Related papers: Closed-form analytic expressions for shadow estima…
Randomized measurements are increasingly appreciated as powerful tools to estimate properties of quantum systems, e.g., in the characterization of hybrid classical-quantum computation. On many platforms they constitute natively accessible…
We investigate the problem of evaluating the output probabilities of Clifford circuits with nonstabilizer product input states. First, we consider the case when the input state is mixed, and give an efficient classical algorithm to…
Efficiently estimating properties of large and strongly coupled quantum systems is a central focus in many-body physics and quantum information theory. While quantum computers promise speedups for many such tasks, near-term devices are…
The Clifford group is a finite subgroup of the unitary group generated by the Hadamard, the CNOT, and the Phase gates. This group plays a prominent role in quantum error correction, randomized benchmarking protocols, and the study of…
The classical shadows protocol, introduced by Huang et al. [Nat. Phys. 16, 1050 (2020)], makes use of the median-of-means (MoM) estimator to efficiently estimate the expectation values of $M$ observables with failure probability $\delta$…
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…
Outcome probability estimation via classical methods is an important task for validating quantum computing devices. Outcome probabilities of any quantum circuit can be estimated using Monte Carlo sampling, where the amount of negativity…
Classical shadows are succinct classical representations of quantum states which allow one to encode a set of properties P of a quantum state rho, while only requiring measurements on logarithmically many copies of rho in the size of P. In…
Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Here we study the sample complexity of learning the expectation value of Pauli…
Solving the electronic structure problem of molecules and solids to high accuracy is a major challenge in quantum chemistry and condensed matter physics. The rapid emergence and development of quantum computers offer a promising route to…
We study classical simulation of quantum computation, taking the Gottesman-Knill theorem as a starting point. We show how each Clifford circuit can be reduced to an equivalent, manifestly simulatable circuit (normal form). This provides a…
Extracting classical information from quantum systems is of fundamental importance, and classical shadows allow us to extract a large amount of information using relatively few measurements. Conventional shadow estimators are unbiased and…
Classical shadows constitute a protocol to estimate the expectation values of a collection of M observables acting on O(1) qubits of an unknown n-qubit state with a number of measurements that is independent of n and that grows only…
Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, non-destructive measurements of Pauli observables. Any quantum circuit written in terms of the Clifford+$T$ gate set and having $t$ $T$ gates can be compiled into a…
Classical simulation of quantum circuits plays a crucial role in validating quantum hardware and delineating the boundaries of quantum advantage. Among the most effective simulation techniques are those based on the stabilizer extent, which…
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…
The applications of random quantum circuits range from quantum computing and quantum many-body systems to the physics of black holes. Many of these applications are related to the generation of quantum pseudorandomness: Random quantum…
Characterising quantum processes is a key task in and constitutes a challenge for the development of quantum technologies, especially at the noisy intermediate scale of today's devices. One method for characterising processes is randomised…
We tackle the problem of Clifford isometry compilation, i.e, how to synthesize a Clifford isometry into an executable quantum circuit. We propose a simple framework for synthesis that only exploits the elementary properties of the Clifford…
We study the sample complexity of the classical shadows task: what is the fewest number of copies of an unknown state you need to measure to predict expected values with respect to some class of observables? Large joint measurements are…