Universal quantum computation via quantum controlled classical operations

Abstract A universal set of gates for (classical or quantum) computation is a set of gates that can be used to approximate any other operation. It is well known that a universal set for classical computation augmented with the Hadamard gate results in universal quantum computing. Motivated by the latter, we pose the following question: can one perform universal quantum computation by supplementing a set of classical gates with a quantum control, and a set of quantum gates operating solely on the latter? In this work we provide an affirmative answer to this question by considering a computational model that consists of 2n target bits together with a set of classical gates controlled by log(2n + 1) ancillary qubits. We show that this model is equivalent to a quantum computer operating on n qubits. Furthermore, we show that even a primitive computer that is capable of implementing only SWAP gates, can be lifted to universal quantum computing, if aided with an appropriate quantum control of logarithmic size. Our results thus exemplify the information processing power brought forth by the quantum control system.

Download Full-text

QUANTUM DOT COMPUTING GATES

International Journal of Quantum Information ◽

10.1142/s0219749906001761 ◽

2006 ◽

Vol 04 (02) ◽

pp. 233-296 ◽

Cited By ~ 3

Author(s):

GOONG CHEN ◽

ZIJIAN DIAO ◽

JONG U. KIM ◽

ARUP NEOGI ◽

KERIM URTEKIN ◽

...

Keyword(s):

Quantum Dots ◽

Quantum Computing ◽

Quantum Dot ◽

Quantum Computer ◽

Semiconductor Quantum Dots ◽

Quantum Gates ◽

Promising Candidate ◽

Universal Quantum ◽

Physical Attributes

Semiconductor quantum dots are a promising candidate for future quantum computer devices. Presently, there are three major proposals for designing quantum computing gates based on quantum dot technology: (i) electrons trapped in microcavity; (ii) spintronics; (iii) biexcitons. We survey these designs and show mathematically how, in principle, they will generate 1-bit rotation gates as well as 2-bit entanglement and, thus, provide a class of universal quantum gates. Some physical attributes and issues related to their limitations, decoherence and measurement are also discussed.

Download Full-text

QUANTUM COMPUTATION WITH BALLISTIC ELECTRONS

International Journal of Modern Physics B ◽

10.1142/s0217979201003521 ◽

2001 ◽

Vol 15 (02) ◽

pp. 125-133 ◽

Cited By ~ 26

Author(s):

RADU IONICIOIU ◽

GEHAN AMARATUNGA ◽

FLORIN UDREA

Keyword(s):

Quantum Computation ◽

Electric Fields ◽

Quantum Computer ◽

Quantum Gates ◽

Initial State ◽

Final State ◽

Single Electrons ◽

State Measurement ◽

Universal Quantum ◽

Static Electric Fields

We describe a solid state implementation of a quantum computer using ballistic single electrons as flying qubits in 1D nanowires. We show how to implement all the steps required for universal quantum computation: preparation of the initial state, measurement of the final state and a universal set of quantum gates. An important advantage of this model is the fact that we do not need ultrafast optoelectronics for gate operations. We use cold programming (or pre-programming), i.e. the gates are set before launching the electrons; all programming can be done using static electric fields only.

Download Full-text

Quantum computing and polynomial equations over Z_2

Quantum Information and Computation ◽

10.26421/qic5.2-2 ◽

2005 ◽

Vol 5 (2) ◽

pp. 102-112

Author(s):

C.M. Dawson ◽

H.L. Haselgrove ◽

A.P. Hines ◽

D. Mortimer ◽

M.A. Nielsen ◽

...

Keyword(s):

Quantum Computing ◽

Finite Field ◽

Quantum Computation ◽

Quantum Computer ◽

Complexity Classes ◽

Polynomial Equations ◽

Computational Power ◽

Number Of Solutions

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z_2. This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes, namely BQP/P/\#P and BQP/PP.

Download Full-text

Quantum Algorithms

Limitations and Future Applications of Quantum Cryptography - Advances in Information Security, Privacy, and Ethics ◽

10.4018/978-1-7998-6677-0.ch005 ◽

2021 ◽

pp. 82-101

Author(s):

Renata Wong ◽

Amandeep Singh Bhatia

Keyword(s):

Quantum Computing ◽

Fault Tolerance ◽

Quantum Computation ◽

Quantum Computer ◽

Quantum Algorithms ◽

Computer Hardware ◽

Quantum Mechanical ◽

Computational Power ◽

Quantum Devices ◽

The Core

In the last two decades, the interest in quantum computation has increased significantly among research communities. Quantum computing is the field that investigates the computational power and other properties of computers on the basis of the underlying quantum-mechanical principles. The main purpose is to find quantum algorithms that are significantly faster than any existing classical algorithms solving the same problem. While the quantum computers currently freely available to wider public count no more than two dozens of qubits, and most recently developed quantum devices offer some 50-60 qubits, quantum computer hardware is expected to grow in terms of qubit counts, fault tolerance, and resistance to decoherence. The main objective of this chapter is to present an introduction to the core quantum computing algorithms developed thus far for the field of cryptography.

Download Full-text

On the design of molecular excitonic circuits for quantum computing: the universal quantum gates

Physical Chemistry Chemical Physics ◽

10.1039/c9cp05625d ◽

2020 ◽

Vol 22 (5) ◽

pp. 3048-3057 ◽

Cited By ~ 1

Author(s):

Maria A. Castellanos ◽

Amro Dodin ◽

Adam P. Willard

Keyword(s):

Quantum Computing ◽

Organic Dye ◽

Quantum Gates ◽

Dye Molecules ◽

Universal Quantum ◽

Excitonic States

This manuscript presents a strategy for controlling the transformation of excitonic states through the design of circuits made up of coupled organic dye molecules.

Download Full-text

Quantum Computing, Seifert Surfaces, and Singular Fibers

Quantum Reports ◽

10.3390/quantum1010003 ◽

2019 ◽

Vol 1 (1) ◽

pp. 12-22 ◽

Cited By ~ 2

Author(s):

Michel Planat ◽

Raymond Aschheim ◽

Marcelo M. Amaral ◽

Klee Irwin

Keyword(s):

Quantum Computing ◽

Quantum Computer ◽

Complete Information ◽

Singular Fiber ◽

Dynkin Diagrams ◽

Singular Fibers ◽

Seifert Surfaces ◽

Trefoil Knot ◽

Universal Quantum

The fundamental group π 1 ( L ) of a knot or link L may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving complete information about the processed quantum states. In this paper, one defines braids whose closure is the L of such a quantum computer model and computes their braid-induced Seifert surfaces and the corresponding Alexander polynomial. In particular, some d-fold coverings of the trefoil knot, with d = 3 , 4, 6, or 12, define appropriate links L, and the latter two cases connect to the Dynkin diagrams of E 6 and D 4 , respectively. In this new context, one finds that this correspondence continues with Kodaira’s classification of elliptic singular fibers. The Seifert fibered toroidal manifold Σ ′ , at the boundary of the singular fiber E 8 ˜ , allows possible models of quantum computing.

Download Full-text

Benchmarking an 11-qubit quantum computer

Nature Communications ◽

10.1038/s41467-019-13534-2 ◽

2019 ◽

Vol 10 (1) ◽

Cited By ~ 46

Author(s):

K. Wright ◽

K. M. Beck ◽

S. Debnath ◽

J. M. Amini ◽

Y. Nam ◽

...

Keyword(s):

Quantum Computing ◽

Quantum Physics ◽

Quantum Computer ◽

Success Rates ◽

Single Qubit ◽

The Past ◽

Large Numbers ◽

Universal Quantum ◽

Qubit Gate ◽

Fully Connected

AbstractThe field of quantum computing has grown from concept to demonstration devices over the past 20 years. Universal quantum computing offers efficiency in approaching problems of scientific and commercial interest, such as factoring large numbers, searching databases, simulating intractable models from quantum physics, and optimizing complex cost functions. Here, we present an 11-qubit fully-connected, programmable quantum computer in a trapped ion system composed of 13 171Yb+ ions. We demonstrate average single-qubit gate fidelities of 99.5$$\%$$%, average two-qubit-gate fidelities of 97.5$$\%$$%, and SPAM errors of 0.7$$\%$$%. To illustrate the capabilities of this universal platform and provide a basis for comparison with similarly-sized devices, we compile the Bernstein-Vazirani and Hidden Shift algorithms into our native gates and execute them on the hardware with average success rates of 78$$\%$$% and 35$$\%$$%, respectively. These algorithms serve as excellent benchmarks for any type of quantum hardware, and show that our system outperforms all other currently available hardware.

Download Full-text

GEOMETRIC PHASES AND TOPOLOGICAL QUANTUM COMPUTATION

International Journal of Quantum Information ◽

10.1142/s0219749903000024 ◽

2003 ◽

Vol 01 (01) ◽

pp. 1-23 ◽

Cited By ~ 30

Author(s):

VLATKO VEDRAL

Keyword(s):

Quantum Computation ◽

Large Scale ◽

Quantum Computer ◽

Fault Tolerant ◽

Geometric Phases ◽

Quantum Phases ◽

Topological Quantum ◽

Universal Quantum ◽

The Subject ◽

Topological Quantum Computation

In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also introduce a number of examples that will help the reader understand the basic issues involved. In the second part we show how to perform a universal quantum computation using only geometric effects appearing in quantum phases. It is then finally discussed how this geometric way of performing quantum gates can lead to a stable, large scale, intrinsically fault-tolerant quantum computer.

Download Full-text

Magic-state distillation with the four-qubit code

Quantum Information and Computation ◽

10.26421/qic13.3-4-2 ◽

2013 ◽

Vol 13 (3&4) ◽

pp. 195-209

Author(s):

Adam M. Meier ◽

Bryan Eastin ◽

Emanuel Knill

Keyword(s):

Quantum Computing ◽

Error Probability ◽

Practical Interest ◽

Universal Quantum ◽

Special Subset ◽

Error Detecting ◽

Hadamard Gate ◽

Error Detecting Code

The distillation of magic states is an often-cited technique for enabling universal quantum computing once the error probability for a special subset of gates has been made negligible by other means. We present a routine for magic-state distillation that reduces the required overhead for a range of parameters of practical interest. Each iteration of the routine uses a four-qubit error-detecting code to distill the $+1$ eigenstate of the Hadamard gate at a cost of ten input states per two improved output states. Use of this routine in combination with the $15$-to-$1$ distillation routine described by Bravyi and Kitaev allows for further improvements in overhead.

Download Full-text