Related papers: Efficient classical simulation of random shallow 2…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
Randomized algorithms are crucial subroutines in quantum computing, but the requirement to execute many types of circuits on a real quantum device has been challenging to their extensive implementation. In this study, we propose an…
Recent work of Bravyi et al. and follow-up work by Bene Watts et al. demonstrates a quantum advantage for shallow circuits: constant-depth quantum circuits can perform a task which constant-depth classical (i.e., AC$^0$) circuits cannot.…
Classical simulation of noisy quantum circuits is essential for understanding quantum computing experiments. It enables scalable error characterization, analysis of how noise impacts quantum algorithms, and optimized implementations of…
Understanding the boundary between classical simulatability and the power of quantum computation is a fascinating topic. Direct simulation of noisy quantum computation requires solving an open quantum many-body system, which is very costly.…
The study of quantum circuits composed of commuting gates is particularly useful to understand the delicate boundary between quantum and classical computation. Indeed, while being a restricted class, commuting circuits exhibit genuine…
We consider recent works on the simulation of quantum circuits using the formalism of matrix product states and the formalism of contracting tensor networks. We provide simplified direct proofs of many of these results, extending an…
Let G(A,B) denote the 2-qubit gate which acts as the 1-qubit SU(2) gates A and B in the even and odd parity subspaces respectively, of two qubits. Using a Clifford algebra formalism we show that arbitrary uniform families of circuits of…
An $n$-qubit quantum circuit is said to be peaked if it has an output probability that is at least inverse-polynomially large as a function of $n$. We describe a classical algorithm with quasipolynomial runtime $n^{O(\log{n})}$ that…
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…
Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…
Classical simulations of quantum circuits are limited in both space and time when the qubit count is above 50, the realm where quantum supremacy reigns. However, recently, for the low depth circuit with more than 50 qubits, there are…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
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…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
Recently, constant-depth quantum circuits are proved more powerful than their classical counterparts at solving certain problems, e.g., the two-dimensional (2D) hidden linear function (HLF) problem regarding a symmetric binary matrix. To…
We show that several quantum circuit families can be simulated efficiently classically if it is promised that their output distribution is approximately sparse i.e. the distribution is close to one where only a polynomially small, a priori…