arXiv subjects

Guoding Liu

Publications and source records attributed to Guoding Liu.

15 recordsLinked to original sources

arXiv2026

(Almost) quadruply optimal unitary designs in 1D

We construct $n$-qubit approximate unitary $k$-designs in 1D systems, achieving circuit depth $O(\log(n/\varepsilon) + k\log k)$ with relative error $\varepsilon$ and requiring $O(nk\log k)$ magic gates. This matches existing lower bounds $\Omega(\log(n/\varepsilon) + k)$ for circuit depth, and $\widetilde{\Omega}(nk)$ for the required number of $T$ gates, up to a $\log k$ factor, achieving simultaneous near-optimality in all parameters. Our construction is based on a combination and refinement of two existing results. We reduce the required magic block size for breaking Clifford symmetries in the magic-augmented circuit construction of Zhang et al. from $O(k\log k)$ to $O(\log k)$. We also improve the breakthrough construction of Chen et al. to construct a generating set of 1D local constant-depth circuits for the unitary group with a constant spectral gap, making $O(\log k)$-local random unitaries realizable in depth $O(k\log k)$. As a by-product, we provide a constant-size 1D-local generating set for the Clifford group, which we expect to be of independent interest. Combining the two results with the gluing lemma, we prove the final result.

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arXiv2026

Can scrambling protect quantum state distinguishability under noise?

Quantum state distinguishability is a fundamental concept in quantum information science that underpins a wide range of important practical tasks. Traditionally formulated for pairs of states, quantum state distinguishability is here extended to quantum state ensembles, which we characterize through the average pairwise trace distance. Motivated by both theoretical and practical interest in noisy quantum information processing, we ask whether ``minimally'' scrambled ensembles modeled by 2-designs protect distinguishability under noise, which sheds light on the fundamental competition between noise and information scrambling. Using a rigorous decoupling approach, we establish tight bounds on noisy ensemble distinguishability. We show that the distinguishability of noisy 2-design ensembles exhibits a sharp threshold and phase-transition behavior governed by channel conditional entropy: below the threshold, the states remain mutually distinguishable with high probability, while above it, distinguishability undergoes a sudden power-law decay and then collapses exponentially. On the other hand, under local purity-shrinking noise, post-measured noisy 2-design ensembles become exponentially indistinguishable for any measurement, precluding a noise threshold for learning tasks such as shadow tomography. These results reveal a sharp difference between unmeasured and post-measured scrambled ensembles: the former can retain high distinguishability for sufficiently small noise, whereas the latter exhibits no such protected regime. We discuss the implications of these results for crucial tasks ranging from quantum communication and cryptography to learning.

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arXiv2026

Entanglement distillation based on Hamiltonian dynamics

Efficient entanglement distillation is a central task in quantum information science and future quantum networks. At the core of distillation protocols are the quantum error correction and detection schemes which enhance the fidelity of entangled pairs. Conventional protocols focus on digital systems, which typically require complicated compiled circuits, high-fidelity multi-qubit operations and delicate pulse-level control that impose high demands on near-term hardware. Crucially, the leading physical platforms for quantum networks, trapped ions and neutral atoms, are governed by native many-body Hamiltonians inherently suited for analog, continuous-time evolution. Adopting these natural dynamics is simpler than engineering digital logic via delicate pulse-level control. Motivated by this experimental reality, we seek to leverage the intrinsic analog capabilities for efficient entanglement distillation. In this work, we introduce the Hamiltonian entanglement distillation protocol, which exploits the intrinsic information scrambling generated by random time evolution under native Hamiltonians. We establish a quantitative connection between output fidelity and Out-of-Time-Order Correlators, showing that efficient scrambling directly implies good distillation performance. Since generic Hamiltonians are naturally efficient scramblers, the capability for distillation is ubiquitous: almost all Hamiltonians in the Hilbert space suffice for high-fidelity distillation. Numerical simulations of representative Rydberg-atom and trapped-ion systems further confirm that robust performance could be achieved using only short-range interactions and evolution times feasible in current experiments. By avoiding the complexity of digital circuit control, our approach substantially relaxes experimental requirements, providing a scalable route to entanglement engineering on current analog quantum platforms.

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arXiv2025

Benchmarking non-Clifford gates using only Pauli twirling group

Quantum gate benchmarking is unavoidably influenced by state preparation and measurement errors. Randomized benchmarking addresses this challenge by employing group twirling to regularize the noise channel, then provides a characterization of quantum channels that is robust to these errors through exponential fittings. In practice, local twirling gates are preferred due to their high fidelity and experimental feasibility. However, while existing RB methods leveraging local twirling gates are effective for benchmarking Clifford gates, they face fundamental challenges in benchmarking non-Clifford gates. In this work, we solve this problem by introducing the Pauli Transfer Character Benchmarking. This protocol estimates the Pauli transfer matrix elements for a quantum channel using only local Pauli operations. Building on this protocol, we develop a fidelity benchmarking method for non-Clifford gates $U$ satisfying $U^2=I$. We validate the feasibility of our protocol through numerical simulations applied to Toffoli gates as a concrete example.

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arXiv2025

State complexity and phase identification in adaptive quantum circuits

Adaptive quantum circuits, leveraging measurements and classical feedback, significantly expand the landscape of realizable quantum states compared to their non-adaptive counterparts, enabling the preparation of long-range entangled states and topological phases at constant depths. However, the ancilla overhead for preparing arbitrary states can be prohibitive, raising a fundamental question: which states can be efficiently realized with limited ancilla and low depth? Addressing this question requires a rigorous quantitative characterization of state complexity, or the minimum depth and ancillas, to realize a state in adaptive circuits. In this work, we tackle this problem by introducing two properties of quantum states: state weight and anti-shallowness, connected to the correlation range and correlation strength within a state, respectively. We prove that these quantities are bounded under limited circuit resources, thereby providing rigorous bounds on the approximate complexity of state preparation and gate implementation. Illustrative examples include the GHZ state, W state, QLDPC code states, and the Toffoli gate. Besides complexity, we show that states within the same quantum phase, defined by a set of quantum states connected with constant-depth circuits, must share the same scaling of weight or anti-shallowness. This establishes these quantities as indicators of quantum phases and their essential roles in many-body physics.

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arXiv2025

Calibrating quantum gates up to 52 qubits in a superconducting processor

Benchmarking large-scale quantum gates, typically involving multiple native two-qubit and singlequbit gates, is crucial in quantum computing. Global fidelity, encompassing information about intergate correlations, offers a comprehensive metric for evaluating and optimizing gate performance, unlike the fidelities of individual local native gates. In this work, utilizing the character-average benchmarking protocol implementable in a shallow circuit, we successfully benchmark gate fidelities up to 52 qubits. Notably, we achieved a fidelity of 63.09$\pm $0.23% for a 44-qubit parallel CZ gate. Utilizing the global fidelity of the parallel CZ gate, we explore the correlations among local CZ gates by introducing an inter-gate correlation metric, enabling one to simultaneously quantify crosstalk error when benchmarking gate fidelity. Finally, we apply our methods in gate optimization. By leveraging global fidelity for optimization, we enhance the fidelity of a 6-qubit parallel CZ gate from 87.65% to 92.04% and decrease the gate correlation from 3.53% to 3.22%, compared to local gate fidelitybased optimization. The experimental results align well with our established composite noise model, incorporating depolarizing and ZZ-coupling noises, and provide valuable insight into further study and mitigation of correlated noise.

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arXiv2025

Approximate Quantum Error Correction with 1D Log-Depth Circuits

Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this work, we rigorously prove through information-theoretic analysis that one-dimensional logarithmic-depth random Clifford encoding circuits can achieve high quantum error correction performance. We demonstrate that these random codes typically exhibit good approximate quantum error correction capability by proving that their encoding rate achieves the hashing bound for Pauli noise and the channel capacity for erasure errors. We show that the error correction inaccuracy decays once a threshold of logarithmic depth is exceeded, resulting in negligible recovery errors. This threshold is shown to be lower than that of the simple separate block encoding, and the decay rate is higher. We further establish that these codes are optimal by proving that logarithmic depth is necessary to maintain a constant encoding rate and high error correction performance. To prove our results, we propose decoupling theorems tailored for one-dimensional low-depth circuits. These results also imply strong decoupling and rapid thermalization properties in low-depth random circuits and have potential applications in quantum information science and physics.

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arXiv2024

Optimizing Circuit Reusing and its Application in Randomized Benchmarking

Quantum learning tasks often leverage randomly sampled quantum circuits to characterize unknown systems. An efficient approach known as "circuit reusing," where each circuit is executed multiple times, reduces the cost compared to implementing new circuits. This work investigates the optimal reusing parameter that minimizes the variance of measurement outcomes for a given experimental cost. We establish a theoretical framework connecting the variance of experimental estimators with the reusing parameter R. An optimal R is derived when the implemented circuits and their noise characteristics are known. Additionally, we introduce a near-optimal reusing strategy that is applicable even without prior knowledge of circuits or noise, achieving variances close to the theoretical minimum. To validate our framework, we apply it to randomized benchmarking and analyze the optimal R for various typical noise channels. We further conduct experiments on a superconducting platform, revealing a non-linear relationship between R and the cost, contradicting previous assumptions in the literature. Our theoretical framework successfully incorporates this non-linearity and accurately predicts the experimentally observed optimal R. These findings underscore the broad applicability of our approach to experimental realizations of quantum learning protocols.

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arXiv2024

Advantage Distillation for Quantum Key Distribution

Quantum key distribution promises information-theoretically secure communication, with data post-processing playing a vital role in extracting secure keys from raw data. While hardware advancements have significantly improved practical implementations, optimizing post-processing techniques offers a cost-effective avenue to enhance performance. Advantage distillation, which extends beyond standard information reconciliation and privacy amplification, has proven instrumental in various post-processing methods. However, the optimal post-processing remains an open question. Therefore, it is important to develop a comprehensive framework to encapsulate and enhance these existing methods. In this work, we propose an advantage distillation framework for quantum key distribution, generalizing and unifying existing key distillation protocols. Inspired by entanglement distillation, our framework not only integrates current techniques but also improves upon them. Notably, by employing classical linear codes, we achieve higher key rates, particularly in scenarios where one-time pad encryption is not used for post-processing. Our approach provides insights into existing protocols and offers a systematic way for further enhancements in quantum key distribution.

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arXiv2024

Unconditional quantum magic advantage in shallow circuit computation

Quantum theory promises computational speed-ups over classical approaches. The celebrated Gottesman-Knill Theorem implies that the full power of quantum computation resides in the specific resource of "magic" states -- the secret sauce to establish universal quantum computation. However, it is still questionable whether magic indeed brings the believed quantum advantage, ridding unproven complexity assumptions or black-box oracles. In this work, we demonstrate the first unconditional magic advantage: a separation between the power of generic constant-depth or shallow quantum circuits and magic-free counterparts. For this purpose, we link the shallow circuit computation with the strongest form of quantum nonlocality -- quantum pseudo-telepathy, where distant non-communicating observers generate perfectly synchronous statistics. We prove quantum magic is indispensable for such correlated statistics in a specific nonlocal game inspired by the linear binary constraint system. Then, we translate generating quantum pseudo-telepathy into computational tasks, where magic is necessary for a shallow circuit to meet the target. As a by-product, we provide an efficient algorithm to solve a general linear binary constraint system over the Pauli group, in contrast to the broad undecidability in constraint systems. We anticipate our results will enlighten the final establishment of the unconditional advantage of universal quantum computation.

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arXiv2023

Robust Estimation of Nonlinear Properties of Quantum Processes

Accurate and robust estimation of quantum process properties is crucial for quantum information processing and quantum many-body physics. Combining classical shadow tomography and randomized benchmarking, Helsen et al. introduced a method to estimate the linear properties of quantum processes. In this work, we focus on the estimation protocols of nonlinear process properties that are robust to state preparation and measurement errors. We introduce two protocols, both utilizing random gate sequences but employing different post-processing methods, which make them suitable for measuring different nonlinear properties. The first protocol offers a robust and sound method to estimate the out-of-time-ordered correlation, as demonstrated numerically in an Ising model. The second protocol estimates unitarity, effectively characterizing the incoherence of quantum channels. We expect the two protocols to be useful tools for exploring quantum many-body physics and characterizing quantum processes.

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arXiv2023

Group twirling and noise tailoring for multi-qubit controlled phase gates

Group twirling is crucial in quantum information processing, particularly in randomized benchmarking and random compiling. While protocols based on Pauli twirling have been effectively crafted to transform arbitrary noise channels into Pauli channels for Clifford gates -- thereby facilitating efficient benchmarking and mitigating worst-case errors -- practical twirling groups for multi-qubit non-Clifford gates are lacking. In this work, we study the issue of finding twirling groups for generic quantum gates within a widely used circuit structure in randomized benchmarking or random compiling. For multi-qubit controlled phase gates, which are essential in both the quantum Fourier transform and quantum search algorithms, we identify optimal twirling groups within the realm of classically replaceable unitary operations. In contrast to the simplicity of the Pauli twirling group for Clifford gates, the optimal groups for such gates are much larger, highlighting the overhead of tailoring noise channels in the presence of global non-Clifford gates.

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arXiv2023

Realizing Non-Physical Actions through Hermitian-Preserving Map Exponentiation

Quantum mechanics features a variety of distinct properties such as coherence and entanglement, which could be explored to showcase potential advantages over classical counterparts in information processing. In general, legitimate quantum operations must adhere to principles of quantum mechanics, particularly the requirements of complete positivity and trace preservation. Nonetheless, non-physical maps, especially Hermitian-preserving maps, play a crucial role in quantum information science. To date, there exists no effective method for implementing these non-physical maps with quantum devices. In this work, we introduce the Hermitian-preserving map exponentiation algorithm, which can effectively realize the action of an arbitrary Hermitian-preserving map by encoding its output into a quantum process. We analyze the performances of this algorithm, including its sample complexity and robustness, and prove its optimality in certain cases. When combined with algorithms such as the Hadamard test and quantum phase estimation, it allows for the extraction of information and generation of states from outputs of Hermitian-preserving maps, enabling various applications. Utilizing positive but not completely positive maps, this algorithm provides exponential advantages in entanglement detection and quantification compared to protocols based on single-copy operations. In addition, it facilitates the recovery of noiseless quantum states from multiple copies of noisy states by implementing the inverse map of the corresponding noise channel, offering an intriguing approach to handling quantum errors. Our findings present a pathway for systematically and efficiently implementing non-physical actions with quantum devices, thereby boosting the exploration of potential quantum advantages across a wide range of information processing tasks.

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arXiv2022

Classically Replaceable Operations

Quantum information science provides powerful technologies beyond the scope of classical physics. In practice, accurate control of quantum operations is a challenging task with current quantum devices. The implementation of high fidelity and multi-qubit quantum operations consumes massive resources and requires complicated hardware design to fight against noise. An approach to alleviating this problem is to replace quantum operations with classical processing. Despite the common practice of this approach, rigorous criteria to determine whether a given quantum operation is replaceable classically are still missing. In this work, we define the classically replaceable operations in four general scenarios. In each scenario, we provide their necessary and sufficient criteria and point out the corresponding classical processing. For a practically favorable case of unitary classically replaceable operations, we show that the replaced classical processing is deterministic. Beyond that, we regard the irreplaceability of quantum operations by classical processing as a quantum resource and relate it to the performance of a channel in a non-local game, as manifested in a robustness measure.

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arXiv2022

Scalable fast benchmarking for individual quantum gates with local twirling

With the development of controllable quantum systems, fast and practical characterization for multi-qubit gates is essential for building high-fidelity quantum computing devices. The usual way to fulfill this requirement via randomized benchmarking asks for the complicated implementation of numerous multi-qubit twirling gates. How to efficiently and reliably estimate the fidelity of a quantum process remains an open problem. In this work, we propose a character-cycle benchmarking protocol and a character-average benchmarking protocol only using local twirling gates to estimate the process fidelity of an individual multi-qubit operation. Our protocols can characterize a large class of quantum gates including and beyond the Clifford group via the local gauge transformation, which forms a universal gate set for quantum computing. We numerically demonstrate our protocols for a non-Clifford gate -- controlled-$(TX)$ and a Clifford gate -- five-qubit quantum error-correcting encoding circuit. The numerical results show that our protocols can efficiently and reliably characterize the gate process fidelities. Compared with the cross-entropy benchmarking, the simulation results show that the character-average benchmarking achieves three orders of magnitude improvements in terms of sampling complexity.

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