Matchgate circuit representation of fermionic Gaussian states: optimal preparation, approximation, and classical simulation

• URL: http://arxiv.org/abs/2603.05675v1
• Date: Thu, 05 Mar 2026 21:06:06 GMT
• Title: Matchgate circuit representation of fermionic Gaussian states: optimal preparation, approximation, and classical simulation
• Abstract summary: We address the question of how to optimally create such states when using matchgate circuits acting on product states.<n>We present explicit algorithms whose constructions saturate these bounds, thereby proving their optimality.<n>Our results have direct applications to (approximate) state preparation and to disentangling procedures.
• Score: 0.006396529661340102
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Fermionic Gaussian states (FGSs) and the associated matchgate circuits play a central role in quantum information theory and condensed matter physics. Despite being possibly highly entangled, they can still be efficiently simulated on classical computers. We address the question of how to optimally create such states when using matchgate circuits acting on product states. To this end, we derive lower bounds on the number of gates required to prepare an arbitrary pure FGS: We establish both an asymptotic bound on the minimal gate count over general nearest-neighbor gate sets and an exact bound for circuits composed solely of matchgates. We present explicit algorithms whose constructions saturate these bounds, thereby proving their optimality. We furthermore determine when an FGS can be prepared with a circuit of any given depth, and derive an algorithm that constructs such a circuit whenever this condition is satisfied, either exactly or approximately. Our results have direct applications to (approximate) state preparation and to disentangling procedures. Moreover, we introduce a new classical simulation algorithm for matchgate circuits, based entirely on manipulating the generating circuits of the FGSs. Finally, we briefly study an extension of our framework for $t$-doped Gaussian states and circuits.

Related papers

• Optimization and Synthesis of Quantum Circuits with Global Gates [41.99844472131922]
  We use global interactions, such as the Global Molmer-Sorensen gate present in ion trap hardware, to optimize and synthesize quantum circuits.<n>The algorithm is based on the ZX-calculus and uses a specialized circuit extraction routine that groups entangling gates into Global MolmerSorensen gates.<n>We benchmark the algorithm in a variety of circuits, and show how it improves their performance under state-of-the-art hardware considerations.
  arXiv  Detail & Related papers  (2025-07-28T10:25:31Z)
• 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)
• 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)
• Near-optimal quantum circuit construction via Cartan decomposition [4.900041609957432]
  We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation.
  arXiv  Detail & Related papers  (2022-12-25T17:01:13Z)
• Automatic and effective discovery of quantum kernels [41.61572387137452]
  Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data.<n>We present an approach to this problem, which employs optimization techniques, similar to those used in neural architecture search and AutoML.<n>The results obtained by testing our approach on a high-energy physics problem demonstrate that, in the best-case scenario, we can either match or improve testing accuracy with respect to the manual design approach.
  arXiv  Detail & Related papers  (2022-09-22T16:42:14Z)
• Approximate encoding of quantum states using shallow circuits [0.0]
  A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. Here, we aim at creating an approximate encoding of the target state using a limited number of gates. Our work offers a universal method to prepare target states using local gates and represents a significant improvement over known strategies.
  arXiv  Detail & Related papers  (2022-06-30T18:00:04Z)
• Adaptive constant-depth circuits for manipulating non-abelian anyons [65.62256987706128]
  Kitaev's quantum double model based on a finite group $G$. We describe quantum circuits for (a) preparation of the ground state, (b) creation of anyon pairs separated by an arbitrary distance, and (c) non-destructive topological charge measurement.
  arXiv  Detail & Related papers  (2022-05-04T08:10:36Z)
• Hybrid quantum-classical circuit simplification with the ZX-calculus [0.0]
  This work uses an extension of the formal graphical ZX-calculus called ZX-ground as an intermediary representation of the hybrid circuits. We derive a number of gFlow-preserving optimization rules for ZX-ground diagrams that reduce the size of the graph. We present a general procedure for detecting segments of circuit-like ZX-ground diagrams which can be implemented with classical gates in the extracted circuit.
  arXiv  Detail & Related papers  (2021-09-13T15:45:56Z)
• 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)
• Random quantum circuits anti-concentrate in log depth [118.18170052022323]
  We study the number of gates needed for the distribution over measurement outcomes for typical circuit instances to be anti-concentrated. Our definition of anti-concentration is that the expected collision probability is only a constant factor larger than if the distribution were uniform. In both the case where the gates are nearest-neighbor on a 1D ring and the case where gates are long-range, we show $O(n log(n)) gates are also sufficient.
  arXiv  Detail & Related papers  (2020-11-24T18:44:57Z)
• Local optimization on pure Gaussian state manifolds [63.76263875368856]
  We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm. The method is based on notions of descent gradient attuned to the local geometry. We use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.
  arXiv  Detail & Related papers  (2020-09-24T18:00:36Z)
• Machine Learning Optimization of Quantum Circuit Layouts [63.55764634492974]
  We introduce a quantum circuit mapping, QXX, and its machine learning version, QXX-MLP. The latter infers automatically the optimal QXX parameter values such that the layed out circuit has a reduced depth. We present empiric evidence for the feasibility of learning the layout method using approximation.
  arXiv  Detail & Related papers  (2020-07-29T05:26:19Z)
• Efficient classical simulation of random shallow 2D quantum circuits [104.50546079040298]
  Random quantum circuits are commonly viewed as hard to simulate classically. We show that approximate simulation of typical instances is almost as hard as exact simulation. We also conjecture that sufficiently shallow random circuits are efficiently simulable more generally.
  arXiv  Detail & Related papers  (2019-12-31T19:00:00Z)

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.