Classical simulation of circuits with realistic odd-dimensional Gottesman-Kitaev-Preskill states

• URL: http://arxiv.org/abs/2412.13136v2
• Date: Tue, 14 Oct 2025 14:18:59 GMT
• Title: Classical simulation of circuits with realistic odd-dimensional Gottesman-Kitaev-Preskill states
• Authors: Cameron Calcluth, Oliver Hahn, Juani Bermejo-Vega, Alessandro Ferraro, Giulia Ferrini,
• Abstract summary: We propose an algorithm to simulate circuits with encoded Gottesman-Kitaev-Preskill (GKP) states.<n>Our approach is tailored to be especially effective in the most challenging but practically relevant regime.
• Score: 37.54293136411193
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Classically simulating circuits with bosonic codes is challenging due to the prohibitive cost of simulating quantum systems with many, possibly infinite, energy levels. We propose an algorithm to simulate circuits with encoded Gottesman-Kitaev-Preskill (GKP) states, specifically for odd-dimensional encoded qudits. Our approach is tailored to be especially effective in the most challenging but practically relevant regime, where the codeword states exhibit high (but finite) squeezing. Our algorithm leverages the Zak-Gross Wigner function introduced by J. Davis et al. [arXiv:2407.18394], which represents infinitely squeezed encoded stabilizer states positively. The runtime of the algorithm scales with the negativity of the Wigner function, allowing for efficient simulation of certain large-scale circuits - namely, input stabilizer GKP states undergoing generalized GKP-encoded Clifford operations followed by modular measurements - with a high degree of squeezing. For stabilizer GKP states exhibiting 12 dB of squeezing, our algorithm can simulate circuits with up to 1,000 modes with less than double the number of samples required for a single input mode, in stark contrast to existing simulators. Therefore, this approach holds significant potential for benchmarking early implementations of quantum computing architectures utilizing bosonic codes.

Related papers

• Enhancing classical simulation with noisy quantum devices [11.834807045442057]
  We show that noisy quantum devices can be leveraged as computational resources to enhance the classical simulation of quantum circuits.<n>We introduce the Noisy-device-enhanced Classical Simulation (NDE-CS) protocol, which improves stabilizer-based Monte Carlo simulation methods.<n>NDE-CS achieves orders-of-magnitude reductions in sampling cost compared to the underlying purely classical Monte Carlo approaches.
  arXiv  Detail & Related papers  (2026-01-13T18:01:46Z)
• Classical Simulations of Low Magic Quantum Dynamics [0.1666604949258699]
  We develop algorithms for adaptive quantum circuits that produce states with low levels of magic.<n>These algorithms are particularly well-suited to circuits with high rates of Pauli measurements.<n>We study the dynamics of all-to-all monitored quantum circuits with a sub-extensive rate of T-gates per unit of circuit depth.
  arXiv  Detail & Related papers  (2025-08-27T20:17:15Z)
• Scalable Simulation of Fermionic Encoding Performance on Noisy Quantum Computers [0.0]
  We study the performance of a local encoding known as the Derby-Klassen encoding.<n>We find that the high sampling requirements of postselection methods with the Derby-Klassen encoding pose a limitation to its applicability in near-term devices.
  arXiv  Detail & Related papers  (2025-06-06T18:00:01Z)
• Quantum Simulation-Based Optimization of a Cooling System [0.0]
  Quantum algorithms promise up to exponential speedups for specific tasks relevant to numerical simulations. However, these advantages quickly vanish when considering data input and output on quantum computers. The recently introduced Quantum Simulation-Based Optimization (QuSO) treats simulations as subproblems within a larger optimization.
  arXiv  Detail & Related papers  (2025-04-21T21:58:21Z)
• Practical Application of the Quantum Carleman Lattice Boltzmann Method in Industrial CFD Simulations [44.99833362998488]
  This work presents a practical numerical assessment of a hybrid quantum-classical approach to CFD based on the Lattice Boltzmann Method (LBM)<n>We evaluate this method on three benchmark cases featuring different boundary conditions, periodic, bounceback, and moving wall.<n>Our results confirm the validity of the approach, achieving median error fidelities on the order of $10-3$ and success probabilities sufficient for practical quantum state sampling.
  arXiv  Detail & Related papers  (2025-04-17T15:41:48Z)
• Learning State Preparation Circuits for Quantum Phases of Matter [0.294944680995069]
  We introduce a flexible and efficient framework for obtaining a state preparation circuit for a large class of many-body ground states. We use a variant of the quantum Markov chain condition that remains robust against constant-depth circuits.
  arXiv  Detail & Related papers  (2024-10-31T01:10:46Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [62.46800898243033]
  Recent progress in quantum learning theory prompts a question: can linear properties of a large-qubit circuit be efficiently learned from measurement data generated by varying classical inputs?<n>We prove that the sample complexity scaling linearly in $d$ is required to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d.<n>We propose a kernel-based method leveraging classical shadows and truncated trigonometric expansions, enabling a controllable trade-off between prediction accuracy and computational overhead.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Compact quantum algorithms for time-dependent differential equations [0.0]
  We build on an idea based on linear combination of unitaries to simulate non-unitary, non-Hermitian quantum systems. We generate hybrid quantum-classical algorithms that efficiently perform iterative matrix-vector multiplication and matrix inversion operations.
  arXiv  Detail & Related papers  (2024-05-16T02:14:58Z)
• Classical simulation of non-Gaussian bosonic circuits [0.4972323953932129]
  We propose efficient classical algorithms to simulate bosonic linear optics circuits applied to superpositions of Gaussian states. We present an exact simulation algorithm whose runtime is in the number of modes and the size of the circuit. We also present a faster approximate randomized algorithm whose runtime is quadratic in this number.
  arXiv  Detail & Related papers  (2024-03-27T23:52:35Z)
• Simulating Quantum Circuits by Model Counting [0.0]
  We show for the first time that a strong simulation of universal quantum circuits can be efficiently tackled through weighted model counting. Our work paves the way to apply the existing array of powerful classical reasoning tools to realize efficient quantum circuit compilation.
  arXiv  Detail & Related papers  (2024-03-11T22:40:15Z)
• Bosonic Pauli+: Efficient Simulation of Concatenated Gottesman-Kitaev-Preskill Codes [0.4893345190925179]
  A promising route towards fault-tolerant quantum error correction is the concatenation of a Gottesman-Kitaev-Preskill code with a qubit code. Development of such codes requires simulation tools which realistically model noise, while being able to simulate the dynamics of many modes. Here, we introduce the Bosonic Pauli+ model (BP+), which can be simulated efficiently for a large number of modes, while capturing rich dynamics in the bosonic multi-mode Hilbert space.
  arXiv  Detail & Related papers  (2024-02-14T17:28:10Z)
• Deep Quantum Circuit Simulations of Low-Energy Nuclear States [51.823503818486394]
  We present advances in high-performance numerical simulations of deep quantum circuits. circuits up to 21 qubits and more than 115,000,000 gates can be efficiently simulated.
  arXiv  Detail & Related papers  (2023-10-26T19:10:58Z)
• Scalable noisy quantum circuits for biased-noise qubits [37.69303106863453]
  We consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. For realistic noise models, phase-flip will not be negligible, but in the Pauli-Twirling approximation, we show that our benchmark could check the correctness of circuits containing up to $106$ gates.
  arXiv  Detail & Related papers  (2023-05-03T11:27:50Z)
• Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits [68.8204255655161]
  We study the classical simulatability of Gottesman-Kitaev-Preskill (GKP) states in combination with arbitrary displacements, a large set of symplectic operations and homodyne measurements. For these types of circuits, neither continuous-variable theorems based on the non-negativity of quasi-probability distributions nor discrete-variable theorems can be employed to assess the simulatability.
  arXiv  Detail & Related papers  (2022-03-21T17:57:02Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)
• Efficient simulatability of continuous-variable circuits with large Wigner negativity [62.997667081978825]
  Wigner negativity is known to be a necessary resource for computational advantage in several quantum-computing architectures. We identify vast families of circuits that display large, possibly unbounded, Wigner negativity, and yet are classically efficiently simulatable. We derive our results by establishing a link between the simulatability of high-dimensional discrete-variable quantum circuits and bosonic codes.
  arXiv  Detail & Related papers  (2020-05-25T11:03:42Z)
• 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.