Measurement-free implementations of small-scale surface codes for quantum-dot qubits

Abstract

The performance of quantum error correction schemes depends sensitively on the physical realizations of the qubits and the implementations of various operations. For example, in quantum dot spin qubits, readout is typically much slower than gate operations, and conventional surface code implementations that rely heavily on syndrome measurements could therefore be challenging. However, fast and accurate reset of quantum dot qubits-without readout-can be achieved via tunneling to a reservoir. Here, we propose small-scale surface code implementations for which syndrome measurements are replaced by a combination of Toffoli gates and qubit reset. For quantum dot qubits, this enables much faster error correction than measurement-based schemes, but requires additional ancilla qubits and non-nearest-neighbor interactions. We have performed numerical simulations of two different coding schemes, obtaining error thresholds on the orders of 10 −2 for a 1D architecture that only corrects bit-flip errors, and 10 −4 for a 2D architecture that corrects bit-and phase-flip errors.

Towards a realistic GaAs-spin qubit device for a classical error-corrected quantum memory

“…If a 2D device architecture were available, one may ask whether the use of the phase-flip code would still be of interest. For example, one could directly use the surface code with limited "cross-bar" control as envisioned in [9] or consider faster, measurement-free, use of small surface codes [41]. One could imagine using a clustered 2D layout with each cluster representing a logical qubit encoded by the phase-flip code connected by long-range CNOT gates with other clusters or ancilla qubits, while short-range CNOT gates are used inside the cluster.…”

“…This slow measurement bottleneck can in principle be circumvented by supplying fresh ancillas for new QEC cycles while the current ancillas are still being measured (see, e.g., the analysis in [40]), or by avoiding measurement all together [41]. However, we choose to treat qubits as a scarce resource, which seems more reasonable in the near term, and thus reuse the measurement qubits to keep the number of qubits minimal.…”

Materials for Silicon Quantum Dots and their Impact on Electron Spin Qubits

“…Potentially with some form of multiplexing, these resources could be shared among groups of physical qubits. [ 79 ] Moreover, quantum error correction schemes that are less based on real time readout of syndromes [ 87 ] could be an important development to relax the need for high fidelity individualized qubit readout.…”

Towards a realistic GaAs-spin qubit device for a classical error-corrected quantum memory

“…This slow measurement bottleneck can in principle be circumvented by supplying fresh ancillas for new QEC cycles while the current ancillas are still being measured, see e.g. the analysis in [36], or by avoiding measurement all together [37]. However, we choose to treat qubits as a scarce resource, which seems more reasonable in the near-term, and thus re-use the measurement qubits to keep the number of qubits minimal.…”