Yuri Alexeev

While quantum computers have the potential to perform a wide range of practically important tasks beyond the capabilities of classical computers, realizing this potential remains a challenge. One such task is to use an untrusted remote device to generate random bits that can be certified to contain a certain amount of entropy. Certified randomness has many applications but is fundamentally impossible to achieve solely by classical computation. In this work, we demonstrate the generation of certifiably random bits using the 56-qubit Quantinuum H2-1 trapped-ion quantum computer accessed over the internet. Our protocol leverages the classical hardness of recent random circuit sampling demonstrations: a client generates quantum "challenge" circuits using a small randomness seed, sends them to an untrusted quantum server to execute, and verifies the server's results. We analyze the security of our protocol against a restricted class of realistic near-term adversaries. Using classical verification with measured combined sustained performance of $1.1\times10^{18}$ floating-point operations per second across multiple supercomputers, we certify $71,313$ bits of entropy under this restricted adversary and additional assumptions. Our results demonstrate a step towards the practical applicability of today's quantum computers.

The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here, we perform an extensive numerical investigation of QAOA on the low autocorrelation binary sequences (LABS) problem, which is classically intractable even for moderately sized instances. We perform noiseless simulations with up to 40 qubits and observe that the runtime of QAOA with fixed parameters scales better than branch-and-bound solvers, which are the state-of-the-art exact solvers for LABS. The combination of QAOA with quantum minimum finding gives the best empirical scaling of any algorithm for the LABS problem. We demonstrate experimental progress in executing QAOA for the LABS problem using an algorithm-specific error detection scheme on Quantinuum trapped-ion processors. Our results provide evidence for the utility of QAOA as an algorithmic component that enables quantum speedups.

Trapped-ion qubits are a leading technology for practical quantum computing. In this work, we present an architectural analysis of a linear-tape architecture for trapped ions. In order to realize our study, we develop and evaluate mapping and scheduling algorithms for this architecture. In particular, we introduce TILT, a linear "Turing-machine-like" architecture with a multilaser control "head", where a linear chain of ions moves back and forth under the laser head. We find that TILT can substantially reduce communication as compared with comparable-sized Quantum Charge Coupled Device (QCCD) architectures. We also develop two important scheduling heuristics for TILT. The first heuristic reduces the number of swap operations by matching data traveling in opposite directions into an "opposing swap", and also avoids the maximum swap distance across the width of the head, as maximum swap distances make scheduling multiple swaps in one head position difficult. The second heuristic minimizes ion chain motion by scheduling the tape to the position with the maximal executable operations for every movement. We provide application performance results from our simulation, which suggest that TILT can outperform QCCD in a range of NISQ applications in terms of success rate (up to 4.35x and 1.95x on average). We also discuss using TILT as a building block to extend existing scalable trapped-ion quantum computing proposals.