Experienced academic writing professionals are at your fingertips.
Use this handy tool to get a price estimate for your project.

Quantum computing offers powerful new techniques for speeding up the calculation of many classically intractable problems. Quantum algorithms can allow for the efficient simulation of physical systems, with applications to basic research, chemical modeling, and drug discovery; other algorithms have important implications for cryptography and internet security. At the same time, building a quantum computer is a daunting task, requiring the coherent manipulation of systems with many quantum degrees of freedom while preventing environmental noise from interacting too strongly with the system. Fortunately, we know that, under reasonable assumptions, we can use the techniques of quantum error correction and fault tolerance to achieve an arbitrary reduction in the noise level. In this thesis, we look at how additional information about the structure of noise, or "noise bias," can improve or alter the performance of techniques in quantum error correction and fault tolerance. In Chapter 2, we explore the possibility of designing certain quantum gates to be extremely robust with respect to errors in their operation. This naturally leads to structured noise where certain gates can be implemented in a protected manner, allowing the user to focus their protection on the noisier unprotected operations.In Chapter 3, we examine how to tailor error-correcting codes and fault-tolerant quantum circuits in the presence of dephasing biased noise, where dephasing errors are far more common than bit-flip errors. By using an appropriately asymmetric code, we demonstrate the ability to improve the amount of error reduction and decrease the physical resources required for error correction.In Chapter 4, we analyze a variety of protocols for distilling magic states, which enable universal quantum computation, in the presence of faulty Clifford operations. Here again there is a hierarchy of noise levels, with a fixed error rate for faulty gates, and a second rate for errors in the distilled states which decreases as the states are distilled to better quality. The interplay of of these different rates sets limits on the achievable distillation and how quickly states converge to that limit.

In Chapter 4, we analyze a variety of protocols for distilling magic states, which enable universal quantum computation, in the presence of faulty Clifford operations. Here again there is a hierarchy of noise levels, with a fixed error rate for faulty gates, and a second rate for errors in the distilled states which decreases as the states are distilled to better quality. The interplay of of these different rates sets limits on the achievable distillation and how quickly states converge to that limit.

The idea of a computational device based on quantum mechanics wasexplored already in the 1970s by physicists and computerscientists. As early as 1969 Steven Wiesner suggested quantuminformation processing as a possible way to better accomplishcryptologic tasks. But the first four published papers on quantuminformation (Wiesner published his only in 1983), belong to AlexanderHolevo (1973), R.P. Poplavskii (1975), Roman Ingarden (1976) and YuriManin (1980). Better known are contributions made in the early 1980sby Charles H. Bennett of the IBM Thomas J. Watson Research Center,Paul A. Benioff of Argonne National Laboratory in Illinois, DavidDeutsch of the University of Oxford, and the late Richard P. Feynmanof the California Institute of Technology. The idea emerged whenscientists were investigating the fundamental physical limits ofcomputation. If technology continued to abide by “Moore’s Law” (theobservation made in 1965 by Gordon Moore, co-founder of Intel, thatthe number of transistors per square inch on integrated circuits haddoubled every 18 months since the integrated circuit was invented),then the continually shrinking size of circuitry packed onto siliconchips would eventually reach a point where individual elements wouldbe no larger than a few atoms. But since the physical laws thatgovern the behavior and properties of the putative circuit at theatomic scale are inherently quantum mechanical in nature, notclassical, the natural question arose whether a new kind of computercould be devised based on the principles of quantum physics.

In Chapter 4, we analyze a variety of protocols for distilling magic states, which enable universal quantum computation, in the presence of faulty Clifford operations. Here again there is a hierarchy of noise levels, with a fixed error rate for faulty gates, and a second rate for errors in the distilled states which decreases as the states are distilled to better quality. The interplay of of these different rates sets limits on the achievable distillation and how quickly states converge to that limit.

In Chapter 4, we analyze a variety of protocols for distilling magic states, which enable universal quantum computation, in the presence of faulty Clifford operations. Here again there is a hierarchy of noise levels, with a fixed error rate for faulty gates, and a second rate for errors in the distilled states which decreases as the states are distilled to better quality. The interplay of of these different rates sets limits on the achievable distillation and how quickly states converge to that limit.

Overview of classical complexity theory, quantum complexity, efficient quantum algorithms, fault-tolerant quantum computation, physical implementations of quantum computation.

Versatile Services that Make Studying Easy

We write effective, thought-provoking essays from scratch

We create erudite academic research papers

We champion seasoned experts for dissertations

We make it our business to construct successful business papers

What if the quality isn’t so great?

Our writers are sourced from experts, and complete an
obstacle course of testing to join our brigade. Ours
is a top service in the English-speaking world.

How do I know the professor
won’t find out?

Everything is confidential. So you know your student
paper is wholly yours, we use CopyScape and WriteCheck
to guarantee originality (never TurnItIn, which
professors patrol).

What if it doesn’t meet my expectations?

Unchanged instructions afford you 10 days to
request edits after our agreed due date. With
94% satisfaction, we work until your hair is
comfortably cool.

Clients enjoy the breezy experience of working with us

Click to learn our proven method

4.P. E. Falloon, J. Rodriguez, J. B. Wang, "QSWalk: a Mathematica package for quantum stochastic walks on arbitrary graphs”, Computer Physics Communications 217, 162 (2017)

The quantum dynamics and computation group conducts research in the areas of quantum dynamics, quantum information processing, and quantum computation. In addition to using advanced mathematical methods and numerical techniques to model the dynamics of quantum systems and to investigate quantum algorithms, the group also has extensive HPC and computer algebra expertise to solve a wide range of science and engineering problems.

Instead of brute-force miniaturisation of basic electronic components, quantum computation utilises entirely new design architecture and promises to solve problems that are intractable on conventional computers. It offers the prospect of harnessing nature at a much deeper level than ever before, as well as a wealth of new possibilities for communication and data processing.

Starting from 2000 the field saw a tremendousgrowth. New paradigms of quantum algorithms have appeared, such asadiabatic algorithms, measurement-based algorithms, andtopological-quantum-field-theory-based algorithms, as well as newphysical models for realizing a large scale quantum computer with coldion traps, quantum optics (using photons and optical cavity),condensed matter systems and solid state physics (meanwhile, the firstNMR model had turned out to be a dead-end with respect to scaling; seeDiVincenzo 2000). The basic questions, however, remain open even today: (1)theoretically, can quantum algorithms efficiently solve classicallyintractable problems? (2) operationally, can we actually realize alarge scale quantum computer to run these algorithms?

In 1996, Lov Grover from Bell Labs invented the quantum searchalgorithm which yields a quadratic “speed-up” compared to itsclassical counterpart. A year later the first NMR model for quantumcomputation was proposed, based on nuclear magnetic resonancetechniques. This technique was realized in 1998 with a 2-qubitregister, and was scaled up to 7 qubits in the Los Alamos National Labin 2000.

Progress in quantum algorithms began in the 1990s, with the discoveryof the Deutsch-Josza oracle (1992) and of Simon’s oracle (1994). Thelatter supplied the basis for Shor’s algorithm for*factoring*. Published in 1994, this algorithm marked a‘phase transition’ in the development of quantum computingand sparked a tremendous interest even outside the physicscommunity. In that year the first experimental realization of thequantum *CNOT* gate with trapped ions was proposed by Cirac andZoller (1995). In 1995, Peter Shor and Andrew Steane proposed(independently) the first scheme for quantum error-correction. In thatsame year the first realization of a quantum logic gate was done inBoulder, Colorado, following Cirac and Zoller’s proposal.

Inspired by Ed Fredkin’s ideas on reversible computation (see Hagar forthcoming),Feynman was among the first to attempt to provide an answer to thisquestion by producing an abstract model in 1982 that showed how aquantum system could be used to do computations. He also explainedhow such a machine would be able to act as a simulator for quantumphysics. Feynman also conjectured that any classical computer thatwill be harnessed for this task will do so only inefficiently,incurring an exponential slowdown in computation time. In 1985 DavidDeutsch proposed the first universal quantum Turing machine and pavedthe way to the quantum circuit model. The young and thriving domainalso attracted philosophers’ attention. In 1983 David Albert showedhow a quantum mechanical automaton behaves remarkably differently froma classical automaton, and in 1990 Itamar Pitowsky raised the questionwhether the superposition principle will allow quantum computers tosolve **NP**-complete problems. He also stressed thatalthough one could in principle ‘squeeze’ information ofexponential complexity into polynomially many quantum states, the realproblem lay in the efficient retrieval of this information.

89%

of clients claim significantly improved grades thanks to our work.

98%

of students agree they have more time for other things thanks to us.

Clients Speak

“I didn’t expect I’d be thanking you for actually
improving my own writing, but I am. You’re like a second professor!”