Quantum computers are expected to break modern public key cryptography owing to Shor's
algorithm. As a result, these cryptosystems need to be replaced by quantum-resistant …

Quantum random sampling is the leading proposal for demonstrating a computational
advantage of quantum computers over classical computers. Recently the first large-scale …

Suppressing errors is the central challenge for useful quantum computing, requiring
quantum error correction (QEC),,,–for large-scale processing. However, the overhead in the …

Practical quantum computing will require error rates well below those achievable with
physical qubits. Quantum error correction, offers a path to algorithmically relevant error rates …

Quantum error correction protects fragile quantum information by encoding it into a larger
quantum system,. These extra degrees of freedom enable the detection and correction of …

Recently, several quantum machine learning algorithms have been proposed that may offer
quantum speed-ups over their classical counterparts. Most of these algorithms are either …

Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and
good code distance scaling, potentially enabling low-overhead fault-tolerant quantum …

Performing large calculations with a quantum computer will likely require a fault-tolerant
architecture based on quantum error-correcting codes. The challenge is to design practical …

Realizing the potential of quantum computing will require achieving sufficiently low logical
error rates. Many applications call for error rates in the $10^{-15} $ regime, but state-of-the …

We describe quantum circuits with only O~(N) Toffoli complexity that block encode the
spectra of quantum chemistry Hamiltonians in a basis of N arbitrary (eg, molecular) orbitals …