Related papers: A Criterion for Post-Selected Quantum Advantage
The Clifford hierarchy is a set of gates that appears in the theory of fault-tolerant quantum computation, but its precise structure remains elusive. We give a complete characterization of the diagonal gates in the Clifford hierarchy for…
We show that single-qudit universality in Clifford-based gate sets follows a trichotomy determined by the prime factorization of the local dimension $d$. For prime $d$, any gate outside the Clifford group is universal. For prime-power…
Determining the quantum-classical boundary between quantum circuits which can be efficiently simulated classically and those which cannot remains a fundamental question. One approach to classical simulation is to represent the output of a…
We improve on the results of [A. Jackson et al. Proc. Natl. Acad. Sci. U.S.A 121 (6). 2024] on the verification of analogue quantum simulators by eliminating the use of universal Hamiltonians, removing the need for two-qubit gates, and no…
A leading proposal for verifying near-term quantum supremacy experiments on noisy random quantum circuits is linear cross-entropy benchmarking. For a quantum circuit $C$ on $n$ qubits and a sample $z \in \{0,1\}^n$, the benchmark involves…
To ensure a long-term quantum computational advantage, the quantum hardware should be upgraded to withstand the competition of continuously improved classical algorithms and hardwares. Here, we demonstrate a superconducting quantum…
Standard randomized benchmarking protocols entail sampling from a unitary 2 design, which is not always practical. In this article we examine randomized benchmarking protocols based on subgroups of the Clifford group that are not unitary 2…
One learned from Gottesman-Knill theorem that the Clifford model of quantum computing \cite{Clark07} may be generated from a few quantum gates, the Hadamard, Phase and Controlled-Z gates, and efficiently simulated on a classical computer.…
We present two classical algorithms for the simulation of universal quantum circuits on $n$ qubits constructed from $c$ instances of Clifford gates and $t$ arbitrary-angle $Z$-rotation gates such as $T$ gates. Our algorithms complement each…
We consider the problem of synthesizing Clifford quantum circuits for devices with all-to-all qubit connectivity. We approach this task as a reinforcement learning problem in which an agent learns to discover a sequence of elementary…
We consider the possibility of adding noise to a quantum circuit to make it efficiently simulatable classically. In previous works this approach has been used to derive upper bounds to fault tolerance thresholds - usually by identifying a…
Quantum resources outperform classical ones for certain communication and computational tasks. Remarkably, in some cases, the quantum advantage cannot be improved using hypothetical postquantum resources. A class of tasks with this property…
We show that states obtained from deep random Clifford circuits doped with non-Clifford phase gates (including T-gates and $\sqrt{\mathrm{T}}$-gates) can be disentangled completely, provided the number of non-Clifford gates is smaller or…
The efficient certification of classically intractable quantum devices has been a central research question for some time. However, to observe a "quantum advantage", it is believed that one does not need to build a large scale universal…
The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…
Many quantum mechanical experiments can be viewed as multi-round interactive protocols between known quantum circuits and an unknown quantum process. Fully quantum "coherent" access to the unknown process is known to provide an advantage in…
In fault-tolerant quantum computation and quantum error-correction one is interested on Pauli matrices that commute with a circuit/unitary. We provide a fast algorithm that decomposes any Clifford gate as a $\textit{minimal}$ product of…
In a series of recent works, an interesting quantum generative model based on parameterized instantaneous polynomial quantum (IQP) circuits has emerged as they can be trained efficiently classically using any loss function that depends only…
Diagonal quantum circuits are quantum circuits comprising only diagonal gates in the computational basis. In spite of a classical feature of diagonal quantum circuits in the sense of commutativity of all gates, their computational power is…
We propose and analyze a novel interactive protocol for demonstrating quantum computational advantage, which is efficiently classically verifiable. Our protocol relies upon the cryptographic hardness of trapdoor claw-free functions (TCFs).…