Related papers: Efficient classical simulation of Clifford circuit…
Quantum normalizer circuits were recently introduced as generalizations of Clifford circuits [arXiv:1201.4867]: a normalizer circuit over a finite Abelian group $G$ is composed of the quantum Fourier transform (QFT) over G, together with…
Clifford circuits -- i.e. circuits composed of only CNOT, Hadamard, and $\pi/4$ phase gates -- play a central role in the study of quantum computation. However, their computational power is limited: a well-known result of Gottesman and…
We estimate the success probability of quantum protocols composed of Clifford operations in the presence of Pauli errors. Our method is derived from the fault-point formalism previously used to determine the success rate of low-distance…
We investigate how non-stabilizer resources enable the emergence of quantum state designs within the projected ensemble. Starting from initial states with finite magic and applying resource-free Clifford circuits to scramble them, we…
The performance of quantum algorithms for ground-state energy estimation is directly impacted by the quality of the initial state, where quality is traditionally defined in terms of the overlap of the input state with the target state. An…
While there is strong evidence for advantages of quantum over classical computation, the repertoire of computational primitives with proven or conjectured quantum advantage remains limited. A big challenge of quantum algorithmic design is a…
Matchgates are a restricted set of two-qubit gates known to be classically simulable under particular conditions. Specifically, if a circuit consists only of nearest-neighbour matchgates, an efficient classical simulation is possible if…
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…
We give a pair of algorithms that efficiently learn a quantum state prepared by Clifford gates and $O(\log n)$ non-Clifford gates. Specifically, for an $n$-qubit state $|\psi\rangle$ prepared with at most $t$ non-Clifford gates, our…
We study how much noise can be tolerated by a universal gate set before it loses its quantum-computational power. Specifically we look at circuits with perfect stabilizer operations in addition to imperfect non-stabilizer gates. We prove…
We consider the problem of testing whether an unknown $n$-qubit quantum state $|\psi\rangle$ is a stabilizer state, with only single-copy access. We give an algorithm solving this problem using $O(n)$ copies, and conversely prove that…
Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…
Verification of NISQ era quantum devices demands fast classical simulation of large noisy quantum circuits. We present an algorithm based on the stabilizer formalism that can efficiently simulate noisy stabilizer circuits. Additionally, the…
We describe a simple algorithm for sampling $n$-qubit Clifford operators uniformly at random. The algorithm outputs the Clifford operators in the form of quantum circuits with at most $5n + 2n^2$ elementary gates and a maximum depth of…
We describe and analyze algorithms for classically simulating measurement of an $n$-qubit quantum state $\psi$ in the standard basis, that is, sampling a bit string $x$ from the probability distribution $|\langle x|\psi\rangle|^2$. Our…
For a quantum computer acting on d-dimensional systems, we analyze the computational power of circuits wherein stabilizer operations are perfect and we allow access to imperfect non-stabilizer states or operations. If the noise rate…
Exact classical simulation of fault-tolerant quantum circuits remains limited by a tradeoff between exponential state vector scaling, exponential $T$-count scaling in stabilizer-rank approaches, and per-shot tracking overhead in sparse…
We propose an efficient scheme for verifying quantum computations in the `high complexity' regime i.e. beyond the remit of classical computers. Previously proposed schemes remarkably provide confidence against arbitrarily malicious…
Classical simulations of quantum systems are notoriously difficult computational problems, with conventional state vector and tensor network methods restricted to quantum systems that feature only a small number of qudits. The recently…
Classical simulations of noisy quantum circuits are instrumental to our understanding of the behavior of real-world quantum systems and the identification of regimes where one expects quantum advantage. In this work, we present a highly…