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Quantum error correction is a crucial step beyond the current noisy-intermediate-scale quantum device towards fault-tolerant quantum computing. However, most of the error corrections ever demonstrated rely on post-selection of events or…
Current quantum technology is approaching the system sizes and fidelities required for quantum error correction. It is therefore important to determine exactly what is needed for proof-of-principle experiments, which will be the first major…
The surface code is a powerful quantum error correcting code that can be defined on a 2-D square lattice of qubits with only nearest neighbor interactions. Syndrome and data qubits form a checkerboard pattern. Information about errors is…
Given a quantum gate circuit, how does one execute it in a fault-tolerant architecture with as little overhead as possible? In this paper, we discuss strategies for surface-code quantum computing on small, intermediate and large scales.…
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated…
Scalable and fault-tolerant quantum computation will require error correction. This will demand constant measurement of many-qubit observables, implemented using a vast number of CNOT gates. Indeed, practically all operations performed by a…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process---it is the algorithm which computes…
A remarkable characteristic of quantum computing is the potential for reliable computation despite faulty qubits. This can be achieved through quantum error correction, which is typically implemented by repeatedly applying static syndrome…
The fault-tolerant operation of logical qubits is an important requirement for realizing a universal quantum computer. Spin qubits based on quantum dots have great potential to be scaled to large numbers because of their compatibility with…
Spin qubits in silicon quantum dots are one of the most promising building blocks for large scale quantum computers thanks to their high qubit density and compatibility with the existing semiconductor technologies. High fidelity…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…
We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality…
In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…
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…
Quantum computers promise to solve certain problems exponentially faster than possible classically but are challenging to build because of their increased susceptibility to errors. Remarkably, however, it is possible to detect and correct…
Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an…
Quantum error correction is a critical technique for transitioning from noisy intermediate-scale quantum (NISQ) devices to fully fledged quantum computers. The surface code, which has a high threshold error rate, is the leading quantum…
Quantum error-correcting codes are a vital technology for demonstrating reliable quantum computation. They require data qubits for encoding quantum information and ancillary qubits for taking error syndromes necessary for error correction.…
We describe and analyze leakage errors of singlet-triplet qubits. Even though leakage errors are a natural problem for spin qubits encoded using quantum dot arrays, they have obtained little attention in previous studies. We describe the…