arXiv subjects

Synge Todo

Publications and source records attributed to Synge Todo.

At least 19 recordsLinked to original sources

arXiv2026

Matrix Product Evolution: A Method for Simulating Quantum Circuits Using Tensor Networks

Classical simulation of quantum circuits is an essential tool in quantum information science, but its applicability is constrained by the exponential growth of the Hilbert space and the entanglement structure of quantum states. In this work, we introduce Matrix Product Evolution (MPE), a tensor-train representation of quantum circuits constructed along the circuit depth rather than along the qubit index. Within this formulation, the simulation of a quantum circuit is modeled as the contraction of multiple MPE tensors. We develop an efficient contraction strategy based on a zip-up procedure to carry out this contraction in practice. We investigate the numerical behavior of this MPE-based contraction framework through simulations of random quantum circuits and the time evolution of a quantum many-body state. Our results characterize the growth of temporal bond dimensions, clarify how post-selection modifies the contraction cost and approximation accuracy, and identify regimes in which depth-oriented tensor-network contractions provide a useful complement to standard MPS-based simulation approaches.

quant-ph↗

arXiv2026

Parallel Hadamard Test

The Hadamard test is a fundamental building block widely used in many quantum computing algorithms. It estimates the real or imaginary part of $\langle \psi \vert U \vert \psi \rangle$, where $\vert \psi \rangle$ is a quantum state and $U$ is a unitary operator. In many algorithms, however, many such quantities must be estimated, leading to a large number of distinct circuit types, long computational times, and high financial costs. In this work, we propose the parallel Hadamard test, which combines multiple Hadamard tests into a single circuit type. We demonstrate how the parallel Hadamard test applies to three structural classes of workloads: arbitrary sets of unitary operators, prefix-product arrays, and Gram-matrix elements. For each class, we compare the cost of the parallel Hadamard test with that of the conventional one. Our unified approach significantly reduces the number of distinct circuit types, and can lower both computational time and financial costs in regimes where fixed per-circuit overheads dominate the total cost. In Gram-matrix workloads, it can also reduce the total number of shots when typical off-diagonal overlaps are small.

quant-ph↗

arXiv2026

Unbiased Hamiltonian Simulation by Reversing Trotter Error Dynamics

Owing to their simplicity and low overhead, Suzuki-Trotter formulas remain the de facto Hamiltonian simulation methods on current quantum computing platforms. Systematic Trotter errors, however, will quickly become limiting when scaling to larger problems and aiming for higher accuracy. We present a mechanism that removes the systematic error of any $k$-th order Suzuki-Trotter simulation, at the cost of a constant sampling overhead. The key insight is that the Trotter error is itself a coherent dynamics to be reversed, rather than a deviation to be bounded. By identifying the structure of this error in closed form, we carry out that reversal through quasi-probabilistic decompositions. The resulting algorithm, called Probabilistic Trotter Error Reversal (PTER), is unbiased and still improves the gate-count scaling of Suzuki-Trotter formulas while retaining their simplicity. Numerical simulations of a Heisenberg spin chain support the predicted resource advantage already at modest system sizes.

quant-ph↗

arXiv2026

Error-Mitigated Hamiltonian Simulation: Complexity Analysis and Optimization for Near-Term and Early-Fault-Tolerant Quantum Computers

Simulating real-time dynamics under a Hamiltonian is a central goal of quantum information science. While numerous Hamiltonian-simulation quantum algorithms have been proposed, the effects of physical noise have rarely been incorporated into their performance analysis, despite the non-negligible noise levels of quantum devices. We present an end-to-end complexity analysis of noisy Hamiltonian simulation combined with quantum error mitigation (QEM) to answer how many circuit runs are required to reach a given target accuracy. Because the QEM sampling overhead grows exponentially with the circuit depth while the algorithmic error decreases with it, the circuit depth becomes an optimization variable, and we derive an analytic depth-selection rule for two algorithm families. For the order-$k$ Suzuki--Trotter formula, the optimized cost exhibits a critical error $\epsilon_c$, below which the required number of circuit runs grows exponentially. QEM improves the noise dependence of $\epsilon_c$ from sublinear to $k$th-power scaling, an exponent improvement by a factor of $k+1$. For randomized-LCU-based simulation, optimizing the repetition number yields a square-root improvement in the simulation-time dependence of the sampling-overhead exponent over the standard parameter choice. We further quantify the noise-characterization cost required for error mitigation via gate set tomography and the recently proposed space-time noise inversion method, showing that the latter can significantly reduce this cost.

quant-ph↗

arXiv2026

Exchange Monte Carlo for continuous-space Path Integral Monte Carlo simulation

We present a novel Exchange Monte Carlo (EMC) method designed for application in continuous-space Path Integral Monte Carlo (PIMC) simulations at finite temperature. Traditional PIMC methods for bosonic systems suffer from long autocorrelation times, particularly when measuring observables affected by particle permutations, such as the winding number. To address this issue, we introduce an exchange update scheme that facilitates replica transitions between different interaction regimes, significantly accelerating Monte Carlo dynamics-especially for global observables sensitive to permutation effects. Furthermore, we incorporate Stochastic Potential Switching (SPS) to efficiently decompose interactions, substantially enhancing computational efficiency for long-range interatomic pair potentials such as the Lennard-Jones and Aziz potentials.

cond-mat.stat-mech↗

arXiv2025

Accelerated spin-adapted ground state preparation with non-variational quantum algorithms

Various methods have been explored to prepare the spin-adapted ground state, the lowest energy state within the Hilbert space constrained by externally specified values of the total spin magnitude and the spin-$z$ component. In such problem settings, variational and non-variational methods commonly incorporate penalty terms into the original Hamiltonian to enforce the desired constraints. While in variational approaches, only $O(n_{\textrm{spin}}^2)$ measurements are required for the calculation of the penalty terms for the total spin magnitude, non-variational approaches, such as probabilistic imaginary-time evolution or adiabatic time evolution, are expected to be more computationally intensive, requiring $O(n_{\textrm{spin}}^4)$ gates naively. This paper proposes a new procedure based on non-variational quantum algorithms to obtain the spin-adapted ground state. The proposed method consists of two steps: the first step is to prepare a spin-magnitude adapted state and the second step is post-processing for the desired $S_z$. By separating into two steps, the procedure achieves the desired spin-adapted ground state while reducing the number of penalty terms from $O(n_{\textrm{spin}}^4)$ to $O(n_{\textrm{spin}}^2)$. We conducted numerical experiments for spin-1/2 Heisenberg ring models and manganese trimer systems. The results confirmed the effectiveness of our method, demonstrating a significant reduction in gate complexity and validating its practical usefulness.

quant-ph↗

arXiv2025

Embedding of Tree Tensor Networks into Shallow Quantum Circuits

Variational Quantum Algorithms (VQAs) are being highlighted as key quantum algorithms for demonstrating quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) devices, which are limited to executing shallow quantum circuits because of noise. However, the barren plateau problem, where the gradient of the loss function becomes exponentially small with system size, hinders this goal. Recent studies suggest that embedding tensor networks into quantum circuits and initializing the parameters can avoid the barren plateau. Yet, embedding tensor networks into quantum circuits is generally difficult, and methods have been limited to the simplest structure, Matrix Product States (MPSs). This study proposes a method to embed Tree Tensor Networks (TTNs), characterized by their hierarchical structure, into shallow quantum circuits. TTNs are suitable for representing two-dimensional systems and systems with long-range correlations, which MPSs are inadequate for representing. Our numerical results show that embedding TTNs provides better initial quantum circuits than MPS. Additionally, our method has a practical computational complexity, making it applicable to a wide range of TTNs. This study is expected to extend the application of VQAs to two-dimensional systems and those with long-range correlations, which have been challenging to utilize.

quant-ph↗

arXiv2025

Two-color lattice QCD in $(1+1)$ dimensions with Grassmann tensor renormalization group

The $(1+1)$-dimensional two-color lattice QCD is studied with the Grassmann tensor renormalization group. We construct tensor network representations of theories with the staggered fermion and the Wilson fermion and show that Grassmann tensor networks can describe both cases with the same bond dimension. We also propose an efficient initial tensor compression scheme to gauge degrees of freedom. We compute the number density, chiral condensate, and diquark condensate at finite density, employing the staggered fermions. For the theory with Wilson fermion, a critical point in the negative mass region is identified by inspecting the pseudoscalar condensate and the conformal field theory data.

hep-lat↗

arXiv2025

Local Basis Transformation to Mitigate Negative Sign Problems

Quantum Monte Carlo (QMC) methods for the frustrated quantum spin systems occasionally suffer from the negative sign problem, which makes simulations exponentially harder for larger systems at lower temperatures and severely limits QMC's application across a wide range of spin systems. This problem is known to depend on the choice of representation basis. We propose a systematic approach for mitigating the sign problem independent of the given Hamiltonian or lattice structure. We first introduce the concept of negativity to characterize the severity of the negative sign problem. We then demonstrate the existence of a locally defined quantity, the L1 adaptive loss function, which effectively approximates negativity, especially in frustration-free systems. Using the proposed loss function, we demonstrate that optimizing the representation basis can mitigate the negative sign. This is evidenced by several frustration-free models and other important quantum spin systems. Furthermore, we compare the effectiveness of unitary transformations against the standard orthogonal transformation and reveal that unitary transformations can effectively mitigate the sign problem in certain cases.

cond-mat.str-el↗

arXiv2024

LSQCA: Resource-Efficient Load/Store Architecture for Limited-Scale Fault-Tolerant Quantum Computing

Current fault-tolerant quantum computer (FTQC) architectures utilize several encoding techniques to enable reliable logical operations with restricted qubit connectivity. However, such logical operations demand additional memory overhead to ensure fault tolerance. Since the main obstacle to practical quantum computing is the limited qubit count, our primary mission is to design floorplans that can reduce memory overhead without compromising computational capability. Despite extensive efforts to explore FTQC architectures, even the current state-of-the-art floorplan strategy devotes 50% of memory space to this overhead, not to data storage, to ensure unit-time random access to all logical qubits. In this paper, we propose an FTQC architecture based on a novel floorplan strategy, Load/Store Quantum Computer Architecture (LSQCA), which can achieve almost 100% memory density. The idea behind our architecture is to separate all memory regions into small computational space called Computational Registers (CR) and space-efficient memory space called Scan-Access Memory (SAM). We define an instruction set for these abstract structures and provide concrete designs named point-SAM and line-SAM architectures. With this design, we can improve the memory density by allowing variable-latency memory access while concealing the latency with other bottlenecks. We also propose optimization techniques to exploit properties of quantum programs observed in our static analysis, such as access locality in memory reference timestamps. Our numerical results indicate that LSQCA successfully leverages this idea. In a resource-restricted situation, a specific benchmark shows that we can achieve about 90% memory density with 5% increase in the execution time compared to a conventional floorplan, which achieves at most 50% memory density for unit-time random access. Our design ensures broad quantum applicability.

quant-ph↗

arXiv2024

Markov Chain Monte Carlo in Tensor Network Representation

Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the convergence of statistical error. We propose a novel MCMC formulation based on tensor network representations to reduce the population variance and mitigate these issues systematically. By introducing stochastic projectors into the tensor network framework and employing Markov chain sampling, our method eliminates the systematic error associated with low-rank approximation in tensor contraction while maintaining the high accuracy of the tensor network method. We demonstrate the effectiveness of the proposed method on the two-dimensional Ising model, achieving an exponential reduction in statistical error with increasing bond dimension cutoff. Furthermore, we address the sign problem in systems with negative weights, showing significant improvements in average signs as bond dimension cutoff increases. The proposed framework provides a robust solution for accurate statistical estimation in complex systems, paving the way for broader applications in computational physics and beyond.

cond-mat.stat-mech↗

arXiv2024

Grassmann tensor renormalization group approach to $(1+1)$-dimensional two-color lattice QCD at finite density

We construct a Grassmann tensor network representing the partition function of (1+1)-dimensional two-color QCD with staggered fermions. The Grassmann path integral is rewritten as the trace of a Grassmann tensor network by introducing two-component auxiliary Grassmann fields on every edge of the lattice. We introduce an efficient initial tensor compression scheme to reduce the size of initial tensors. The Grassmann bond-weighted tensor renormalization group approach is adopted to evaluate the quark number density, fermion condensate, and diquark condensate at different gauge couplings as a function of the chemical potential. Different transition behavior is observed as the quark mass is varied. We discuss the efficiency of our initial tensor compression scheme and the future application toward the corresponding higher-dimensional models.

hep-lat↗

arXiv2024

Systematic construction of multi-controlled Pauli gate decompositions with optimal $T$-count

Multi-controlled Pauli gates are typical high-level qubit operations that appear in the quantum circuits of various quantum algorithms. We find multi-controlled Pauli gate decompositions with smaller CNOT-count or $T$-depth while keeping the currently known minimum $T$-count. For example, for the CCCZ gate, we find decompositions with CNOT-count 7 or $T$-depth 2 while keeping the $T$-count at the currently known minimum of 6. The discovery of these efficient decompositions improves the computational efficiency of many quantum algorithms. What led to this discovery is the systematic procedure for constructing multi-controlled Pauli gate decompositions. This procedure not only deepens our theoretical understanding of quantum gate decomposition but also leads to more efficient decompositions that have yet to be discovered.

quant-ph↗

arXiv2024

Bayesian inference of general noise-model parameters from the syndrome statistics of surface codes

The performance of error correction in the surface code can be enhanced by leveraging the knowledge of the noise model for physical qubits. To provide accurate noise information to the decoder in parallel with quantum computation, an adaptive estimation of the noise model based on syndrome measurement statistics is an effective approach. While noise model estimation based on syndrome measurement statistics is well-established for Pauli noise, it remains unexplored for more complex and realistic scenarios such as amplitude damping which cannot be represented as a Pauli channel. In this paper, we propose Bayesian inference methods for general noise models, integrating a tensor network simulator of surface code, which can efficiently simulate various noise models, with Monte Carlo sampling techniques. For stationary noise, we propose a method based on the Markov chain Monte Carlo. For time-varying noise, which is a more realistic scenario, we introduce another method based on the sequential Monte Carlo. We present numerical results of applying our proposed methods to various noise models, such as static, time-varying, and nonuniform cases, and evaluate their performance in detail.

quant-ph↗

arXiv2024

Simplification of tensor updates toward performance-complexity balanced quantum computer simulation

Matrix Product States (MPS) provide a powerful framework for simulating quantum circuits. In practical simulations, tensor updates are typically performed in the canonical form (CF), which corresponds to the Schmidt decomposition and improves approximation accuracy. However, maintaining the canonical form introduces significant computational overhead. An alternative approach, known as the Simple Update (SU), does not enforce the Schmidt decomposition and is expected to reduce computational complexity. In this work, we systematically compare the performance and computational cost of SU and CF in quantum circuit simulations. We benchmark both methods on highly entangled circuits and on a QASM benchmark suite covering a wide range of circuit types. Our results show that SU achieves accuracy comparable to CF while reducing computational complexity, indicating that SU provides an efficient alternative for practical quantum circuit simulations.

quant-ph↗

arXiv2023

Update of $\mathcal{H}\Phi$: Newly added functions and methods in versions 2 and 3

$\mathcal{H}\Phi$ [$aitch$-$phi$] is an open-source software package of numerically exact and stochastic calculations for a wide range of quantum many-body systems. In this paper, we present the newly added functions and the implemented methods in vers. 2 and 3. In ver. 2, we implement spectrum calculations by the shifted Krylov method, and low-energy excited state calculations by the locally optimal blocking preconditioned conjugate gradient (LOBPCG) method. In ver. 3, we implement the full diagonalization method using ScaLAPACK and GPGPU computing via MAGMA. We also implement a real-time evolution method and the canonical thermal pure quantum (cTPQ) state method for finite-temperature calculations. The Wannier90 format for specifying the Hamiltonians is also implemented. Using the Wannier90 format, it is possible to perform the calculations for the $ab$ $initio$ low-energy effective Hamiltonians of solids obtained by the open-source software RESPACK. We also update Standard mode $\unicode{x2014}$simplified input format in $\mathcal{H}\Phi$$\unicode{x2014}$ to use these functions and methods. We explain the basics of the implemented methods and how to use them.

cond-mat.str-el↗

arXiv2023

Universal Scaling Laws of Absorbing Phase Transitions in Artificial Deep Neural Networks

We demonstrate that conventional artificial deep neural networks operating near the phase boundary of the signal propagation dynamics, also known as the edge of chaos, exhibit universal scaling laws of absorbing phase transitions in non-equilibrium statistical mechanics. We exploit the fully deterministic nature of the propagation dynamics to elucidate an analogy between a signal collapse in the neural networks and an absorbing state (a state that the system can enter but cannot escape from). Our numerical results indicate that the multilayer perceptrons and the convolutional neural networks belong to the mean-field and the directed percolation universality classes, respectively. Also, the finite-size scaling is successfully applied, suggesting a potential connection to the depth-width trade-off in deep learning. Furthermore, our analysis of the training dynamics under the gradient descent reveals that hyperparameter tuning to the phase boundary is necessary but insufficient for achieving optimal generalization in deep networks. Remarkably, nonuniversal metric factors associated with the scaling laws are shown to play a significant role in concretizing the above observations. These findings highlight the usefulness of the notion of criticality for analyzing the behavior of artificial deep neural networks and offer new insights toward a unified understanding of the essential relationship between criticality and intelligence.

stat.ML↗

arXiv2023

Stochastic parameter optimization analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain

The quantum phase transition of the one-dimensional long-range transverse-field Ising model is explored by combining the quantum Monte Carlo method and stochastic parameter optimization, specifically achieved by tuning correlation ratios so that space and imaginary time are isotropic. In our simulations, the simulator automatically determines the parameters to sample from, even without prior knowledge of the critical point and universality class. The leading-order finite-size corrections are eliminated by comparing two systems with different sizes; this procedure is also performed automatically. Varying the decay exponent of the long-range interaction, $\sigma$, we investigate $\sigma$-dependence of the dynamical exponent and the other critical exponents precisely in the mean-field, non-universal, and two-dimensional classical Ising universality regimes. We successfully obtained numerical evidence supporting $\sigma = 7/4$ as the universality boundary between the latter two.

cond-mat.stat-mech↗