A new family of magic state distillation protocols based on logical Clifford error checking achieves near-linear asymptotic rate despite overhead exponent exceeding one, showing the quantities are not tightly coupled in the sublinear regime.
Lower bounds on the non-Clifford resources for quantum computations
5 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We establish lower-bounds on the number of resource states, also known as magic states, needed to perform various quantum computing tasks, treating stabilizer operations as free. Our bounds apply to adaptive computations using measurements and an arbitrary number of stabilizer ancillas. We consider (1) resource state conversion, (2) single-qubit unitary synthesis, and (3) computational tasks. To prove our resource conversion bounds we introduce two new monotones, the stabilizer nullity and the dyadic monotone, and make use of the already-known stabilizer extent. We consider conversions that borrow resource states, known as catalyst states, and return them at the end of the algorithm. We show that catalysis is necessary for many conversions and introduce new catalytic conversions, some of which are close to optimal. By finding a canonical form for post-selected stabilizer computations, we show that approximating a single-qubit unitary to within diamond-norm precision $\varepsilon$ requires at least $1/7\cdot\log_2(1/\varepsilon) - 4/3$ $T$-states on average. This is the first lower bound that applies to synthesis protocols using fall-back, mixing techniques, and where the number of ancillas used can depend on $\varepsilon$. Up to multiplicative factors, we optimally lower bound the number of $T$ or $CCZ$ states needed to implement the ubiquitous modular adder and multiply-controlled-$Z$ operations. When the probability of Pauli measurement outcomes is 1/2, some of our bounds become tight to within a small additive constant.
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MGT protocols encode the input into a measurement-heralded stabilizer code then apply a logical non-Clifford gate; useful resource states are Clifford-equivalent to diagonal states, and feedforward can often be Pauli.
Unitary designs emerge from the temporal ensemble of two chaotic Hamiltonian evolutions separated by a random Pauli operation, based on the universal Pauli spectrum.
Magic state cultivation prepares high-fidelity T states with an order of magnitude fewer qubit-rounds than prior distillation methods by gradually growing them within a surface code under depolarizing noise.
Logical quantum kernels outperform physical ones when solving differential equations on a neutral-atom processor, with gains traced to noise error detection in the logical encoding.
citing papers explorer
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Asymptotic magic state distillation with almost linear rate
A new family of magic state distillation protocols based on logical Clifford error checking achieves near-linear asymptotic rate despite overhead exponent exceeding one, showing the quantities are not tightly coupled in the sublinear regime.
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Magic Gate Teleportation: Structure, Useful Resource States, and Simpler Feedforward
MGT protocols encode the input into a measurement-heralded stabilizer code then apply a logical non-Clifford gate; useful resource states are Clifford-equivalent to diagonal states, and feedforward can often be Pauli.
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Unitary Designs from Two Chaotic Hamiltonians and a Random Pauli Operation
Unitary designs emerge from the temporal ensemble of two chaotic Hamiltonian evolutions separated by a random Pauli operation, based on the universal Pauli spectrum.
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Magic state cultivation: growing T states as cheap as CNOT gates
Magic state cultivation prepares high-fidelity T states with an order of magnitude fewer qubit-rounds than prior distillation methods by gradually growing them within a surface code under depolarizing noise.
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Benchmarking a machine-learning differential equations solver on a neutral-atom logical processor
Logical quantum kernels outperform physical ones when solving differential equations on a neutral-atom processor, with gains traced to noise error detection in the logical encoding.