity-State Linear Optical Qua…

We prove an accuracy threshold theorem for fault-tolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla…

A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…

We compare two different implementations of fault-tolerant entangling gates on logical qubits. In one instance, a twelve-qubit trapped-ion quantum computer is used to implement a non-transversal logical CNOT gate between two five qubit…

Using an error models motivated by the Knill, Laflamme, Milburn proposal for efficient linear optics quantum computing [Nature 409,46--52, 2001], error rate thresholds for erasure errors caused by imperfect photon detectors using a 7 qubit…

Characterizing how quantum error correction circuits behave under realistic hardware noise is essential for testing the premises that enable scalable fault tolerance. Logical error rates conditioned on syndrome outcomes are needed to enable…

Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…

We develop an error-corrected quantum computation scheme based on concatenating the five-qubit Laflamme code onto the four-qubit Iceberg code. The approach skates a thin line: it is explicitly not fault tolerant, risking higher logical…

We formulate a scheme for fault-tolerant quantum computation that works effectively against highly biased noise, where dephasing is far stronger than all other types of noise. In our scheme, the fundamental operations performed by the…

Typical quantum computing schemes require transformations (gates) to be targeted at specific elements (qubits). In many physical systems, direct targeting is difficult to achieve; an alternative is to encode local gates into globally…

Color codes are promising quantum error correction (QEC) codes because they have an advantage over surface codes in that all Clifford gates can be implemented transversally. However, thresholds of color codes under circuit-level noise are…

We consider the impact of the unitary averaging framework on single and two-mode linear optical gates. We demonstrate that this allows a trade-off between the probability of success and gate fidelity, with perfect fidelity gates being…

With the intense interest in small, noisy quantum computing devices comes the push for larger, more accurate -- and hence more useful -- quantum computers. While fully fault-tolerant quantum computers are, in principle, capable of achieving…

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"…

I discuss how to perform fault-tolerant quantum computation with concatenated codes using local gates in small numbers of dimensions. I show that a threshold result still exists in three, two, or one dimensions when next-to-nearest-neighbor…

Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of quantum codes called low-density parity-check (LDPC) quantum codes. The codes we discuss are…

In quantum error correction using imperfect primitives, errors of high weight arising from a few faults are major concerns since they might not be correctable by the quantum error correcting code. Fortunately, some errors of different…

Today ion traps are among the most promising physical systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics. The standard circuit model of quantum computing requires a universal set…

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…

One of the main problems that optical quantum computing has to overcome is the efficient construction of two-photon gates. Theoretically these gates can be realized using Kerr-nonlinearities, but the techniques involved are experimentally…

I will give an overview of what I see as some of the most important future directions in the theory of fault-tolerant quantum computation. In particular, I will give a brief summary of the major problems that need to be solved in fault…