arXiv subjects

Changhao Yi

Publications and source records attributed to Changhao Yi.

15 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.

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arXiv2026

Certifying entanglement dimensionality by $k$-reduction moments

In this paper, we combine the k-reduction map, the moment method, and the classical shadow method into a practical protocol for certifying the entanglement dimensionality. Our approach is based on the observation that a state with entanglement dimensionality at most k must stay positive under the action of the k-reduction map. The core of our protocol utilizes the moment method to determine whether the k-reduced operator, i.e., the operator obtained after applying the k-reduction map on a quantum state, contains negative eigenvalues or not. Notably, we propose a systematic method for constructing reduction moment criteria, which apply to a much wider range of states than fidelity-based methods. The performance of our approach gets better and better with the moment order employed, which is corroborated by extensive numerical simulation. To apply our approach, it suffices to implement a unitary 3-design instead of a 4-design, which is more feasible in practice than the correlation matrix method. In the course of study, we show that the k-reduction negativity, the absolute sum of the negative eigenvalues of the k-reduced operator, is monotonic under local operations and classical communication for pure states.

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arXiv2026

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.

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arXiv2026

Certifying entanglement dimensionality by random Pauli sampling

We introduce a Pauli-measurement-based algorithm to certify the Schmidt number of $n$-qubit pure states. Our protocol achieves an average-case sample complexity of $\caO(\mathrm{poly}(n)χ^2)$, a substantial improvement over the $\caO(2^n χ)$ worst-case bound. By utilizing local pseudorandom unitaries, we ensure the worst case can be transformed into the average-case with high probability. This work establishes a scalable approach to high-dimensional entanglement certification and introduces a proof framework for random Pauli sampling.

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arXiv2025

Nearly query-optimal classical shadow estimation of unitary channels

Classical shadow estimation (CSE) is a powerful tool for learning the properties of quantum states and quantum processes. Here we consider the CSE task for quantum unitary channels. By querying an unknown unitary channel $\mathcal{U}$ multiple times in quantum experiments, the goal is to learn a classical description from which one can accurately predict many different linear properties of the channel, i.e., the expectation values of arbitrary observables measured on the output of $\mathcal{U}$ upon arbitrary input states. Based on collective measurements on multiple systems, we propose a query efficient protocol for this task, whose query complexity has a quadratic advantage over the previous best approach for this problem, and almost saturates the information-theoretic lower bound. To further enhance practicality, we also present a variant protocol using only single-copy measurements, which still offers much better query performance than previous protocols that do not use quantum memory, and can serve as a key subroutine for learning an arbitrary unknown Hamiltonian from dynamics. In addition to linear properties of unitary channels, our protocol can also be applied to simultaneously predict many non-linear properties, such as out-of-time-ordered correlators.

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arXiv2025

Optimal estimation of three parallel spins with genuine and restricted collective measurements

Collective measurements on identical and independent quantum systems can offer advantages in information extraction compared with individual measurements. However, little is known about the distinction between restricted collective measurements and genuine collective measurements in the multipartite setting. In this work we establish a rigorous performance gap based on a simple and old estimation problem, the estimation of a random spin state given three parallel spins. Notably, we derive an analytical formula for the maximum estimation fidelity of biseparable measurements and clarify its fidelity gap from genuine collective measurements. Moreover, we clarify the structure of optimal biseparable measurements. It turns out that the maximum estimation fidelity can be achieved by two- and one-copy measurements assisted by one-way communication in one direction, but not the other way. Our work reveals a rich landscape of multipartite nonclassicality in quantum measurements instead of quantum states and is expected to trigger further studies.

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arXiv2025

Experimental Realization of Genuine Three-copy Collective Measurements for Optimal Information Extraction

Nonclassical phenomena tied to entangled states are the focus of foundational studies and powerful resources in many applications. By contrast, the counterparts in quantum measurements are still poorly understood. Notably, genuine multipartite nonclassicality is barely discussed, let alone its experimental realization. Here we experimentally demonstrate the power of genuine tripartite nonclassicality in quantum measurements based on a simple estimation problem. To this end we realize an optimal genuine three-copy collective measurement via a nine-step two-dimensional photonic quantum walk with 30 elaborately designed coin operators. Then we realize an optimal estimation protocol and achieve an unprecedented high estimation fidelity, which can beat all strategies based on restricted collective measurements by more than 11 standard deviations. These results clearly demonstrate that genuine collective measurements can extract more information than local measurements and restricted collective measurements. Our work opens the door for exploring genuine multipartite nonclassical measurements and their power in quantum information processing.

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arXiv2025

Qudit Shadow Estimation Based on the Clifford Group and the Power of a Single Magic Gate

Shadow estimation is a sample-efficient protocol for learning the properties of a quantum system using randomized measurements, but the current understanding of qudit shadow estimation is quite limited compared with the qubit setting. Here we clarify the sample complexity of qudit shadow estimation based on the Clifford group, where the local dimension $d$ is an odd prime. Notably, we show that the overhead of qudit shadow estimation over the qubit counterpart is only $\mathcal{O}(d)$, independent of the qudit number $n$, although the set of stabilizer states may deviate exponentially from a 3-design with respect to the third moment operator. Furthermore, by adding one layer of magic gates, we propose a simple circuit that can significantly boost the efficiency. Actually, a single magic gate can already eliminate the $\mathcal{O}(d)$ overhead in qudit shadow estimation and bridge the gap from the qubit setting.

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arXiv2024

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 $\mathcal{O}(ε^{-1}\text{poly}\log(ε^{-1}))$, where $ε$ is the accuracy. Moreover, the maximal runtime satisfies $T_{\max}ε\ll π$, 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.

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arXiv2024

Faster Randomized Dynamical Decoupling

We present a randomized dynamical decoupling (DD) protocol that can improve the performance of any given deterministic DD, by using no more than two additional pulses. Our construction is implemented by probabilistically applying sequences of pulses, which, when combined, effectively eliminate the error terms that scale linearly with the system-environment coupling strength. As a result, we show that a randomized protocol using a few pulses can outperform deterministic DD protocols that require considerably more pulses. Furthermore, we prove that the randomized protocol provides an improvement compared to deterministic DD sequences that aim to reduce the error in the system's Hilbert space, such as Uhrig DD, which had been previously regarded to be optimal. To rigorously evaluate the performance, we introduce new analytical methods suitable for analyzing higher-order DD protocols that might be of independent interest. We also present numerical simulations confirming the significant advantage of using randomized protocols compared to widely used deterministic protocols.

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arXiv2024

Third moments of qudit Clifford orbits and 3-designs based on magic orbits

When the local dimension $d$ is an odd prime, the qudit Clifford group is only a 2-design, but not a 3-design, unlike the qubit counterpart. This distinction and its extension to Clifford orbits have profound implications for many applications in quantum information processing. In this work we systematically delve into general qudit Clifford orbits with a focus on the third moments and potential applications in shadow estimation. First, we introduce the shadow norm to quantify the deviations of Clifford orbits from 3-designs and clarify its properties. Then, we show that the third normalized frame potential and shadow norm are both $\mathcal{O}(d)$ for any Clifford orbit, including the orbit of stabilizer states, although the operator norm of the third normalized moment operator may increase exponentially with the number $n$ of qudits when $d\neq 2\mod 3$. Moreover, we prove that the shadow norm of any magic orbit is upper bounded by the constant $15/2$, so a single magic gate can already eliminate the $\mathcal{O}(d)$ overhead in qudit shadow estimation and bridge the gap between qudit systems and qubit systems. Furthermore, we propose simple recipes for constructing approximate and exact 3-designs (with respect to three figures of merit simultaneously) from one or a few Clifford orbits. Notably, accurate approximate 3-designs can be constructed from only two Clifford orbits. For an infinite family of local dimensions, exact 3-designs can be constructed from two or four Clifford orbits. In the course of study, we clarify the key properties of the commutant of the third Clifford tensor power and the underlying mathematical structures.

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arXiv2022

Success of digital adiabatic simulation with large Trotter step

The simulation of adiabatic evolution has deep connections with Adiabatic Quantum Computation, the Quantum Approximate Optimization Algorithm and adiabatic state preparation. Here we address the error analysis problem in quantum simulation of adiabatic process using Trotter formulas. We show that with additional conditions, the circuit depth can be linear in simulation time $T$. The improvement comes from the observation that the fidelity error here can't be estimated by the norm distance between evolution operators. This phenomenon is termed as the robustness of discretization in digital adiabatic simulation. It can be explained in three steps, from analytical and numerical evidence: (1). The fidelity error should be estimated by applying adiabatic theorem on the effective Hamiltonian instead. (2). Because of the specialty of Riemann-Lebesgue lemma, most adiabatic process is naturally robust against discretization. (3). As the Trotter step gets larger, the spectral gap of effective Hamiltonian tends to close, which results in the failure of digital adiabatic simulation.

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arXiv2021

Spectral Analysis of Product Formulas for Quantum Simulation

We consider Hamiltonian simulation using the first order Lie-Trotter product formula under the assumption that the initial state has a high overlap with an energy eigenstate, or a collection of eigenstates in a narrow energy band. This assumption is motivated by quantum phase estimation (QPE) and digital adiabatic simulation (DAS). Treating the effective Hamiltonian that generates the Trotterized time evolution using rigorous perturbative methods, we show that the Trotter step size needed to estimate an energy eigenvalue within precision $ε$ using QPE can be improved in scaling from $ε$ to $ε^{1/2}$ for a large class of systems (including any Hamiltonian which can be decomposed as a sum of local terms or commuting layers that each have real-valued matrix elements). For DAS we improve the asymptotic scaling of the Trotter error with the total number of gates $M$ from $\mathcal{O}(M^{-1})$ to $\mathcal{O}(M^{-2})$, and for any fixed circuit depth we calculate an approximately optimal step size that balances the error contributions from Trotterization and the adiabatic approximation. These results partially generalize to diabatic processes, which remain in a narrow energy band separated from the rest of the spectrum by a gap, thereby contributing to the explanation of the observed similarities between the quantum approximate optimization algorithm and diabatic quantum annealing at small system sizes. Our analysis depends on the perturbation of eigenvectors as well as eigenvalues, and on quantifying the error using state fidelity (instead of the matrix norm of the difference of unitaries which is sensitive to an overall global phase).

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arXiv2019

Dynamic fast flavor oscillation waves in dense neutrino gases

The flavor transformation in a dense neutrino gas can have a significant impact on the physical and chemical evolution of its surroundings. In this work we demonstrate that a dynamic, fast flavor oscillation wave can develop spontaneously in a one-dimensional (1D) neutrino gas when the angular distributions of the electron neutrino and antineutrino cross each other. Unlike the 2D stationary models which are plagued with small-scale flavor structures, the fast flavor oscillation waves remain coherent in the dynamic 1D model in both the position and momentum spaces of the neutrino. The electron lepton number is redistributed and transported in space as the flavor oscillation wave propagates, although the total lepton number remains constant. This result may have interesting implications in the neutrino emission in and the evolution of the compact objects such as core-collapse supernovae.

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arXiv2019

The dispersion relation of the fast neutrino oscillation wave

A dense neutrino medium can support flavor oscillation waves which are coherent among different momentum modes of the neutrinos. The dispersion relation (DR) branches of such a wave with complex frequencies and/or wave numbers can lead to the exponential growth of the wave amplitude which in turn will engender a collective flavor transformation in the neutrino medium. In this work we propose that the complex DR branches of the neutrino oscillation wave should be bound by the critical points of the DR. We demonstrate how this theory can be applied to the neutrino medium with an (approximate) axial symmetry about the propagation direction of the neutrino oscillation wave. We also show how the flavor instabilities in this medium can be identified by tracing the critical points of the DR as the electron lepton number distribution of the neutrino medium is changed continuously.

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