Abstract
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 single-qubit gates exceeding the threshold of error correction codes like the surface code have been demonstrated, while two-qubit gates have reached 98% fidelity and are improving rapidly. However, there are other types of error --- such as charge leakage and propagation --- that may occur in quantum dot arrays and which cannot be corrected by quantum error correction codes, making them potentially damaging even when their probability is small. We propose a surface code architecture for silicon quantum dot spin qubits that is robust against leakage errors by incorporating multi-electron mediator dots. Charge leakage in the qubit dots is transferred to the mediator dots via charge relaxation processes and then removed using charge reservoirs attached to the mediators. A stabiliser-check cycle, optimised for our hardware, then removes the correlations between the residual physical errors. Through simulations we obtain the surface code threshold for the charge leakage errors and show that in our architecture the damage due to charge leakage errors is reduced to a similar level to that of the usual depolarising gate noise. Spin leakage errors in our architecture are constrained to only ancilla qubits and can be removed during quantum error correction via reinitialisations of ancillae, which ensure the robustness of our architecture against spin leakage as well. Our use of an elongated mediator dots creates spaces throughout the quantum dot array for charge reservoirs, measuring devices and control gates, providing the scalability in the design.
Highlights
Universal quantum computers promise speed-up in crucial areas like simulation of materials and molecules [1], search [2, 3] and sampling [4, 5], yet they all require high-precision control of quantum states
If we can further push down the gate error rate, the charge leakage error threshold will grow, and in the end bounded by the limit in the case of no gate errors (p2 = 0) where the threshold for pleak is 0.66% (see Figure 6 (c))
We have introduced a surface code architecture implemented using spin qubits in silicon quantum dots that is robust against spin leakage errors through its use of single-dot data qubit and robust against charge leakage errors through its use of multi-electron mediator dots
Summary
Universal quantum computers promise speed-up in crucial areas like simulation of materials and molecules [1], search [2, 3] and sampling [4, 5], yet they all require high-precision control of quantum states. The qubit overheads can be significant: it is estimated that > 2 × 108 physical qubits with gate error rate 10−3 might be needed to perform a non-trivial Shor’s factoring algorithm using surface codes [11] These considerations motivate the development of qubit implementations which offer the prospect for high-density 2D arrays. Such shuttling architectures require distribution of entanglement between modules and this is likely to impact the fidelity and speed of inter-module operations While such influential architectures have been designed to accommodate error correcting codes that compensate for computational errors, they do not address so-called ‘leakage errors’ in which the quantum system escapes out of the computational subspace. We summarise the key features of this approach and discuss possible improvements and extensions
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