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Securing Elliptic Curve Cryptocurrencies against Quantum Vulnerabilities: Resource Estimates and Mitigations
Ryan Babbush, Adam Zalcman, Craig Gidney +6
This whitepaper seeks to elucidate implications that the capabilities of developing quantum architectures have on blockchain vulnerabilities and mitigation strategies. First, we pr…
A log-depth in-place quantum Fourier transform that rarely needs ancillas
Gregory D. Kahanamoku-Meyer, John Blue, Thiago Bergamaschi +2
When designing quantum circuits for a given unitary, it can be much cheaper to achieve a good approximation on most inputs than on all inputs. In this work we formalize this idea,…
A Constant Rate Quantum Computer on a Line
Craig Gidney, Thiago Bergamaschi
We prove by construction that the Bravyi-Poulin-Terhal bound on the spatial density of stabilizer codes does not generalize to stabilizer circuits. To do so, we construct a fault t…
When can classical neural networks represent quantum states?
Tai-Hsuan Yang, Mehdi Soleimanifar, Thiago Bergamaschi +1
A naive classical representation of an n-qubit state requires specifying exponentially many amplitudes in the computational basis. Past works have demonstrated that classical neura…