We give a deterministic classical algorithm that estimates $|\langle x|U|0^n\rangle|^2$ to additive error $\varepsilon$ in $\mathrm{poly}(n, 1/\varepsilon)$ time, where $U$ is a constant-depth quantum circuit comprised of gates with bounded fan-in and arbitrary connectivity, and $x$ is an arbitrary $n$-bit output strin...
Matthew Coudron, M. Gullans, Jon Nelson et al.· 1 citation
Fault-tolerant quantum simulation requires compiling symmetry-preserving time evolutions into discrete gate sets. Standard Clifford+T synthesis can break continuous symmetries even when the target evolution preserves them, causing compiled simulations to lose essential features of the original system. We develop a faul...
M. Mudassar, Zhi-Yuan Wei, A. Schuckert et al.· 0 citations
Non-Clifford gates are essential for avoiding classical simulability under the Gottesman-Knill theorem. An error-corrected circuit with non-Clifford gates will therefore be an important element for realizing useful fault-tolerant quantum algorithms. However, accurately understanding the fault-tolerant performance of su...
Xiao Xiao, Dominik Hangleiter, J. P. Ataides 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
Publicly accessible fault-tolerant quantum computers must preserve scientific utility while limiting cryptanalytic power. We propose the restricted model of computation, 1/2BQP_1: a quantum server provides random computational-basis inputs, revealed only after execution, and one designated output bit. This interface pe...
S. A. Yadavalli, Joel Rajakumar, A. Schuckert et al.· 1 citation
Developing classical simulation algorithms for noisy quantum circuits is essential to delineating the limits of quantum advantage. Existing classical sampling approaches for general circuits require circuit depths to grow logarithmically with system size, so that noise drives the global output state close to a trivial...
Jon Nelson, Joel Rajakumar, Chao Yin et al.· 1 citation
Topological quantum memories need decoders that are both reliable and scalable, but these goals compete: globally informed decoders are accurate near threshold yet expensive, while strictly local rules are fast but can miss long-range structure. Motivated by recent recoverability and mixed-state viewpoints, we make thi...
Hossein Dehghani, Sarang Gopalakrishnan, M. Gullans· 0 citations
A central question in the theory of quantum advantage is whether there are quantum advantage protocols with similar resource requirements as random circuit sampling that are also verifiable just from the classical outputs of the quantum computation. Here, we develop the idea of simulation secrets for verifiable advanta...
Markus Bläser, M. Gullans, Dominik Hangleiter et al.· 1 citation
Quantum error mitigation relies on accurate noise characterization, but mismatches between the actual and characterized noise can be amplified and drive a sharp threshold between successful and failed mitigation. In random circuits, this threshold maps onto a random-field Ising transition, but previous exact numerics w...
Jia-Yao Zhao, Zhi-Yuan Wei, M. Gullans· 0 citations
This work considers a qubit noise model where the probability of phase-flip errors is exponentially smaller (in qubit number) compared to the probability of bit-flip errors that occur with probability p, and demonstrates that Heisenberg scaling can be attained for times up to T\propto 1/p^{(N+1)/2} for a N-qubit repeti...
Lorcán O. Conlon, Yu-Xin Wang, E. Abbasgholinejad et al.· 1 citation
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