Related papers: Classical simulability of quantum circuits followe…
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…
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…
The class of commuting quantum circuits known as IQP (instantaneous quantum polynomial-time) has been shown to be hard to simulate classically, assuming certain complexity-theoretic conjectures. Here we study the power of IQP circuits in…
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…
Sampling from the output distributions of quantum computations comprising only commuting gates, known as instantaneous quantum polynomial (IQP) computations, is believed to be intractable for classical computers, and hence this task has…
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.…
We study the classical simulatability of commuting quantum circuits with n input qubits and O(log n) output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an…
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…
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…
Classical simulations of quantum circuits are essential for verifying and benchmarking quantum algorithms, particularly for large circuits, where computational demands increase exponentially with the number of qubits. Among available…
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…
Investigating the classical simulability of quantum circuits provides a promising avenue towards understanding the computational power of quantum systems. Whether a class of quantum circuits can be efficiently simulated with a probabilistic…
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…
We propose examples of a hybrid quantum-classical simulation where a classical computer assisted by a small quantum processor can efficiently simulate a larger quantum system. First we consider sparse quantum circuits such that each qubit…
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…
While quantum computing can accomplish tasks that are classically intractable, the presence of noise may destroy this advantage in the absence of fault tolerance. In this work, we present a classical algorithm that runs in…
We construct a polynomial-time classical algorithm that samples from the output distribution of noisy geometrically local Clifford circuits with any product-state input and single-qubit measurements in any basis. Our results apply to…
In breakthrough work, Bravyi, Gosset, and K\"{o}nig (BGK) [Science, 2018] unconditionally proved that constant depth quantum circuits are more powerful than their classical counterparts. Their result is equivalent to saying that a…
Quantum simulation advantage over classical memory limitations would allow compact quantum circuits to yield insight into intractable quantum many-body problems, but the interrelated obstacles of large circuit depth in quantum time…
We study the effect of noise on the classical simulatability of quantum circuits defined by computationally tractable (CT) states and efficiently computable sparse (ECS) operations. Examples of such circuits, which we call CT-ECS circuits,…