arXiv subjects

Yuguo Shao

Publications and source records attributed to Yuguo Shao.

11 recordsLinked to original sources

arXiv2026

Complexity of tensor network simulation for noisy quantum circuits

We aim to rigorously address how local noise affects classical simulability of quantum dynamics benchmarked by tensor-network methods. Using operator entanglement entropy (OEE), we prove the following: (1) For single-qubit depolarizing noise on arbitrary circuits, tensor networks with $\mathrm{poly}(n)$ bond dimension suffice for fixed absolute Hilbert-Schmidt error after $\order{1}$ depth, while relative error demands $\order{\log n}$ depth; and this bound is optimal. (2) For single-qubit depolarizing noise on 1D local circuits, the existence of whole-trajectory error-bounded matrix product operator (MPO) of $\mathrm{poly}(n)$ bond dimension at all depths. (3) For general single-qubit noise in 1D brickwall circuits, random two-design gates with contraction coefficient $c<1/3$ yield an $\order{1}$ OEE plateau with probability $1-Te^{-\Omega(n)}$, while arbitrary gates with $c<1/48$ give $\order{\log n}$ OEE in the worst case. (4) In higher dimensions, these bounds yield uniform-in-depth $\mathrm{poly}(n)$ average boundary-bond dimensions for projected entangled pair operators~(PEPO) across every cut -- under depolarizing noise at either absolute or relative accuracy, and under general noise with strong contraction at absolute accuracy. Our results establish a rigorous connection between certain noise models, circuit types, and their classical simulability.

cond-mat.str-el↗

arXiv2026

Theory of (Co)homological Invariants on Quantum LDPC Codes

With recent breakthroughs in the construction of good qLDPC codes and nearly good qLTCs, the study of (co)homological invariants of quantum code complexes, which fundamentally underlie their logical operations, has become evidently important. In this work, we establish a systematic framework for mathematically analyzing these invariants across a broad spectrum of constructions, from HGP codes to sheaf codes, by synthesizing advanced math tools. We generalize the notion of canonical logical representatives from HGP codes to the sheaf code setting, resolving a long-standing challenge in explicitly characterizing sheaf codewords. Building on this foundation, we present the first comprehensive computation of cup products within the intricate framework of sheaf codes. Given Artin's primitive root conjecture which holds under the generalized Riemann hypothesis, we prove that $\tilde{\Theta}(N)$ independent cup products can be supported on almost good qLDPC codes and qLTCs of length N, opening the possibility of achieving linearly many parallel, nontrivial, constant-depth multi-controlled-Z gates. Moreover, by interpreting sheaf codes as covering spaces of HGP codes via graph lifts, we propose a scheme that inductively generates families of both HGP and sheaf codes in an interlaced fashion from a constant-size HGP code. Notably, the induction preserves all (co)homological invariants of the initial code. This provides a general framework for lifting invariants or logical gates from small codes to infinite code families, and enables efficient verification of such features by checking on small instances. Our theory provides a substantive methodology for studying invariants in HGP codes and extends it to sheaf codes. In doing so, we reveal deep and unexpected connections between qLDPC codes and math, thereby laying the groundwork for future advances in quantum coding, fault tolerance, and physics.

quant-ph↗

arXiv2025

Taming Barren Plateaus in Arbitrary Parameterized Quantum Circuits without Sacrificing Expressibility

Quantum algorithms based on parameterized quantum circuits (PQCs) have enabled a wide range of applications on near-term quantum devices. However, existing PQC architectures face several challenges, among which the ``barren plateaus" phenomenon is particularly prominent. In such cases, the loss function concentrates exponentially with increasing system size, thereby hindering effective parameter optimization. To address this challenge, we propose a general and hardware-efficient method for eliminating barren plateaus in an arbitrary PQC. Specifically, our approach achieves this by inserting a layer of easily implementable quantum channels into the original PQC, each channel requiring only one ancilla qubit and four additional gates, yielding a modified PQC (MPQC) that is provably at least as expressive as the original PQC and, under mild assumptions, is guaranteed to be free from barren plateaus. Furthermore, by appropriately adjusting the structure of MPQCs, we rigorously prove that any parameter in the original PQC can be made trainable. Importantly, the absence of barren plateaus in MPQCs is robust against realistic noise, making our approach directly applicable to near-term quantum hardware. Numerical simulations demonstrate that MPQC effectively eliminates barren plateaus in PQCs for preparing thermal states of systems with up to 100 qubits and 2400 layers. Furthermore, in end-to-end simulations, MPQC significantly outperforms PQC in finding the ground-state energy of a complex Hamiltonian.

quant-ph↗

arXiv2025

Characterizing Pauli Propagation via Operator Complexity

Pauli-propagation simulation represents observables in the Pauli basis and evolves their coefficients in the Heisenberg picture. Its efficiency depends on whether the evolving operator can be accurately compressed by retaining only a limited number of Pauli terms. In this work, we bridge operator complexity and the resource cost of Pauli-propagation methods by proving that the truncation error is governed by the Operator Stabilizer R\'enyi entropy (OSE) $\mathcal{S}^\alpha(O)$. Our a priori bounds quantify how OSE controls the compressibility of the evolving operator and give explicit prescriptions for the Top-$K$ budget required to achieve a target accuracy. As an analytic test case, we prove that for the 1D Heisenberg model at $J_z=0$, the number of non-zero Pauli coefficients generated from a local operator grows at most quadratically with the number of Trotter steps. We then benchmark the Top-$K$ Pauli propagation on XXZ Heisenberg chains. The numerical results show high accuracy with a small truncation number $K$ in the free regime ($J_z=0$) and competitive performance against tensor-network methods, such as TDVP, in the interacting case ($J_z=0.5$). These results position OSE as a resource measure for Pauli-propagation methods.

quant-ph↗

arXiv2025

Diagnosing Quantum Circuits: Noise Robustness, Trainability, and Expressibility

Achieving practical quantum advantage on near-term noisy hardware is a central goal of quantum computation. However, without efficient pre-execution diagnostics, circuit design and scheme selection often rely on costly hardware-in-the-loop trial-and-error, inflating experimental overhead and impeding progress. To address this challenge, we introduce 2MC-OBPPP, a polynomial-time classical estimator that, for parameterized quantum circuits, jointly estimates trainability, expressibility, and robustness to noise. For example, our approach visually demonstrates that moderate amplitude damping alleviates barren plateaus (improving trainability) while decreasing expressibility. Moreover, the method produces a spatiotemporal ``noise-hotspot" map that pinpoints the most noise-sensitive qubits/gates, enabling targeted noise suppression. In a representative circuit, interventions on fewer than $2\%$ qubits reduce the error up to $90\%$. Together, before execution, our approach provides an efficient diagnostic benchmark for circuit/scheme design, and in deployment, guides for targeted interventions that substantially reduce the cost of error suppression.

quant-ph↗

arXiv2025

BELT: Block Encoding of Linear Transformation on Density Matrices

Linear maps that are not completely positive play a crucial role in the study of quantum information, yet their non-completely positive nature renders them challenging to realize physically. The core difficulty lies in the fact that when acting such a map $\mathcal{N}$ on a state $\rho$, $\mathcal{N}(\rho)$ may not correspond to a valid density matrix, making it difficult to prepare directly in a physical system. We introduce Block Encoding of Linear Transformation (BELT), a systematic protocol that simulates arbitrary linear maps by embedding the output $\mathcal{N}(\rho)$ into a block of a unitary operator. BELT enables the manipulation and extraction of information about $\mathcal{N}(\rho)$ through coherent quantum evolution. Notably, BELT accommodates maps that fall outside the scope of quantum singular value transformation, such as the transpose map. BELT finds applications in entanglement detection, quantum channel inversion, and simulating pseudo-differential operators, and demonstrates improved sample complexity compared to protocols based on Hermitian-preserving map exponentiation.

quant-ph↗

arXiv2024

Clifford Perturbation Approximation for Quantum Error Mitigation

Quantum error mitigation (QEM) is critical for harnessing the potential of near-term quantum devices. Particularly, QEM protocols can be designed based on machine learning, where the mapping between noisy computational outputs and ideal ones can be learned on a training set consisting of Clifford circuits or near-Clifford circuits that contain only a limited number of non-Clifford gates. This learned mapping is then applied to noisy target circuits to estimate the ideal computational output. In this work, we propose a learning-based error mitigation framework called Clifford Perturbation Data Regression (CPDR), which constructs training sets by Clifford circuits with small perturbations. Specifically, these circuits are parameterized quantum circuits, where the rotation angles of the gates are restricted to a narrow range, ensuring that the gates remain close to Clifford gates. This design enables the efficient simulation of the training circuits using the Sparse Pauli Dynamics method. As a result, CPDR is able to utilize training sets with a better diversity to train the model, compared with previous learning-based QEM models that construct training sets with only Clifford or near-Clifford circuits. Numerical simulations on small-scale Ising model circuits demonstrate that the performance of CPDR dramatically outperforms that of existing methods such as Zero-Noise Extrapolation and learning-based Probabilistic Error Cancellation. Furthermore, using the experimental data from IBM's 127-qubit Eagle processor, our findings suggest that CPDR demonstrates improved accuracy compared to the original mitigation results reported in [Nature 618, 500 (2023)].

quant-ph↗

arXiv2024

Variational Graphical Quantum Error Correction Codes

Quantum error correction is essential for achieving fault-tolerant quantum computation. However, most typical quantum error-correcting codes are designed for generic noise models, which may fail to accurately capture the intricate noise characteristics of real quantum devices, limiting their practical performance. This work introduces a learning-based framework for the constructing of quantum error-correcting codes, termed Variational Graphical Quantum Error Correction (VGQEC) codes, which adapts to specific noise profiles of different quantum devices, enabling the design of noise-tailored codes. Specifically, inspired by Quon, a graphical language for quantum information, VGQEC codes incorporate tunable parameters embedded within their Quon graphs, allowing dynamic reconfigurations of the graph structures through parameter adjustments. As the first application of this approach, we show that this flexibility in code designs facilitates seamless transitions between various code families, exemplified by the establishment of a bridge between the five-qubit repetition code and the [[5,1,3]] code, thereby combining their respective advantages. Additionally, a VGQEC code derived from the three-qubit repetition code is fine-tuned for the amplitude damping noise, showcasing the approach's ability for noise-specific code design. Moreover, we experimentally demonstrate the effectiveness of the three-qubit VGQEC code in the low-to-medium noise regime with a photonic system, highlighting its potential for real-world applications.

quant-ph↗

arXiv2024

The sudden death of quantum advantage in correlation generations

As quantum error corrections still cannot be realized physically, quantum noise is the most profound obstacle to the implementations of large-scale quantum algorithms or quantum schemes. It has been well-known that if a quantum computer suffers from too strong quantum noise, its running can be easily simulated by a classical computer, making the quantum advantage impossible. Generally speaking, however, the dynamical process that how quantum noise of varying strengths from 0 to a fatal level impacts and destroys quantum advantage has not been understood well. Undoubtedly, achieving this will be extremely valuable for us to understand the power of noisy intermediate-scale quantum computers. Meanwhile, correlation generation is a precious theoretical model of information processing tasks in which the quantum advantage can be precisely quantified. Here we show that this model also provides us a valuable insight into understanding the impact of noise on quantum advantage. Particularly, we will rigorously prove that when the strength of quantum noise continuously goes up from 0, the quantum advantage gradually declines, and eventually fades away completely. Surprisingly, in some cases we observe an unexpected phenomenon we call the sudden death of the quantum advantage, i.e., when the strength of quantum noise exceeds a certain point, the quantum advantage disappears suddenly from a non-negligible level. This interesting phenomenon reveals the tremendous harm of noise to quantum information processing tasks from a new viewpoint.

quant-ph↗

arXiv2023

Simulating Noisy Variational Quantum Algorithms: A Polynomial Approach

Large-scale variational quantum algorithms are widely recognized as a potential pathway to achieve practical quantum advantages. However, the presence of quantum noise might suppress and undermine these advantages, which blurs the boundaries of classical simulability. To gain further clarity on this matter, we present a novel polynomial-scale method based on the path integral of observable's back-propagation on Pauli paths (OBPPP). This method efficiently approximates expectation values of operators in variational quantum algorithms with bounded truncation error in the presence of single-qubit Pauli noise. Theoretically, we rigorously prove: 1) For a constant minimal non-zero noise rate $\gamma$, OBPPP's time and space complexity exhibit a polynomial relationship with the number of qubits $n$, the circuit depth $L$. 2) For variable $\gamma$, in scenarios where more than two non-zero noise factors exist, the complexity remains $\mathrm{Poly}\left(n,L\right)$ if $\gamma$ exceeds $1/\log{L}$, but grows exponential with $L$ when $\gamma$ falls below $1/L$. Numerically, we conduct classical simulations of IBM's zero-noise extrapolated experimental results on the 127-qubit Eagle processor [Nature \textbf{618}, 500 (2023)]. Our method attains higher accuracy and faster runtime compared to the quantum device. Furthermore, our approach allows us to simulate noisy outcomes, enabling accurate reproduction of IBM's unmitigated results that directly correspond to raw experimental observations. Our research reveals the vital role of noise in classical simulations and the derived method is general in computing the expected value for a broad class of quantum circuits and can be applied in the verification of quantum computers.

quant-ph↗

arXiv2022

Efficient quantum imaginary time evolution by drifting real time evolution: an approach with low gate and measurement complexity

Quantum imaginary time evolution (QITE) is one of the promising candidates for finding eigenvalues and eigenstates of a Hamiltonian. However, the original QITE proposal [Nat. Phys. 16, 205-210 (2020)], which approximates the imaginary time evolution by real time evolution, suffers from large circuit depth and measurements due to the size of the Pauli operator pool and Trotterization. To alleviate the requirement for deep circuits, we propose a time-dependent drifting scheme inspired by the qDRIFT algorithm [Phys. Rev. Lett 123, 070503 (2019)], which randomly draws a Pauli term out of the approximated unitary operation generators of QITE according to the strength and rescales that term by the total strength of the Pauli terms. We show that this drifting scheme removes the depth dependency on size of the operator pool and converges inverse linearly to the number of steps. We further propose a deterministic algorithm that selects the dominant Pauli term to reduce the fluctuation for the ground state preparation. Meanwhile, we introduce an efficient measurement reduction scheme across Trotter steps, which removes its cost dependence on the number of iterations, and a measurement distribution protocol for different observables within each time step. We also analyze the main source of error for our scheme both theoretically and numerically. We numerically test the validity of depth reduction, convergence performance, and faithfulness of measurement reduction approximation of our algorithms on LiH, BeH$_2$ and N$_2$ molecules. In particular, the results on LiH molecule give circuit depths comparable to that of the advanced adaptive variational quantum eigensolver~(VQE) methods while requiring much fewer measurements.

quant-ph↗