arXiv subjects

Peter D Drummond

Publications and source records attributed to Peter D Drummond.

8 recordsLinked to original sources

arXiv2026

Quest for quantum advantage: Monte Carlo wave-function simulations of the Coherent Ising Machine

The Coherent Ising Machine (CIM) is a quantum network of optical parametric oscillators (OPOs) intended to find ground states of the Ising model. This is an NP-hard problem, related to several important minimization problems, including the max-cut graph problem. In order to enhance its potential performance, we analyze the coherent coupling strategy for the CIM in a highly quantum regime. To explore this limit, without assuming gaussianity, we employ accurate numerical simulations. Due to the inherent complexity of the system, the maximum network size is limited. While master equation methods can be used, their scalability diminishes rapidly for larger systems. Instead, we use Monte Carlo wave-function methods, which scale as the wave-function dimension, and use large numbers of samples. These simulations involve Hilbert spaces exceeding $10^{7}$ dimensions. To evaluate success probabilities, we use quadrature probabilities. We demonstrate the potential for quantum computational advantage by reducing the time required to reach maximum success probability in a low-dissipation regime enabled by initial quantum superpositions and entanglement. Furthermore, we demonstrate that tailored time-dependent couplings can amplify these quantum effects. Comparisons with classical CIM models give evidence that quantum tunneling effects in this strong coupling limit can overcome trapping in false minima. This can greatly increase success rates, indicating a potential for quantum advantage. Finally, we perform a coherence analysis based on the state purity to examine the role of quantum coherence in CIM performance and to determine how state purity correlates with improved optimization outcomes.

quant-ph↗

arXiv2025

Complexity order of multiple resource algorithms

Algorithmic efficiency is essential to reducing energy and time usage for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random ensemble competes with the time-step. We define the complexity order of an algorithm needing multiple resources as the exponent of inverse total error with respect to the total resources used. The optimum order is predicted for independent, factorable resources. We show that it equals the inverse sum of the inverse resource orders. This is applied to computing averages in a stochastic differential equation. We treat numerical examples for multiple different algorithms and for stochastic partial differential equations, all giving quantitative results in excellent agreement with our more general analytic theory.

physics.comp-ph↗

arXiv2022

The coherent Ising machine with quantum feedback: the total and conditional master equation methods

We give a detailed theoretical derivation of the quantum master equation for the coherent Ising machine. This is a quantum computational network with feedback, that solves NP hard combinatoric problems, including the traveling salesman problem and various extensions and analogs. There are two types of master equation that are obtained, either conditional on the feedback current or unconditional. We show that both types can be accurately simulated in a scalable way using stochastic equations in the positive-P phase-space representation. This depends on the nonlinearity present, and we use parameter values that are typical of current experiments. However, while the two approaches are in excellent agreement, they are not equivalent with regard to efficiency. We find that unconditional simulation has much greater efficiency, and is scalable to larger sizes. This is a case where too much knowledge is a dangerous thing. Conditioning the simulations on the feedback current is not essential to determining the success probability, but it greatly increases the computational complexity. To illustrate the speed improvements obtained with the unconditional approach, we carry out full quantum simulations of the quantum master equation with up to 1000 nodes.

quant-ph↗

arXiv2022

Phase-space simulations of feedback coherent Ising machines

A new technique is demonstrated for carrying out exact positive-P phase-space simulations of the coherent Ising machine quantum computer. By suitable design of the coupling matrix, general hard optimization problems can be solved. Here, computational quantum simulations of a feedback type of photonic parametric network are carried out, which is the implementation of the coherent Ising machine. Results for success rates are obtained using this scalable phase-space algorithm for quantum simulations of quantum feedback devices.

quant-ph↗

arXiv2021

Objective quantum fields, retrocausality and ontology

We compare different approaches to quantum ontology. In particular, we discuss an interpretation of quantum mechanics that we call objective quantum field theory (OQFT), which involves retrocausal fields. Here, objective implies the existence of fields independent of an observer, but not that the results of conjugate measurements are predetermined: the theory is contextual. The ideas and analyses of Einstein and Bohr through to more recent approaches to objective realism are discussed. We briefly describe measurement induced projections, the guided wave interpretation, many-universes, consistent histories, and modal theories. These earlier interpretations are compared with OQFT. We argue that this approach is compatible both with Bohr's quantum complementarity, and Einstein's objective realism.

quant-ph↗

arXiv2021

Interacting fermion dynamics in Majorana phase-space

The problem of fermion dynamics is studied using the Q-function for fermions. This is a probabilistic phase-space representation, which we express using Majorana operators, so that the phase-space variable is a real antisymmetric matrix. We consider a general interaction Hamiltonian with four Majorana operators and arbitrary properties. Our model includes the Majorana Hubbard and Fermi Hubbard Hamiltonians, as well as general quantum field theories of interacting fermions. Using the Majorana Q-function we derive a generalized Fokker-Planck equation, with results for the drift and diffusion terms. The diffusion term is proved to be traceless, which gives a dynamical interpretation as a forwards-backwards stochastic process. This approach leads to a model of quantum measurement in terms of an ontology with real vacuum fluctuations.

quant-ph↗

arXiv2018

Quantum software for linear photonic simulations

The search for new, application-specific quantum computers designed to outperform any classical computer is driven by the ending of Moore's law and the quantum advantages potentially obtainable. Photonic networks are promising examples, with experimental demonstrations and potential for obtaining a quantum computer to solve problems believed classically impossible. This introduces a challenge: how does one design or understand such photonic networks? We develop novel complex phase-space software for simulating these photonic networks, and apply this to boson sampling experiments. Our techniques give sampling errors orders of magnitude lower than experimental measurements of correlations, for the same number of samples. We show that these techniques remove systematic errors in previous algorithms for estimating correlations, with order of magnitude improvements in errors in some cases. In addition to that, we obtain a scalable channel-combination strategy for assessment of boson sampling devices.

quant-ph↗

arXiv2011

High temperature thermodynamics of strongly interacting s-wave and p-wave Fermi gases in a harmonic trap

We theoretically investigate the high-temperature thermodynamics of a strongly interacting trapped Fermi gas near either s-wave or p-wave Feshbach resonances, using a second order quantum virial expansion. The second virial coefficient is calculated based on the energy spectrum of two interacting fermions in a harmonic trap. We consider both isotropic and anisotropic harmonic potentials. For the two-fermion interaction, either s-wave or p-wave, we use a pseudopotential parametrized by a scattering length and an effective range. This turns out to be the simplest way of encoding the energy dependence of the low-energy scattering amplitude or phase shift. This treatment of the pseudopotential can be easily generalized to higher partial-wave interactions. We discuss how the second virial coefficient and thermodynamics are affected by the existence of these finite-range interaction effects. The virial expansion result for a strongly interacting s -wave Fermi gas has already been proved very useful. In the case of p-wave interactions, our results for the high-temperature equation of state are applicable to future high-precision thermodynamic measurements for a spin-polarized Fermi gas near a p-wave Feshbach resonance.

cond-mat.quant-gas↗