English
Related papers

Related papers: Quantum Lower Bounds for Fanout

200 papers

Efficient quantum arithmetic circuits are commonly found in numerous quantum algorithms of practical significance. Till date, the logarithmic-depth quantum adders includes a constant coefficient k >= 2 while achieving the Toffoli-Depth of…

Quantum Physics · Physics 2024-05-07 Siyi Wang , Suman Deb , Ankit Mondal , Anupam Chattopadhyay

We show that any quantum circuit of treewidth $t$, built from $r$-qubit gates, requires at least $\Omega(\frac{n^{2}}{2^{O(r\cdot t)}\cdot \log^4 n})$ gates to compute the element distinctness function. Our result generalizes a…

Computational Complexity · Computer Science 2016-10-03 Mateus de Oliveira Oliveira

The decomposition for controlled-$ZX$ gate in [Phys. Rev. A, 87, 062318 (2013)] has a shallow circuit depth $8n-20$ with no ancilla. Here we modify this decomposition to decompose $n$-qubit Toffoli gate with only $2n-3$ additional…

Quantum Physics · Physics 2023-05-25 Jian Leng , Fan Yang , Xiang-Bin Wang

Quantum computing has the potential to solve many complex algorithms in the domains of optimization, arithmetics, structural search, financial risk analysis, machine learning, image processing, and others. Quantum circuits built to…

Quantum Physics · Physics 2024-07-26 Vladimir V. Arsoski

Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…

A crucial subroutine in quantum computing is to load the classical data of $N$ complex numbers into the amplitude of a superposed $n=\lceil \log_2N\rceil$-qubit state. It has been proven that any algorithm universally implementing this…

Quantum Physics · Physics 2021-08-13 Xiao-Ming Zhang , Man-Hong Yung , Xiao Yuan

Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…

Quantum Physics · Physics 2026-03-02 Guoding Liu , Zhenyu Du , Zi-Wen Liu , Xiongfeng Ma

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 give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log (1/epsilon)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2^n…

Quantum Physics · Physics 2007-05-23 Richard Cleve , John Watrous

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

We provide evidence that commonly held intuitions when designing quantum circuits can be misleading. In particular we show that: a) reducing the T-count can increase the total depth; b) it may be beneficial to trade CNOTs for measurements…

Quantum Physics · Physics 2021-01-14 Alexandru Paler , Oumarou Oumarou , Robert Basmadjian

In this work, we investigate the trade-off between the circuit depth and the number of ancillary qubits for preparing sparse quantum states. We prove that any $n$-qubit $d$-spare quantum state (i.e., it has only $d$ non-zero amplitudes) can…

Quantum Physics · Physics 2025-06-23 Jingquan Luo , Guanzhong Li , Lvzhou Li

We prove that one-way quantum computations have the same computational power as quantum circuits with unbounded fan-out. It demonstrates that the one-way model is not only one of the most promising models of physical realisation, but also a…

Quantum Physics · Physics 2010-08-12 Dan E. Browne , Elham Kashefi , Simon Perdrix

We propose an approach for quantifying a quantum circuit's quantumness as a means to understand the nature of quantum algorithmic speedups. Since quantum gates that do not preserve the computational basis are necessary for achieving quantum…

Quantum Physics · Physics 2011-11-04 Yaoyun Shi

Adaptive quantum circuits, leveraging measurements and classical feedback, significantly expand the landscape of realizable quantum states compared to their non-adaptive counterparts, enabling the preparation of long-range entangled states…

Quantum Physics · Physics 2025-09-23 Guoding Liu , Junjie Chen , Xiongfeng Ma

Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…

Quantum Physics · Physics 2018-01-23 Sergio Boixo , Sergei V. Isakov , Vadim N. Smelyanskiy , Hartmut Neven

Nielsen \cite{Nielsen05} recently asked the following question: "What is the minimal size quantum circuit required to exactly implement a specified $% \mathit{n}$-qubit unitary operation $U$, without the use of ancilla qubits?" Nielsen was…

Quantum Physics · Physics 2010-01-19 Milosh Drezgich , Shankar Sastry

In quantum computation every unitary operation can be decomposed into quantum circuits-a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are important when…

Quantum Physics · Physics 2011-03-07 Martin Plesch , Časlav Brukner

The quantum query complexity of evaluating any read-once formula with n black-box input bits is Theta(sqrt(n)). However, the corresponding problem for read-many formulas (i.e., formulas in which the inputs have fanout) is not well…

Quantum Physics · Physics 2012-09-06 Andrew M. Childs , Shelby Kimmel , Robin Kothari

We present the first exact quantum adder with sublinear depth and no ancilla qubits. Our construction is based on classical reversible logic only and employs low-depth implementations for the CNOT ladder operator and the Toffoli ladder…

Quantum Physics · Physics 2025-08-04 Maxime Remaud , Vivien Vandaele