English
Related papers

Related papers: Counting, Fanout, and the Complexity of Quantum AC…

200 papers

A major open problem in understanding shallow quantum circuits (QAC$^0$) is whether they can compute Parity. We show that this question is solely about the Fourier spectrum of QAC$^0$: any QAC$^0$ circuit with non-negligible high-level…

Quantum Physics · Physics 2026-04-06 Lucas Gretta , Meghal Gupta , Malvika Raj Joshi

We explore the power of the unbounded Fan-Out gate and the Global Tunable gates generated by Ising-type Hamiltonians in constructing constant-depth quantum circuits, with particular attention to quantum memory devices. We propose two types…

Quantum Physics · Physics 2024-11-26 Jonathan Allcock , Jinge Bao , Joao F. Doriguello , Alessandro Luongo , Miklos Santha

We present a novel implementation of an n-qubit fanout gate using resonance engineering. Our proposed mechanism uses Jaynes-Cummings interactions between multiple qubits and a common harmonic oscillator to realize a fanout gate at the…

Quantum Physics · Physics 2026-05-13 Johannes Alexander Jaeger , Elias Zapusek , Florentin Reiter

We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a…

Low depth measurement-based quantum computation with qudits ($d$-level systems) is investigated and a precise relationship between this powerful model and qudit quantum circuits is derived in terms of computational depth and size…

Quantum Physics · Physics 2015-10-23 Timothy J. Proctor

A recent line of work has shown the unconditional advantage of constant-depth quantum computation, or $\mathsf{QNC^0}$, over $\mathsf{NC^0}$, $\mathsf{AC^0}$, and related models of classical computation. Problems exhibiting this advantage…

Quantum Physics · Physics 2023-12-01 Joseph Slote

Recent work of Bravyi et al. and follow-up work by Bene Watts et al. demonstrates a quantum advantage for shallow circuits: constant-depth quantum circuits can perform a task which constant-depth classical (i.e., AC$^0$) circuits cannot.…

Quantum Physics · Physics 2019-11-07 Daniel Grier , Luke Schaeffer

This paper shows that, in measurement-based quantum computation, it is possible to write any quantum oracle implementing a classical function in constant depth. The result is shown through the equivalence between MBQC and the circuit model…

Quantum Physics · Physics 2014-06-18 Benoît Valiron

We show that, for even n, evolving n qubits according to a simple Hamiltonian can be used to exactly implement an (n+1)-qubit parity gate, which is equivalent in constant depth to an (n+1)-qubit fanout gate. We also observe that evolving…

Quantum Physics · Physics 2007-05-23 Stephen A. Fenner

It has been shown that, for even $n$, evolving $n$ qubits according to a Hamiltonian that is the sum of pairwise interactions between the particles, can be used to exactly implement an $(n+1)$-qubit fanout gate using a particular…

Quantum Physics · Physics 2023-06-21 Stephen Fenner , Rabins Wosti

We continue the study of the circuit class GC^0, which augments AC^0 with unbounded-fan-in gates that compute arbitrary functions inside a sufficiently small Hamming ball but must be constant outside it. While GC^0 can compute functions…

Quantum Physics · Physics 2025-12-03 Sabee Grewal , Vinayak M. Kumar

One of the many challenges of developing an open user testbed such as QSCOUT is providing an interface that maintains simplicity without compromising expressibility or control. This interface comprises two distinct elements: a quantum…

We systematically construct and classify fault-tolerant logical gates implemented by constant-depth circuits for quantum codes using cohomology operations and symmetry. These logical gates are obtained from unitary operators given by…

Quantum Physics · Physics 2025-06-30 Po-Shen Hsin , Ryohei Kobayashi , Guanyu Zhu

When using unitary gate sequences, the growth in depth of many quantum circuits with output size poses significant obstacles to practical quantum computation. The quantum fan-out operation, which reduces the circuit depth of quantum…

Prior work has shown that there exists a relation problem which can be solved with certainty by a constant-depth quantum circuit composed of geometrically local gates in two dimensions, but cannot be solved with high probability by any…

Quantum Physics · Physics 2020-07-14 Sergey Bravyi , David Gosset , Robert Koenig , Marco Tomamichel

The depth of quantum circuits is a critical factor when running them on state-of-the-art quantum devices due to their limited coherence times. Reducing circuit depth decreases noise in near-term quantum computations and reduces overall…

Quantum Physics · Physics 2025-05-08 Elisa Bäumer , Stefan Woerner

A defining feature in the field of quantum computing is the potential of a quantum device to outperform its classical counterpart for a specific computational task. By now, several proposals exist showing that certain sampling problems can…

Quantum Physics · Physics 2020-09-23 Rawad Mezher , Joe Ghalbouni , Joseph Dgheim , Damian Markham

Recently, Bravyi, Gosset, and K\"{o}nig (Science, 2018) exhibited a search problem called the 2D Hidden Linear Function (2D HLF) problem that can be solved exactly by a constant-depth quantum circuit using bounded fan-in gates (or QNC^0…

Quantum Physics · Physics 2019-06-24 Adam Bene Watts , Robin Kothari , Luke Schaeffer , Avishay Tal

We introduce a novel quantum optimization paradigm: the Fixed-Parameter-Count Quantum Approximate Optimization Algorithm (FPC-QAOA). It is a scalable variational framework that maintains a constant number of trainable parameters regardless…

We present the first direct comparison between gate-based quantum computing (GQC) and adiabatic quantum computing (AQC) paradigms for solving the AC power flow (PF) equations. The PF problem is reformulated as a combinatorial optimization…

Quantum Physics · Physics 2026-03-09 Zeynab Kaseb , Matthias Moller , Peter Palensky , Pedro P. Vergara