In order to circumvent that no universal set of gates can be achieved on a given quantum error-correcting codes, additional gates can be performed through magic state injection. This however requires to have access to high fidelity magic state, which can be obtained by the distillation of low quality states to fewer higher quality ones. In this paper, we provide a family of distillation protocols able to produce diagonal states at every level of the Clifford hierarchy. This family is obtained recursively using code doubling techniques and leveraging qubit recycling, the fact that some idle qubits of the protocols can be measured and re-used. At a given level of the Clifford hierarchy, we show that the protocols we derive can be performed at arbitrary high distance on a fix number of logical qubits. This family recovers many known efficient protocols, and uncovers new ones, such as a $111 \to 1$ protocol for $|T\rangle$ state distillation at distance $7$, which are the most compact in term of volume. Finally, we discuss possible extension of this framework for distillation protocols producing more than one output state.
Recent work established that, for independent erasures, storing $K$ logical qubits for $S$ time steps with error at most $\varepsilon$ requires a spacetime cost of $\Omega(S(K+\log(S/\varepsilon)))$. A matching construction was also given, but assumes ideal error correction. Here we show that the same scaling can be ac...
Kishor Bharti, Tobias Haug, Derek Khu et al.· 0 citations
Additional qubits can reduce the depth of a quantum circuit by providing workspace for parallel computation, but standard constructions assume that this workspace is initialized in a known state. In this work we study catalytic implementations, i.e. asking whether dirty qubits can instead be used provided that their jo...
Marten Folkertsma, Ian Mertz, S. Strelchuk et al.· 0 citations
By consuming multiple copies of an unknown qubit state, one can modify its purity while preserving the direction of its Bloch vector. We determine the maximum linear rate at which qubit states of different purities can be interconverted, allowing a nonzero error, quantified, for instance, by the trace distance, provide...
This work uses algebraic geometric techniques to construct codes over binary extension fields $\mathbb{F}_{2^s}$, thus discovering new protocols for the distillation of qubit magic states, where the focus is on the regime of practical qubit-based quantum computing architectures.
An-Qi Gong, Christopher A. Pattison, Patrick Rall et al.· 4 citations· ⚡2
Bona is presented, the first scheduler for dirty-qubit borrowing, built on a novel depth-aware heuristic algorithm, and it reduces nearly 99% of dirty ancillas on average with controlled depth overhead, providing concrete evidence that dirty ancillas offer unique optimization advantages in circuits with certain paralle...
Xiao-Quan Xu, Chen-Ke Liu, Bo-Ning Meng et al.· 1 citation
The Eastin-Knill theorem rules out a universal set of transversal logical gates on any code that detects single-qubit errors. The theorem constrains one partition of the qubits at a time. We show that depth-one layers of few-qubit gates, each respecting its own partition, can together generate a universal logical gate...
Arpit Dua, Adam Holmes, M. Gullans et al.· 0 citations
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