Dax Enshan Koh

The Quantum Approximate Optimisation Algorithm (QAOA) tackles combinatorial optimisation problems by encoding their solutions into the ground state of an Ising Hamiltonian prepared by a p -level parameterised circuit, with the angles tuned classically. Parameter optimisation is widely regarded as a central bottleneck, even for the shallowest circuits. Focusing on QAOA at p = 1 (QAOA 1 ), we show that tuning the two angles ( γ , β ) for weighted Ising models is not a black-box search but a structured signal-processing problem. We prove that the QAOA 1 expectation value is a partial Fourier series in γ whose frequencies are determined explicitly by the problem's couplings and fields, giving instance-wise bandwidth bounds and, via the Nyquist–Shannon theorem, the sampling resolution needed to avoid the aliasing that causes coarse-grid searches to return spurious optima. We then eliminate the mixer angle analytically, computing β ∗ ( γ ) in closed form to reduce the search to one dimension, and apply a subdivision algorithm that locates the globally optimal γ in polynomial time with a certificate of optimality when the weights are commensurable and bounded. For regular weighted graphs, we further prove the conventional wisdom that the globally optimal γ ∗ ∈ R + concentrates near zero and coincides with the first local optimum, giving a rigorous account of the empirical success of small-angle initialisation and allowing gradient descent to replace exhaustive line searches. Validated within Recursive QAOA (RQAOA) on weighted instances of 128 and 256 qubits, our method consistently outperforms both coarsely optimised RQAOA and semidefinite programming.

Decoded quantum interferometry (DQI) is a recently proposed quantum optimization algorithm that exploits sparsity in the Fourier spectrum of objective functions, with the potential for exponential speedups over classical algorithms on suitably structured problems. While highly promising in idealized settings, its resilience to noise has until now been largely unexplored. To address this, we conduct a rigorous analysis of DQI under noise, focusing on local depolarizing noise. For the maximum linear satisfiability problem, we prove that, in the presence of noise, performance is governed by a noise-weighted sparsity parameter of the instance matrix, with solution quality decaying exponentially as sparsity decreases. We demonstrate this decay through numerical simulations on two special cases: the optimal polynomial intersection problem and the maximum XOR satisfiability problem. The Fourier-analytic methods we develop can be readily adapted to other classes of random Pauli noise, making our framework applicable to a broad range of noisy quantum settings and offering guidance on preserving DQI’s potential quantum advantage under realistic noise.

Dissipation can drive striking dynamics in lossy quantum systems. Instead of a uniform decay, the system’s energy density can transiently surge toward its boundaries, a phenomenon known as the non-Hermitian edge burst. Thus far, this effect has only been observed in single-particle contexts. Extending it to an interacting, many-body setting is challenging as tunable interactions are difficult to realize in conventional platforms, and simulating non-Hermitian evolution is demanding on quantum processors. Here, we overcome these challenges by developing a digital quantum simulation approach that, for the first time in non-Hermitian simulation, composes a linear combination of unitaries scheme and product formulae. Our framework is efficient in classical preprocessing costs and circuit sizes, thus enabling the study of long-time behavior on large systems. By realizing an interacting quantum ladder model on a superconducting quantum processor, we uncover novel interaction-driven phenomena of spatially extended edge patterns and cluster bursts emerging deep within the bulk, which are unexpected departures from single-particle behavior. Our experiments reveal clear edge-burst signatures in systems of up to 64 unit cells and directly probe the closing of the dissipative gap, a necessary condition for the edge burst. Beyond establishing these generalized forms of edge burst phenomena, our study opens a pathway for digital quantum processors to be harnessed as a versatile platform for non-Hermitian physics.

Current quantum computing platforms suffer from readout errors, where faulty measurement outcomes are reported by the device. These errors are particularly harmful in quantum programs that rely on branch statements, where operations in later parts of the program are dynamically determined by mid-circuit measurements. We propose a general protocol for mitigating mid-circuit measurement errors. Our solution works for any number of mid-circuit measurement and feedforward layers without increasing circuit depth or two-qubit gate counts, is efficient under structural assumptions on error channels, and is suitable for immediate application on noisy intermediate-scale quantum devices. We experimentally demonstrate up to a ∼ 60 % reduction in error on superconducting quantum processors across several practically relevant feedforward circuits, including dynamic qubit resets, shallow-depth Greenberger–Horne–Zeilinger state preparation, and multistage quantum teleportation. This work paves the way for more error-resilient adaptive quantum circuits, crucial for current and future quantum computing applications.

In adversarial settings, where attackers can deliberately and strategically corrupt quantum data, standard quantum error correction reaches its limits. It can only correct up to half the code distance and must output a unique answer. Quantum list decoding offers a promising alternative. By allowing the decoder to output a short list of possible errors, it becomes possible to tolerate far more errors, even under worst-case noise. But two fundamental questions remain: which quantum codes support list decoding, and can we design decoding schemes that are secure against efficient, computationally bounded adversaries? In this work, we answer both. To identify which codes are list-decodable, we provide a generalized version of the Knill-Laflamme conditions. Then, using tools from quantum cryptography, we build an unambiguous list decoding protocol based on pseudorandom unitaries. Our scheme is secure against any quantum polynomial-time adversary, even across multiple decoding attempts, in contrast to previous schemes. Our approach connects coding theory with complexity-based quantum cryptography, paving the way for secure quantum information processing in adversarial settings.

Decoded Quantum Interferometry (DQI) is a recently proposed quantum optimization algorithm that exploits sparsity in the Fourier spectrum of objective functions, with the potential for exponential speedups over classical algorithms on suitably structured problems. While highly promising in idealized settings, its resilience to noise has until now been largely unexplored. To address this, we conduct a rigorous analysis of DQI under noise, focusing on local depolarizing noise. For the maximum linear satisfiability problem, we prove that, in the presence of noise, performance is governed by a noise-weighted sparsity parameter of the instance matrix, with solution quality decaying exponentially as sparsity decreases. We demonstrate this decay through numerical simulations on two special cases: the Optimal Polynomial Intersection problem and the Maximum XOR Satisfiability problem. The Fourier-analytic methods we develop can be readily adapted to other classes of random Pauli noise, making our framework applicable to a broad range of noisy quantum settings and offering guidance on preserving DQI's potential quantum advantage under realistic noise.