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Kean Chen

Publications and source records attributed to Kean Chen.

At least 19 recordsLinked to original sources
arXiv2026

Near-optimal incoherent tomography of low-rank quantum channels

We study tomography for quantum channels with input dimension $d_1$, output dimension $d_2$, and Kraus rank at most $r$, to within diamond norm error $\varepsilon$, using adaptive experiments that retain no quantum memory between channel queries. - For quantum channels whose non-zero Choi eigenvalues are bounded below by $Ω(d_1/r)$, we establish optimal query upper and lower bounds $Θ(d_1d_2r^2/ε^2)$. The upper bound is achieved by a nonadaptive algorithm that uses the estimator from [Surawy-Stepney et al., Quantum (2022)], together with a new diamond-norm analysis. The lower bound applies to arbitrary adaptive incoherent protocols and follows from a new local family of channels and a uniform one-query Fisher-information bound. - For general channels, we establish an upper bound $O(d_1d_2r^2\log(2d_1)/ε^2)$, nearly matching the above lower bound $Ω(d_1d_2r^2/\varepsilon^2)$. To achieve this, we generalize the above nonadaptive algorithm by adapting the input state over $O(\log(2d_1))$ rounds with the Matrix Multiplicative Weight Update algorithm.

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arXiv2026

Local Test for Unitarily Invariant Properties of Bipartite Quantum States

We study the power of local test for bipartite quantum states. Our central result is that, for properties of bipartite pure states, unitary invariance on one part implies an \textit{optimal} (over all global testers) local tester acting only on the other part. As an application, we demonstrate - Purified samples offer no advantage in property testing of mixed states. - A matching lower bound $Ω(r^2/\varepsilon^2)$ for testing the Schmidt rank of bipartite states with perfect completeness, settling an open question raised in the survey of Montanaro and de Wolf (ToC 2016). - A lower bound $Ω((\sqrt{n}+\sqrt{r})\cdot\sqrt{r}/\varepsilon^2)$ for testing whether an $n$-partite state is a matrix product state of bond dimension $r$ or $\varepsilon$-far, improving the prior lower bounds $Ω(\sqrt{n}/\varepsilon^2)$ by Soleimanifar and Wright (SODA 2022) and $Ω(\sqrt{r})$ by Aaronson et al. (ITCS 2024). - A matching lower bound $Ω(d/\varepsilon^2)$ for testing whether a $d$-dimensional bipartite state is maximally entangled or $\varepsilon$-far, showing that the algorithm of O'Donnell and Wright (STOC 2015) is optimal for this task. - A query lower bound $\widetildeΩ(\sqrt{d/Δ})$ for the $d$-dimensional entanglement entropy problem with gap $Δ$, improving the prior lower bounds $Ω(\sqrt[4]{d})$ by She and Yuen (ITCS 2023) and $\widetildeΩ(1/\sqrtΔ)$ by Wang and Zhang (SICOMP 2025) and Weggemans (Quantum 2025). Moreover, we extend our central result to a robust version where the tested states are subject to noise and are not guaranteed to be pure: in this case, one-way LOCC is sufficient to realize the optimal tester.

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arXiv2026

Simultaneous Estimation of Nonlinear Functionals of a Quantum State

We consider a fundamental task in quantum information theory, estimating the values of $tr(Oρ)$, $tr(Oρ^2)$, $\ldots$, $tr(Oρ^k)$ for an observable $O$ and a quantum state $ρ$. We show that $\widetildeΘ(k)$ samples of $ρ$ are sufficient and necessary to simultaneously estimate all the $k$ values. This means that estimating all the $k$ values is almost as easy as estimating only one of them, $tr(Oρ^k)$. As an application, our approach advances the sample complexity of entanglement spectroscopy and the virtual cooling for quantum many-body systems. Moreover, we extend our approach to estimating general functionals by polynomial approximation.

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arXiv2026

Quantisation of Abstract Data Types

In this paper, we introduce a notion of abstract quantum data type within the framework of universal algebra. This notion provides an algebraic foundation for describing data abstraction in quantum programming. We formally define a quantisation of classical data types and show that their equational specifications can be soundly lifted to the quantum setting. Two standard quantisation methods for classical functions, namely the bit oracle and the phase oracle, arise as special cases of this general construction. We illustrate the framework with applications to quantum arrays and quantum error-correcting codes, showing how they can be understood through the lens of data-type quantisation. We further establish conditions under which quantisation preserves structural relationships and constructions of classical data types, including embeddings, isomorphisms, and products.

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arXiv2026

Nearly Sample-Optimal Estimators for Quantum Rényi and Tsallis Entropies

In this paper, we provide estimators for quantum Rényi and Tsallis entropies with nearly optimal sample complexity. Specifically, for order $α$, dimension $d$, and additive error $\varepsilon$, 1. For $0 < α< 1$, the sample complexity is $O(d^{1+1/α}/\varepsilon^{1/α} + d^{1/α-1}/\varepsilon^{2})$ for Rényi entropy and $O(d^{1+1/α}/\varepsilon^{1/α} + d^{2-2α}/\varepsilon^2)$ for Tsallis entropy. In particular, for $0 < α\leq 1/2$, the sample complexity for both entropies is $O(d^{1+1/α}/\varepsilon^{1/α})$. 2. For non-integer $α> 1$, the sample complexity is $O(d^2/\varepsilon^{1/α} + d^{1-1/α}/\varepsilon^2)$ for Rényi entropy. Our upper bounds improve the quantum Rényi entropy estimators due to Acharya, Issa, Shende, and Wagner (2017) and the quantum Tsallis entropy estimators due to Chen, Liu, and Wang (2026), and match the lower bounds recently established by Wang (2026).

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arXiv2026

Quantum channel tomography: optimal bounds and a Heisenberg-to-classical phase transition

How many black-box queries to a quantum channel are needed to learn its full classical description? This question lies at the heart of quantum channel tomography (also known as quantum process tomography), a fundamental task in the characterization and validation of quantum hardware. Despite extensive prior work, the optimal query complexity for quantum channel tomography is far from fully understood. In this paper, we study tomography of an unknown quantum channel with input dimension $d_1$, output dimension $d_2$, and Kraus rank at most $r$, to within error $\varepsilon$. We identify the dilation rate $τ= r d_2 / d_1$ (which always satisfies $τ\geq 1$ due to the trace preservation of quantum channels) as a key parameter, and establish that the optimal query complexity of channel tomography exhibits distinct scaling laws across three regimes of $τ$. - In the boundary regime ($τ= 1$): we show that the query complexity is $Θ(r d_1 d_2/\varepsilon)$ for Choi trace norm error $\varepsilon$, and is upper bounded by $O(\min\{r d_1^{1.5} d_2/\varepsilon, r d_1 d_2/\varepsilon^2\})$ and lower bounded by $Ω(r d_1 d_2/\varepsilon)$ for diamond norm error $\varepsilon$. - In the away-from-boundary regime ($τ\geq 1+Ω(1)$): we show that the query complexity is $Θ(r d_1 d_2/\varepsilon^2)$ for both Choi trace norm and diamond norm errors $\varepsilon$. Our results uncover a sharp Heisenberg-to-classical phase transition in the query complexity of quantum channel tomography: at $τ=1$, the optimal query complexity exhibits Heisenberg scaling $1/\varepsilon$, whereas for $τ\geq 1+Ω(1)$, it exhibits classical scaling $1/\varepsilon^2$. In addition, we show that in the near-boundary regime ($1< τ< 1+o(1)$), the query complexity exhibits a mixture of Heisenberg and classical scaling behaviors.

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arXiv2026

Quantum Multi-Level Estimation of Functionals of Discrete Distributions

We propose a quantum multi-level estimation framework for a functional $\sum_{i=1}^n f(p_i)$ of a discrete distribution $(p_i)_{i=1}^n$. We partition the values $p_i$ into logarithmically many intervals whose length decays exponentially. For each interval, we perform non-destructive singular value discrimination to isolate the relevant $p_i$, enabling adaptive estimation of the partial sum over this interval. Unlike previous variable-time approaches, our method avoids high control overhead and requires only constant extra ancilla qubits. As an application, we present efficient quantum estimators for the $q$-Tsallis entropy of discrete distributions. Specifically: (i) For $q > 1$, we obtain a near-optimal quantum algorithm with query complexity $\tildeΘ(1/\varepsilon^{\max\{1/(2(q-1)), 1\}})$, improving the prior best $O(1/\varepsilon^{1+1/(q-1)})$ due to Liu and Wang (SODA 2025; IEEE Trans. Inf. Theory 2026). (ii) For $0 < q < 1$, we obtain a quantum algorithm with query complexity $\tilde{O}(n^{1/q-1/2}/\varepsilon^{1/q})$, exhibiting a quantum speedup over the near-optimal classical estimators due to Jiao, Venkat, Han, and Weissman (IEEE Trans. Inf. Theory 2017). Our results achieve, to our knowledge, the first near-optimal quantum estimators for parameterized $q$-entropy for non-integer $q$.

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arXiv2026

Strict Hierarchy for Quantum Channel Certification to Unitary

We consider the problem of quantum channel certification to unitary, where one is given access to an unknown $d$-dimensional channel $\mathcal{E}$, and wants to test whether $\mathcal{E}$ is equal to a target unitary channel or is $\varepsilon$-far from it in the diamond norm. We present optimal quantum algorithms for this problem, settling the query complexities in three access models with increasing power. Specifically, we show that: (i) $Θ(d/\varepsilon^2)$ queries suffice for incoherent access model, matching the lower bound due to Fawzi, Flammarion, Garivier, and Oufkir (COLT 2023). (ii) $Θ(d/\varepsilon)$ queries suffice for coherent access model, matching the lower bound due to Regev and Schiff (ICALP 2008). (iii) $Θ(\sqrt{d}/\varepsilon)$ queries suffice for source-code access model, matching the lower bound due to Jeon and Oh (npj Quantum Inf. 2026). This demonstrates a strict hierarchy of complexities for quantum channel certification to unitary across various access models.

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arXiv2026

Trace Estimation of Quantum State Powers: Sample Complexity and Computational Hardness

As often emerges in various basic quantum properties such as Rényi and Tsallis entropies, the trace of quantum state powers $\text{tr}(ρ^q)$ has attracted a lot of attention. The recent work of Liu and Wang (SODA 2025) showed that, even for (possibly) non-integer $q>1$, $\text{tr}(ρ^q)$ can be estimated to within additive error $ε$ using a dimension-independent (and also rank-independent) sample complexity of $\widetilde O(1/ε^{3+\frac2{q-1}})$, together with a lower bound of $Ω(1/ε)$. In addition, combining this result with subsequent work of Liu (STACS 2026) shows that the corresponding promise problem is ${\sf BQP}$-complete. In this paper, we significantly improve and extend the sample complexity bounds for this problem. Furthermore, we show that for $0 2$, we settle the sample complexity with matching upper and lower bounds $\widetildeΘ(1/ε^2)$. - For $1 1$. Technically, our upper bounds are obtained by (non-plug-in) quantum estimators based on weak Schur sampling, in sharp contrast to the prior approach based on quantum singular value transformation and samplizer.

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arXiv2026

TopoLS: Lattice Surgery Compilation via Topological Program Transformations

Lattice surgery is a leading approach for implementing fault-tolerant logical operations in surface code quantum computing, but compiling efficient lattice surgery layouts remains challenging. Existing compilers are largely circuit-centric and operate directly on gate sequences, limiting their ability to exploit the topological flexibility of merge-split operations and minimize space--time volume. We present TopoLS, a topology-centric compiler that uses ZX diagrams as an intermediate representation for lattice surgery compilation. TopoLS combines semantic-preserving ZX-level program transformations, including spider fusion and topology-aware slicing, with a Monte Carlo Tree Search (MCTS)-based synthesis procedure that constructs pipe-diagram embeddings by jointly optimizing placement and routing in 3D space--time. To scale to large circuits, TopoLS further introduces topology-aware partitioning that decomposes the compilation task into bounded subproblems and limits the routing frontier during embedding. Across evaluated benchmarks, TopoLS achieves an average $46\%$ reduction in space--time volume over prior circuit-centric compilers, with improvements ranging from $25\%$ to $90\%$, and exhibits strong empirical scalability on large benchmark families. Compared with SAT-based formulations that become intractable on larger instances, TopoLS offers a practical end-to-end solution for optimized lattice surgery compilation. TopoLS has been integrated into the TQEC ecosystem, enabling downstream circuit-level simulation and resource estimation workflows.

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arXiv2026

Approximation does not help in quantum unitary time-reversal

Access to the time-reverse $U^{-1}$ of an unknown quantum unitary process $U$ is widely assumed in quantum learning, metrology, and many-body physics. The fundamental task of unitary time-reversal dictates implementing $U^{-1}$ to within diamond-norm error $ε$ using black-box queries to the $d$-dimensional unitary $U$. Although the query complexity of this task has been extensively studied, existing lower bounds either hold only for the exact case (i.e., $ε=0$) or are suboptimal in $d$. This raises a central question: does approximation help reduce the query complexity of unitary time-reversal? We settle this question in the negative by establishing a robust and tight lower bound $Ω((1-ε)d^2)$ with explicit dependence on the error $ε$. This implies that unitary time-reversal retains optimal exponential hardness (in the number of qubits) even when constant error is allowed. Our bound applies to adaptive and coherent algorithms with unbounded ancillas and holds even when $ε$ is an average-case distance error.

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arXiv2026

AlphaSyndrome: Tackling the Syndrome Measurement Circuit Scheduling Problem for QEC Codes

Quantum error correction (QEC) is essential for scalable quantum computing, yet repeated syndrome-measurement cycles dominate its spacetime and hardware cost. Although stabilizers commute and admit many valid execution orders, different schedules induce distinct error-propagation paths under realistic noise, leading to large variations in logical error rate. Outside of surface codes, effective syndrome-measurement scheduling remains largely unexplored. We present AlphaSyndrome, an automated synthesis framework for scheduling syndrome-measurement circuits in general commuting-stabilizer codes under minimal assumptions: mutually commuting stabilizers and a heuristic decoder. AlphaSyndrome formulates scheduling as an optimization problem that shapes error propagation to (i) avoid patterns close to logical operators and (ii) remain within the decoder's correctable region. The framework uses Monte Carlo Tree Search (MCTS) to explore ordering and parallelism, guided by code structure and decoder feedback. Across diverse code families, sizes, and decoders, AlphaSyndrome reduces logical error rates by 80.6% on average (up to 96.2%) relative to depth-optimal baselines, matches Google's hand-crafted surface-code schedules, and outperforms IBM's schedule for the Bivariate Bicycle code.

cs.ET↗
arXiv2026

Quantum channel tomography and estimation by local test

We study the estimation of an unknown quantum channel $\mathcal{E}$ with input dimension $d_1$, output dimension $d_2$ and Kraus rank at most $r$. We establish a connection between the query complexities in two models: (i) access to $\mathcal{E}$, and (ii) access to a random dilation of $\mathcal{E}$. Specifically, we show that for parallel (possibly coherent) testers, access to dilations does not help. This is proved by constructing a local tester that uses $n$ queries to $\mathcal{E}$ yet faithfully simulates the tester with $n$ queries to a random dilation. As application, we show that: - $O(rd_1d_2/\varepsilon^2)$ queries to $\mathcal{E}$ suffice for channel tomography to within diamond norm error $\varepsilon$. Moreover, when $rd_2=d_1$, we show that the Heisenberg scaling $O(1/\varepsilon)$ can be achieved, even if $\mathcal{E}$ is not a unitary channel: - $O(\min\{d_1^{2.5}/\varepsilon,d_1^2/\varepsilon^2\})$ queries to $\mathcal{E}$ suffice for channel tomography to within diamond norm error $\varepsilon$, and $O(d_1^2/\varepsilon)$ queries suffice for the case of Choi state trace norm error $\varepsilon$. - $O(\min\{d_1^{1.5}/\varepsilon,d_1/\varepsilon^2\})$ queries to $\mathcal{E}$ suffice for tomography of the mixed state $\mathcal{E}(|0\rangle\langle 0|)$ to within trace norm error $\varepsilon$.

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arXiv2026

Optimal lower bound for quantum channel tomography in away-from-boundary regime

Consider quantum channels with input dimension $d_1$, output dimension $d_2$ and Kraus rank at most $r$. Any such channel must satisfy the constraint $rd_2\geq d_1$, and the parameter regime $rd_2=d_1$ is called the boundary regime. In this paper, we show an optimal query lower bound $Ω(rd_1d_2/\varepsilon^2)$ for quantum channel tomography to within diamond norm error $\varepsilon$ in the away-from-boundary regime $rd_2\geq 2d_1$, matching the existing upper bound $O(rd_1d_2/\varepsilon^2)$. In particular, this lower bound fully settles the query complexity for the commonly studied case of equal input and output dimensions $d_1=d_2=d$ with $r\geq 2$, in sharp contrast to the unitary case $r=1$ where Heisenberg scaling $Θ(d^2/\varepsilon)$ is achievable.

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arXiv2025

A List of Complexity Bounds for Property Testing by Quantum Sample-to-Query Lifting

Quantum sample-to-query lifting, a relation between quantum sample complexity and quantum query complexity presented in Wang and Zhang (SIAM J. Comput. 2025), was significantly strengthened by Tang, Wright, and Zhandry (2025) to the case of state-preparation oracles. In this paper, we compile a list of quantum lower and upper bounds for property testing that are obtained by quantum sample-to-query lifting. The problems of interest include testing properties of probability distributions and quantum states, such as entropy and closeness. This collection contains new results, as well as new proofs of known bounds. In total, we present 49 complexity bounds, where 41 are new and 18 are (near-)optimal.

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arXiv2025

Inverse-free quantum state estimation with Heisenberg scaling

In this paper, we present an inverse-free pure quantum state estimation protocol that achieves Heisenberg scaling. Specifically, let $\mathcal{H}\cong \mathbb{C}^d$ be a $d$-dimensional Hilbert space with an orthonormal basis $\{|1\rangle,\ldots,|d\rangle\}$ and $U$ be an unknown unitary on $\mathcal{H}$. Our protocol estimates $U|d\rangle$ to within trace distance error $\varepsilon$ using $O(\min\{d^{3/2}/\varepsilon,d/\varepsilon^2\})$ forward queries to $U$. This complements the previous result $O(d\log(d)/\varepsilon)$ by van Apeldoorn, Cornelissen, Gilyén, and Nannicini (SODA 2023), which requires both forward and inverse queries. Moreover, our result implies a query upper bound $O(\min\{d^{3/2}/\varepsilon,1/\varepsilon^2\})$ for inverse-free amplitude estimation, improving the previous best upper bound $O(\min\{d^{2}/\varepsilon,1/\varepsilon^2\})$ based on optimal unitary estimation by Haah, Kothari, O'Donnell, and Tang (FOCS 2023), and disproving a conjecture posed in Tang and Wright (2025).

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arXiv2025

Verifying Fault-Tolerance of Quantum Error Correction Codes

Quantum computers have advanced rapidly in qubit count and gate fidelity. However, large-scale fault-tolerant quantum computing still relies on quantum error correction code (QECC) to suppress noise. Manually or experimentally verifying the fault-tolerance property of complex QECC implementation is impractical due to the vast error combinations. This paper formalizes the fault-tolerance of QECC implementations within the language of quantum programs. By incorporating the techniques of quantum symbolic execution, we provide an automatic verification tool for quantum fault-tolerance. We evaluate and demonstrate the effectiveness of our tool on a universal set of logical operations across different QECCs.

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arXiv2024

Automatic Test Pattern Generation for Robust Quantum Circuit Testing

Quantum circuit testing is essential for detecting potential faults in realistic quantum devices, while the testing process itself also suffers from the inexactness and unreliability of quantum operations. This paper alleviates the issue by proposing a novel framework of automatic test pattern generation (ATPG) for robust testing of logical quantum circuits. We introduce the stabilizer projector decomposition (SPD) for representing the quantum test pattern, and construct the test application (i.e., state preparation and measurement) using Clifford-only circuits, which are rather robust and efficient as evidenced in the fault-tolerant quantum computation. However, it is generally hard to generate SPDs due to the exponentially growing number of the stabilizer projectors. To circumvent this difficulty, we develop an SPD generation algorithm, as well as several acceleration techniques which can exploit both locality and sparsity in generating SPDs. The effectiveness of our algorithms are validated by 1) theoretical guarantees under reasonable conditions, 2) experimental results on commonly used benchmark circuits, such as Quantum Fourier Transform (QFT), Quantum Volume (QV) and Bernstein-Vazirani (BV) in IBM Qiskit.

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