arXiv subjects

Cunlu Zhou

Publications and source records attributed to Cunlu Zhou.

9 recordsLinked to original sources

arXiv2026

Modular-Annihilator Parent Hamiltonians for Purified Gibbs States: Spectral Design and Controlled Approximation

Purified Gibbs states provide a bridge between finite-temperature physics, dissipative dynamics, and ground-state methods. In this work, we study the exact finite sum-of-squares (SoS) construction of their parent Hamiltonians and the associated Lindbladian based on modular annihilators. Given a finite set of Hermitian generators, the corresponding modular annihilators yield a frustration-free SoS representation without continuous time integrals or an explicit decomposition into Bohr-frequency sectors. The purified Gibbs state remains a common zero mode while the freedom to choose and combine the generators can be used to optimize the spectral properties of the parent Hamiltonian. For free-fermion Hamiltonians, modular transformations act linearly on Majorana operators, leading to an analytically solvable family of parent Hamiltonians parameterized by a real symmetric coefficient matrix $S$. For the scalar-functional subclass $S=f(h)$, we show that, at fixed operator norm, the choice $S_{\mathrm{opt}}\propto 1/\sqrt{\cosh(2\beta h)}$ has mixing time upper bound $2\log(2N/\epsilon)$ for any $\beta$, which exhibits rapid mixing and is irrelevant to the inverse temperature $\beta$. For interacting systems, where the modularly dressed generators are not available in closed form, we introduce a Krylov--Lanczos approximation scheme and bound the resulting ground-state error in terms of the modular-approximation error and the parent-Hamiltonian gap. Numerical results illustrate the free-fermion spectral advantage and show how the accuracy of the interacting construction depends on temperature, interaction strength, and Krylov dimension.

quant-ph↗

arXiv2026

Generative Learning for Quantum Measurement Design

Extracting quantum information from a quantum state is a fundamental task of quantum computation, often requiring the estimation of many non-commuting observables under a finite measurement budget. For both near-term and early fault-tolerant settings, the measurement protocol must balance statistical efficiency against implementation resources such as circuit depth, connectivity, and entangling-gate count. Many existing strategies focus on two extremes: hardware-friendly product measurements with high sampling cost, and fully commuting measurements with deep circuits. Here we recast resource-constrained measurement design as a generative learning problem. We introduce FlowMeas, which uses a generative flow network to directly sample finite ensembles of shallow Clifford measurement circuits subject to a prescribed shot budget and hardware constraints. At zero entangling depth, FlowMeas learns qubit-wise commuting measurement schedules and already matches or improves leading product-measurement methods on nearly all molecular benchmarks. Allowing one or two entangling gate layers yields further reductions in energy estimation error of up to $27\%$ relative to the strongest state-independent product-measurement baseline. The learned policy can also be reused across related Hamiltonians, substantially accelerating retraining along a molecular potential-energy surface. We further obtain results for molecular Hamiltonians with up to 20 qubits and apply the framework to a compactly encoded 54-qubit interacting fermionic model, extending the demonstrated scale beyond prior molecular benchmarks. These results establish generative learning as a flexible and unified framework for quantum measurement design under practical resource constraints.

quant-ph↗

arXiv2025

A Symmetry-Enabled Direct Quantum Protocol for Many-Body Green's Functions

We present a symmetry-enabled direct quantum protocol for computing many-body Green's functions, a central tool for studying strongly correlated quantum systems. Our protocol relies only on native time evolution and straightforward measurements available on current hardware platforms. By exploiting parity symmetry -- satisfied by a broad class of Hamiltonians in condensed matter physics and quantum chemistry, including the Fermi--Hubbard and Heisenberg models -- we introduce a tailored quench spectroscopy scheme that recovers both the real and imaginary parts of two-point time correlators, from which Green's functions can be reconstructed via efficient classical signal processing. We further develop a tailored symmetric quantum Gibbs sampler that prepares parity-resolved (symmetric and antisymmetric) thermal states, enabling finite-temperature extensions within the same framework. Finally, we show that the same symmetry-based measurement primitive extends naturally to out-of-time-ordered correlators (OTOCs). Our results provide a practical route to estimating symmetry-resolved dynamical correlators on near-term and early fault-tolerant quantum hardware.

quant-ph↗

arXiv2023

An SU(2)-symmetric Semidefinite Programming Hierarchy for Quantum Max Cut

Understanding and approximating extremal energy states of local Hamiltonians is a central problem in quantum physics and complexity theory. Recent work has focused on developing approximation algorithms for local Hamiltonians, and in particular the ``Quantum Max Cut'' (QMax-Cut) problem, which is closely related to the antiferromagnetic Heisenberg model. In this work, we introduce a family of semidefinite programming (SDP) relaxations based on the Navascues-Pironio-Acin (NPA) hierarchy which is tailored for QMaxCut by taking into account its SU(2) symmetry. We show that the hierarchy converges to the optimal QMaxCut value at a finite level, which is based on a new characterization of the algebra of SWAP operators. We give several analytic proofs and computational results showing exactness/inexactness of our hierarchy at the lowest level on several important families of graphs. We also discuss relationships between SDP approaches for QMaxCut and frustration-freeness in condensed matter physics and numerically demonstrate that the SDP-solvability practically becomes an efficiently-computable generalization of frustration-freeness. Furthermore, by numerical demonstration we show the potential of SDP algorithms to perform as an approximate method to compute physical quantities and capture physical features of some Heisenberg-type statistical mechanics models even away from the frustration-free regions.

quant-ph↗

arXiv2023

Quantum Phase Estimation by Compressed Sensing

As a signal recovery algorithm, compressed sensing is particularly useful when the data has low-complexity and samples are rare, which matches perfectly with the task of quantum phase estimation (QPE). In this work we present a new Heisenberg-limited QPE algorithm for early quantum computers based on compressed sensing. More specifically, given many copies of a proper initial state and queries to some unitary operators, our algorithm is able to recover the frequency with a total runtime $\mathcal{O}(\epsilon^{-1}\text{poly}\log(\epsilon^{-1}))$, where $\epsilon$ is the accuracy. Moreover, the maximal runtime satisfies $T_{\max}\epsilon \ll \pi$, which is comparable to the state of art algorithms, and our algorithm is also robust against certain amount of noise from sampling. We also consider the more general quantum eigenvalue estimation problem (QEEP) and show numerically that the off-grid compressed sensing can be a strong candidate for solving the QEEP.

quant-ph↗

arXiv2021

Measurement-induced entanglement phase transitions in variational quantum circuits

Variational quantum algorithms (VQAs), which classically optimize a parametrized quantum circuit to solve a computational task, promise to advance our understanding of quantum many-body systems and improve machine learning algorithms using near-term quantum computers. Prominent challenges associated with this family of quantum-classical hybrid algorithms are the control of quantum entanglement and quantum gradients linked to their classical optimization. Known as the barren plateau phenomenon, these quantum gradients may rapidly vanish in the presence of volume-law entanglement growth, which poses a serious obstacle to the practical utility of VQAs. Inspired by recent studies of measurement-induced entanglement transition in random circuits, we investigate the entanglement transition in variational quantum circuits endowed with intermediate projective measurements. Considering the Hamiltonian Variational Ansatz (HVA) for the XXZ model and the Hardware Efficient Ansatz (HEA), we observe a measurement-induced entanglement transition from volume-law to area-law with increasing measurement rate. Moreover, we provide evidence that the transition belongs to the same universality class of random unitary circuits. Importantly, the transition coincides with a "landscape transition" from severe to mild/no barren plateaus in the classical optimization. Our work paves an avenue for greatly improving the trainability of quantum circuits by incorporating intermediate measurement protocols in currently available quantum hardware.

quant-ph↗

arXiv2020

Exploring entanglement and optimization within the Hamiltonian Variational Ansatz

Quantum variational algorithms are one of the most promising applications of near-term quantum computers; however, recent studies have demonstrated that unless the variational quantum circuits are configured in a problem-specific manner, optimization of such circuits will most likely fail. In this paper, we focus on a special family of quantum circuits called the Hamiltonian Variational Ansatz (HVA), which takes inspiration from the quantum approximation optimization algorithm and adiabatic quantum computation. Through the study of its entanglement spectrum and energy gradient statistics, we find that HVA exhibits favorable structural properties such as mild or entirely absent barren plateaus and a restricted state space that eases their optimization in comparison to the well-studied "hardware-efficient ansatz." We also numerically observe that the optimization landscape of HVA becomes almost trap free when the ansatz is over-parameterized. We observe a size-dependent "computational phase transition" as the number of layers in the HVA circuit is increased where the optimization crosses over from a hard to an easy region in terms of the quality of the approximations and speed of convergence to a good solution. In contrast with the analogous transitions observed in the learning of random unitaries which occur at a number of layers that grows exponentially with the number of qubits, our Variational Quantum Eigensolver experiments suggest that the threshold to achieve the over-parameterization phenomenon scales at most polynomially in the number of qubits for the transverse field Ising and XXZ models. Lastly, as a demonstration of its entangling power and effectiveness, we show that HVA can find accurate approximations to the ground states of a modified Haldane-Shastry Hamiltonian on a ring, which has long-range interactions and has a power-law entanglement scaling.

quant-ph↗

arXiv2019

Long-Step Path-Following Algorithm for Quantum Information Theory: Some Numerical Aspects and Applications

We consider some important computational aspects of the long-step path-following algorithm developed in our previous work and show that a broad class of complicated optimization problems arising in quantum information theory can be solved using this approach. In particular, we consider one difficult and important optimization problem in quantum key distribution and show that our method can solve problems of this type much faster in comparison with (very few) available options.

math.OC↗

arXiv2018

Free Pseudodistance Growth Rates for Spatially Coupled LDPC Codes over the BEC

The minimum pseudoweight is an important parameter related to the decoding performance of LDPC codes with iterative message-passing decoding. In this paper, we consider ensembles of periodically time-varying spatially coupled LDPC (SC-LDPC) codes and the pseudocodewords arising from their finite graph covers of a fixed degree. We show that for certain $(J,K)$-regular SC-LDPC code ensembles and a fixed cover degree, the typical minimum pseudoweight of the unterminated (and associated tail-biting/terminated) SC-LDPC code ensembles grows linearly with the constraint (block) length as the constraint (block) length tends to infinity. We prove that one can bound the the free pseudodistance growth rate over a BEC from below (respectively, above) using the associated tail-biting (terminated) SC-LDPC code ensemble and show empirically that these bounds coincide for a sufficiently large period, which gives the exact free pseudodistance growth rate for the SC-LDPC ensemble considered.

cs.IT↗