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All-to-all interactions arise naturally in many areas of theoretical physics and across diverse experimental quantum platforms, motivating a systematic study of their information-processing power. Assuming each pair of qubits interacts with…

Quantum Physics · Physics 2025-10-01 Chao Yin

Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type…

Quantum Physics · Physics 2009-11-10 Ville Bergholm , Juha J. Vartiainen , Mikko Mottonen , Martti M. Salomaa

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…

Quantum Physics · Physics 2023-10-04 Filipa C. R. Peres , Ernesto F. Galvão

A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any…

Quantum Physics · Physics 2013-04-18 Fernando G. S. L. Brandao , Michal Horodecki

In this paper we develop a classical algorithm of complexity $O(K \, 2^n)$ to simulate parametrized quantum circuits (PQCs) of $n$ qubits, where $K$ is the total number of one-qubit and two-qubit control gates. The algorithm is developed by…

Quantum Physics · Physics 2024-02-01 Bibhas Adhikari , Aryan Jha

We establish rigorous connections between quantum circuit complexity and approximate quantum error correction (AQEC) capability, two properties of fundamental importance to the physics and practical use of quantum many-body systems,…

Quantum Physics · Physics 2024-11-14 Jinmin Yi , Weicheng Ye , Daniel Gottesman , Zi-Wen Liu

We study the scrambling of quantum information in local random unitary circuits by focusing on the tripartite information proposed by Hosur et al. We provide exact results for the averaged R\'enyi-$2$ tripartite information in two cases:…

Statistical Mechanics · Physics 2020-08-18 Bruno Bertini , Lorenzo Piroli

We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for…

Quantum Physics · Physics 2009-11-13 Winton G. Brown , Yaakov S. Weinstein , Lorenza Viola

We study the problem of constructing strong approximate unitary $k$-designs on $D$-dimensional grids (and more generally on Cartesian products of graphs), building on the work of Schuster et al. arXiv:2509.26310 which establishes strong…

Quantum Physics · Physics 2026-05-06 Marten Folkertsma , Lorenzo Grevink , Jonas Helsen , Alicja Dutkiewicz

We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…

Quantum Physics · Physics 2021-09-22 Mark Bun , Robin Kothari , Justin Thaler

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…

Quantum Physics · Physics 2015-12-18 Yasuhiro Takahashi , Seiichiro Tani , Takeshi Yamazaki , Kazuyuki Tanaka

A variety of quantum algorithms employ Pauli operators as a convenient basis for studying the spectrum or evolution of Hamiltonians or measuring multi-body observables. One strategy to reduce circuit depth in such algorithms involves…

Quantum Physics · Physics 2023-12-21 Edison M. Murairi , Michael J. Cervia

The existence of pseudorandom unitaries (PRUs) -- efficient quantum circuits that are computationally indistinguishable from Haar-random unitaries -- has been a central open question, with significant implications for cryptography,…

Quantum Physics · Physics 2025-05-22 Fermi Ma , Hsin-Yuan Huang

In this paper, we present Clifford+T gates based quantum circuit design of integer division having $n$ ancillary qubits. The proposed quantum circuit is based on restoring division algorithm. The proposed quantum circuit of integer division…

Quantum Physics · Physics 2016-09-06 Himanshu Thapliyal , T. S. S. Varun , Edgard Munoz-Coreas

While many statistical properties of deep random quantum circuits can be deduced, often rigorously and other times heuristically, by an approximation to global Haar-random unitaries, the statistics of constant-depth random quantum circuits…

Quantum Physics · Physics 2024-11-08 Gregory Bentsen , Bill Fefferman , Soumik Ghosh , Michael J. Gullans , Yinchen Liu

We define and construct efficient depth-universal and almost-size-universal quantum circuits. Such circuits can be viewed as general-purpose simulators for central classes of quantum circuits and can be used to capture the computational…

Computational Complexity · Computer Science 2008-04-16 Debajyoti Bera , Stephen Fenner , Frederic Green , Steve Homer

The quantum Fourier transform (QFT) is a ubiquitous quantum operation that is used in numerous quantum computing applications. The major obstacle to constructing a QFT circuit is that numerous elementary gates are required. Among the…

Quantum Physics · Physics 2024-07-23 Byeongyong Park , Doyeol Ahn

In a circuit-based quantum computer, the computing is performed via the discrete-time evolution driven by quantum gates. Accurate simulation of continuoustime evolution requires a large number of quantum gates and therefore suffers from…

Quantum Physics · Physics 2026-05-11 J. L. Shen , P. Wang

We investigate a class of brickwork-like quantum circuits on chains of $d-$level systems (qudits) that share the so-called `dual unitarity' property. Namely, these systems generate unitary dynamics not only when propagating in the time…

Mathematical Physics · Physics 2021-12-10 Bruno Bertini , Pavel Kos , Tomaz Prosen

All quantum gates with one and two qubits may be described by elements of $Spin$ groups due to isomorphisms $Spin(3) \simeq SU(2)$ and $Spin(6) \simeq SU(4)$. However, the group of $n$-qubit gates $SU(2^n)$ for $n > 2$ has bigger dimension…

Quantum Physics · Physics 2023-04-11 Alexander Yu. Vlasov