Optimal and improved gate decompositions for accelerated classical simulation of near-Gaussian fermionic circuits

• URL: http://arxiv.org/abs/2603.18869v1
• Date: Thu, 19 Mar 2026 13:13:41 GMT
• Title: Optimal and improved gate decompositions for accelerated classical simulation of near-Gaussian fermionic circuits
• Abstract summary: We derive analytic decompositions for key non-Gaussian gates and channels.<n>We show that Pauli noise can reduce the effective extent of non-Gaussian rotation gates, but that fermionic magic is substantially more robust to such noise than stabilizer magic.
• Score: 0.13764085113103217
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Fermionic Gaussian circuits can be simulated efficiently on a classical computer, but become universal when supplemented with non-Gaussian operations. Similar to stabilizer circuits augmented with non-stabilizer resources, these non-Gaussian circuits can be simulated classically using rank- or extent-based methods. These methods decompose non-Gaussian states or operations into Gaussian ones, with runtimes that scale polynomially with measures of non-Gaussianity such as the rank and the extent -- quantities that typically grow exponentially with the number of non-Gaussian resources. Current fermionic rank- and extent-based simulators are limited to Gaussian circuits with magic-state injection. Extending them to mixed states and non-unitary channels has been hindered by the lack of known extent-optimized decompositions for physically relevant gates and noisy channels. In this work, we address this gap. First, we derive analytic decompositions for key non-Gaussian gates and channels, including decompositions for arbitrary two-qubit fermionic gates which are provably optimal for diagonal gates or those acting on Jordan-Wigner-adjacent qubit pairs. Second, we show that stochastic Pauli noise can reduce the effective extent of non-Gaussian rotation gates, but that fermionic magic is substantially more robust to such noise than stabilizer magic. Finally, we demonstrate how these decompositions can accelerate classical sampling from the output distribution of a quantum circuit. This involves a generalization of existing sparsification methods, previously limited to convex-unitary channels, to circuits involving intermediate measurements and feed-forward. Our decompositions also yield speedups for emulating noisy Pauli rotations with quasiprobability simulators in the large-angle/arbitrary-strength-noise and small-angle/low-noise parameter regimes.

Related papers

• Conditional-squeezing gate in superconducting circuits [41.99844472131922]
  We present an implementation of a conditional-squeezing gate that squeezes a SQUID-terminated resonator mode along a direction determined by the state of a dispersively coupled qubit.<n>We use the gate to encode an arbitrary qubit state into superpositions of single- and two-mode squeezed states of the resonator.
  arXiv  Detail & Related papers  (2026-09-09T16:16:48Z)
• Noisy quantum circuit simulation with the tensor jump method [4.323508970487569]
  We introduce a variance-aware tensor network framework that combines the tensor jump method with local TDVP gate evolution on matrix product states and sparse Pauli-Lindblad hardware noise models.<n>We demonstrate accurate, scalable noisy-circuit simulation on a 25-qubit noisy XY quench and IBM's 127-qubit kicked-Ising benchmark with long-range depolarizing noise.
  arXiv  Detail & Related papers  (2026-07-01T18:00:01Z)
• Hybrid Gaussian-exponential zero-noise extrapolation for periodic circuits [2.932287734903261]
  We introduce a hybrid Gaussian-exponential extrapolation scheme tailored for quantum circuits with periodic structure.<n>For moderate to large circuit depths, the hybrid model yields measurable reductions in bias relative to previous extrapolation variants.
  arXiv  Detail & Related papers  (2026-05-28T02:01:03Z)
• Deterministic generation of grid states with programmable nonlinear bosonic circuits [37.149543017244234]
  We show how to generate bosonic grid states using programmable nonlinear bosonic circuits composed solely of squeezing, displacement, and Kerr operations.<n>Our results establish programmable nonlinear bosonic circuits as a viable route towards the generation of scalable bosonic quantum error-correcting states.
  arXiv  Detail & Related papers  (2026-04-23T16:16:28Z)
• Efficient simulation of low-entanglement bosonic Gaussian states in polynomial time [21.876059213677966]
  We present an efficient algorithm that converts pure bosonic Gaussian states into matrix product states (MPSs)<n>Our method combines a Gaussian singular value decomposition with a projected-creation-operator mapping that constructs local MPS tensors without computing hafnians.<n>The method provides a scalable classical simulation framework for bosonic Gaussian states with limited entanglement and extends the applicability of MPS-based methods to a broad range of bosonic systems.
  arXiv  Detail & Related papers  (2025-12-11T13:51:03Z)
• Emergence of Generic Entanglement Structure in Doped Matchgate Circuits [37.742691394718086]
  We show how doping random circuits with non-Gaussian resources restores entanglement structures of typical dynamics.<n>Our findings bridge the dynamics of free and interacting fermionic systems, identifying non-Gaussianity as a key resource driving the emergence of non-integrable behavior.
  arXiv  Detail & Related papers  (2025-07-16T18:00:02Z)
• Pauli path simulations of noisy quantum circuits beyond average case [0.3277163122167433]
  For random quantum circuits on $n$ qubits of depth, the task of sampling from the output state can be efficiently performed classically using a Pauli path method.<n>We derive sufficient conditions for simulatability in terms of noise rate and the fraction of gates that are T gates, and show that if noise is introduced at a faster rate, the simulation becomes classically easy.
  arXiv  Detail & Related papers  (2024-07-22T21:58:37Z)
• Solving High Frequency and Multi-Scale PDEs with Gaussian Processes [18.190228010565367]
  PINNs often struggle to solve high-frequency and multi-scale PDEs. We resort to the Gaussian process (GP) framework to solve this problem. We use Kronecker product properties and multilinear algebra to promote computational efficiency and scalability.
  arXiv  Detail & Related papers  (2023-11-08T05:26:58Z)
• A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits [37.84307089310829]
  Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit. Despite their promise, the trainability of these algorithms is hindered by barren plateaus. We present a general Lie algebra that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits.
  arXiv  Detail & Related papers  (2023-09-17T18:14:10Z)
• Classical simulation of non-Gaussian fermionic circuits [0.4972323953932129]
  We argue that this problem is analogous to that of simulating Clifford circuits with non-stabilizer initial states. Our construction is based on an extension of the covariance matrix formalism which permits to efficiently track relative phases in superpositions of Gaussian states. It yields simulation algorithms with complexity in the number of fermions, the desired accuracy, and certain quantities capturing the degree of non-Gaussianity of the initial state.
  arXiv  Detail & Related papers  (2023-07-24T16:12:29Z)
• Improved simulation of quantum circuits dominated by free fermionic operations [1.024113475677323]
  We present an algorithm for simulating universal quantum circuits composed of "free" nearest-neighbour matchgates or equivalently fermionic-linear-optical (FLO) gates, and "resourceful" non-Gaussian gates.<n>Our key contribution is the development of a novel phase-sensitive algorithm for simulating FLO circuits.<n>For a quantum circuit containing arbitrary FLO unitaries and $k$ controlled-Z gates, we obtain an exponential improvement $k$O(4.5k)$O over the prior state-of-the-art.
  arXiv  Detail & Related papers  (2023-07-24T11:36:28Z)
• High-Order Qubit Dephasing at Sweet Spots by Non-Gaussian Fluctuators: Symmetry Breaking and Floquet Protection [55.41644538483948]
  We study the qubit dephasing caused by the non-Gaussian fluctuators. We predict a symmetry-breaking effect that is unique to the non-Gaussian noise.
  arXiv  Detail & Related papers  (2022-06-06T18:02:38Z)
• Accurate methods for the analysis of strong-drive effects in parametric gates [94.70553167084388]
  We show how to efficiently extract gate parameters using exact numerics and a perturbative analytical approach. We identify optimal regimes of operation for different types of gates including $i$SWAP, controlled-Z, and CNOT.
  arXiv  Detail & Related papers  (2021-07-06T02:02:54Z)
• Hartree-Fock on a superconducting qubit quantum computer [30.152226344347064]
  Here, we perform a series of quantum simulations of chemistry the largest of which involved a dozen qubits, 78 two-qubit gates, and 114 one-qubit gates. We model the binding energy of $rm H_6$, $rm H_8$, $rm H_10$ and $rm H_12$ chains as well as the isomerization of diazene. We also demonstrate error-mitigation strategies based on $N$-representability which dramatically improve the effective fidelity of our experiments.
  arXiv  Detail & Related papers  (2020-04-08T18:00:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.