Surface code quantum computing by lattice surgery

Abstract

In recent years, surface codes have become a leading method for quantum error correction in theoretical large-scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural two-dimensional nearest-neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar-and defect-based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantum computation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are 2 further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded cnot between two distance-3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.

Freely Scalable Quantum Technologies Using Cells of 5-to-50 Qubits with Very Lossy and Noisy Photonic Links

“…The basic repeating cycle of the computer involves alternating patterns of parity checks separated by Hadamard rotations to switch between the x and z basis. Remarkably, this simple principle allows for far more than merely protecting quantum information from errors: certain operations between encoded logical qubits can be performed merely by altering the patterns of parity measurements [20,22], and together with a technique such as magic state distillation [23], all the operations required for universal quantum computation can be performed this way. In a monolithic 2D device, there is a natural layout for the physical qubits such that nearest-neighbor interactions suffice to efficiently perform the parity evaluation (see Fig.…”

Quantum error-correction failure distributions: Comparison of coherent and stochastic error models

“…For completeness we run a similar analysis on a surface code simulation. The particular variant we choose is the tilted-17 surface code, which is a variation on the distance 3 surface code that requires less data and ancilla qubits compared to conventional distance 3 surface code [27][28][29]. A diagram of the qubit and stabilizer layout of the code is shown in Fig.…”

Scalable Quantum Circuit and Control for a Superconducting Surface Code

“…The corresponding H gates on the ancillas or data qubits could also be masked to further reduce qubit errors due to qubit control inaccuracies. Logical operations, such as move and braiding operations on defect-based qubits [10], and lattice surgery on planar ones [29], also require dynamically changing the weight of specific stabilizer measurements, i.e., selectively removing specific data qubits from the quantum parity checks. In our scheme, this can easily be achieved by selective on-off masking of flux-pulse primitives.…”

“…Our scheme allows changing the weight of stabilizer measurements by simple on-off masking of detuning pulses, making it applicable to both defect-based and planar logical qubits [10], including lattice surgery [29].…”

“…However, all of these solutions require a growing number of detuning sequences and detuning ranges as the fabric expands, in order to avert all other interactions on the way to and from the j11i ↔ j02i avoided crossings of CZ f gates. Furthermore, these solutions seem practically infeasible already for distance five (Surface 49 [29]). To our knowledge, no fully parallel solution exists with a fixed number of detuning sequences and a fixed detuning range.…”