Related papers: Classical Ising model test for quantum circuits
We contribute to the mathematical theory of the design of low temperature Ising machines, a type of experimental probabilistic computing device implementing the Ising model. Encoding the output of a function in the ground state of a…
A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level…
We introduce a novel method for strong classical simulation of quantum circuits based on optimally k-partitioning ZX-diagrams, reducing each part individually, and then efficiently cross-referencing their results to conclude the overall…
A well known theorem due to Kasteleyn states that the partition function of an Ising model on an arbitrary planar graph can be represented as the Pfaffian of a skew-symmetric matrix associated to the graph. This results both embodies the…
One of the core research questions in the theory of quantum computing is to find out to what precise extent the classical simulation of a noisy quantum circuits is possible and where potential quantum advantages can set in. In this work, we…
Many quantum algorithms make use of oracles which evaluate classical functions on a superposition of inputs. In order to facilitate implementation, testing, and resource estimation of such algorithms, we present quantum circuits for…
We establish a classical heuristic algorithm for exactly computing quantum probability amplitudes. Our algorithm is based on mapping output probability amplitudes of quantum circuits to evaluations of the Tutte polynomial of graphic…
This paper presents an alternative proof of the connection between the partition function of the Ising model on a finite graph $G$ and the set of non-backtracking walks on $G$. The techniques used also give formulas for spin-spin…
With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its…
Quantum computers must meet extremely stringent qualitative and quantitative requirements on their qubits in order to solve real-life problems. Quantum circuit fragmentation techniques divide a large quantum circuit into a number of…
We introduce a distributed classical simulation algorithm for general quantum circuits, and present numerical results for calculating the output probabilities of universal random circuits. We find that we can simulate more qubits to greater…
We present a polynomial-time classical algorithm for estimating expectation values of arbitrary observables on typical quantum circuits under any incoherent local noise, including non-unital or dephasing. Although previous research…
We study Bosonic representation of spin Ising model with the application of simulating two level systems using continuous variable quantum processors. We decompose the time evolution of spin systems into a sequence of continuous variable…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
In a recent work arXiv:2201.07655v2 we showed that there is a constant $\lambda >0$ such that it is possible to efficiently classically simulate a quantum system in which (i) qudits are placed on the nodes of a graph, (ii) each qudit…
We demonstrate a method of exploring the quantum critical point of the Ising universality class using unitary maps that have recently been demonstrated in ion trap quantum gates. We reverse the idea with which Feynman conceived quantum…
We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g. the…
A seminal technique of theoretical physics called Wick's theorem interprets the Gaussian matrix integral of the products of the trace of powers of Hermitian matrices as the number of labelled maps with a given degree sequence, sorted by…
Approximating the partition function of the ferromagnetic Ising model with general external fields is known to be #BIS-hard in the worst case, even for bounded-degree graphs, and it is widely believed that no polynomial-time approximation…
We propose an approach to generative quantum machine learning that overcomes the fundamental scaling issues of variational quantum circuits. The core idea is to use a class of generative models based on instantaneous quantum polynomial…