16 papers · ranked by Valyu relevance
Zhi Li
The complexity of a quantum gate, defined as the minimal number of elementary gates to build it, is an important concept in quantum information and computation. It is shown recently that the complexity of quantum gates built from random quantum circuits almost surely grows linearly with the number of building blocks.…
Laszlo Gyongyosi, Sandor Imre
Quantum computers utilize the fundamentals of quantum mechanics to solve computational problems more efficiently than traditional computers. Gate-model quantum computers are fundamental to implement near-term quantum computer architectures and quantum devices. Here, a quantum algorithm is defined for the circuit depth…
Leonard Susskind
| 1 | How Huge? | 2 | | --- | --- | --- | | 2 | Volume of CP(N) | 3 | | 3 | Relative Complexity | 4 | | 4 | Dual Role of Unitaries | 6 | | 5 | SU(2K) Volume of | 7 | | 6 | Exploring SU(2K) | 8 | | | 6.1 Relative Complexity of Unitaries | 11 | | | 6.2 Complexity is Discontinuous | 13 | | 7 | Graph Theory Perspective |…
J.-H. Bae, Paul M. Alsing, Doyeol Ahn, Warner A. Miller
Every quantum algorithm is represented by set of quantum circuits. Any optimization scheme for a quantum algorithm and quantum computation is very important especially in the arena of quantum computation with limited number of qubit resources. Major obstacle to this goal is the large number of elemental quantum gates…
Pamela B. Rambow, Mingzhen Tian
We present a scalable set of universal and multiply controlled gates in a qudit basis through a bijective mapping from N qubits to qudits with = 2 levels via rotations in (2). For each of the universal gates (H, CNOT, and T), as well as the NOT gate and multiply-controlled-Z gates, we describe a systematic approach to…
Claudio Chamon, Andrei E. Ruckenstein, Eduardo R. Mucciolo, Ran Canetti
'Ran Canetti'] Title: Significance The current paper a) defines a thermodynamic approach to the complexity of circuits of specific functionality; and b) examines the validity of the approach by introducing the notion of “ergodicity” in the space of circuits, which hinges on functionality-preserving “local mixing”…
Claudio Chamon, Andrei E. Ruckenstein, Eduardo R. Mucciolo, Ran Canetti
'Ran Canetti'] Circuit complexity, defined as the minimum circuit size required for implementing a particular Boolean computation, is a foundational concept in computer science. Determining circuit complexity is believed to be a hard computational problem [1]. Recently, in the context of black holes, circuit complexity…
Anh Phong Tran, Dhruv D. Jatkar, M. Ali Al-Radhawi, Elizabeth A. Ernst + 1 more
Minimal synthesis of Boolean functions is an NP-hard problem, and heuristic approaches typically give suboptimal circuits. However, in the emergent field of synthetic biology, genetic logic designs that use even a single additional Boolean gate can render a circuit unimplementable in a cell. This has led to a renewed…
Prateek Chawla, Shivani Singh, Aman Agarwal, Sarvesh Srinivasan + 1 more
'C. M. Chandrashekar'] Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of the scheme is demonstrated by using a set of walk…
Hanxu Zhang, Yifan Sun, Xiangdong Zhang
Fourier transform (FT) is ubiquitous in modern society due to their broad applications in many branches of science and engineering. Improving the speed of FT is a common interest in the fields of signal processing. The quantum FT is generally believed to be superior to classical algorithms, but it requires a special…
Bao Gia Bach, Akash Kundu, Tamal Acharya, Aritra Sarkar + 2 more
'Andrei Khrennikov' 'Karl Svozil'] This work applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. The relations among the statistical, algorithmic, computational, and circuit complexities of states are reviewed. Thereafter, the probability of states in the circuit model of…
M. Ali Al-Radhawi, Anh Phong Tran, Elizabeth A. Ernst, Tianchi Chen + 2 more
Starting in the early 2000s, a sophisticated technology has been developed for the rational construction of synthetic genetic networks that implement specified logical functionalities. Despite impressive progress, however, the scaling necessary in order to achieve greater computational power has been hampered by many…
Ashley Montanaro
In this work we explore a correspondence between quantum circuits and low-degree polynomials over the finite field F2. Any quantum circuit made up of Hadamard, Z, controlled-Z and controlled-controlled-Z gates gives rise to a degree-3 polynomial over F2 such that calculating quantum circuit amplitudes is equivalent to…
Richard Winpenny, Edmund Little, Jacob Mrozek, Ciaran J Rogers + 4 more
Quantum information processing promises to revolutionise computing; quantum algorithms have been discovered that address common tasks significantly more efficiently than their classical counterparts. For a physical system to be a viable quantum computer it must be possible to initialise its quantum state, to realise a…
Authors not listed
The Hidden Subgroup Problem (HSP) unifies several landmark quantum algorithms, yet systematic exploration of its variants and modern applications has slowed. This paper revives HSP-based algorithm design by examining new group structures with direct relevance to post-quantum cryptography, lattice problems, and…
Roberto C. Sotero, Lazaro M. Sanchez-Rodriguez, Narges Moradi
The complexity of brain activity has been observed at many spatial scales and there exists increasing evidence supporting its use in differentiating between mental states and disorders. Here we proposed a new measure of network (global) complexity that is constructed as the sum of the complexities of its nodes (i.e…