Fault-Tolerant Quantum Computation with High Threshold in Two Dimensions

Abstract

We present a scheme of fault-tolerant quantum computation for a local architecture in two spatial dimensions. The error threshold is 0.75% for each source in an error model with preparation, gate, storage and measurement errors.PACS numbers: 03.67. Lx, 03.67.Pp Quantum computation is fragile. Exotic quantum states are created in the process, exhibiting entanglement among large numbers of particles across macroscopic distances. In realistic physical systems, decoherence acts to transform these states into more classical ones, compromising their computational power. Fortunately, the effects of decoherence can be counteracted by quantum error correction [1]. In fact, arbitrarily large quantum computations can be performed with arbitrary accuracy, provided the error level of the elementary components of the quantum computer is below a certain threshold. This is guaranteed by the threshold theorem for quantum computation [2,3,4,5]. Now that the threshold theorem has been established, it is important to devise methods for error correction which yield a high threshold, are robust against variations of the error model, and can be implemented with small operational overhead. An additional desideratum is a simple architecture for the quantum computer, requiring no long-range interaction, for example.Recently, a threshold estimate of 3 × 10 −2 per operation has been obtained for a method using post-selection [6]. An alternative scheme with high threshold combines topological quantum computation with state purification [7]. (See also [8].) In that approach, a subset of the universal gates are assumed to be error-free. Pure topological quantum computation ideally requires no error correction but often picks up a comparable polylogarithmic overhead [9] in the Solovay-Kitaev construction for approximating single-and two-qubit gates (c.f.[10]). fault tolerance is more difficult to achieve in architectures where each qubit can only interact with other qubits in its immediate neighborhood. A fault tolerance threshold for a two-dimensional lattice of qubits with only local and nearest-neighbor gates is 1.9 × 10 −5 [11].In this Letter, we present a scheme for fault-tolerant universal quantum computation on a two-dimensional lattice of qubits, requiring only a nearest-neighbor translation-invariant Ising interaction and single-qubit preparation and measurement. A fault tolerance threshold of 7.5 × 10 −3 for each error source is presented, with moderate resource scaling. This scheme is best suited for implementation with massive qubits where geometric constraints naturally play a role, such as cold atoms in optical lattices [12] or two-dimensional ion traps [13].The presented scheme integrates methods of topological quantum computation, specifically the toric code [14], and magic state distillation [15] into the one-way quantum computer (QC C ) [16] on cluster states. By employing magic state distillation we improve the error threshold significantly beyond [17], with the threshold value and overhead scaling now set by the topologi...

High-threshold universal quantum computation on the surface code

“…This paper is a simplified review of the quantum computing scheme of [1,2]. The scheme requires a 2-D square lattice of nearest neighbor coupled qubits with initialization, readout, memory and quantum gates all operating with error rates less than approximately 1% -the least challenging set of physical requirements devised to date.…”

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We present a comprehensive and self-contained simplified review of the quantum computing scheme of [1,2], which features a 2-D nearest neighbor coupled lattice of qubits, a threshold error rate approaching 1%, natural asymmetric and adjustable strength error correction and low overhead, arbitrarily long-range logical gates. These features make it by far the best and most practical quantum computing scheme devised to date.

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Co-designing a scalable quantum computer with trapped atomic ions

“…Proposals already exist for implementing the surface code 46 and the concatenated Steane code 44 in a modular architecture. There is currently great interest in the surface code due to its high computational threshold around 1% 111,112 in 2D architectures. Early papers on the surface code emphasised computation near the threshold resulting in large overheads.…”

Majorana Fermion Surface Code for Universal Quantum Computation

“…In the surface code, measurements of nontrivial commuting operators (stabilizers) are used to project onto a "code state," and logical qubits are effectively encoded in the anyon charge of a region by ceasing certain stabilizer measurements [26][27][28][29]. The logical gates necessary for universal quantum computation are realized through sequences of measurements used to move and braid the logical qubits.…”