Entangling power in deterministic quantum computation with one qubit

Scalable and efficient quantum computation with photonic qubits requires (i) deterministic sources of single photons, (ii) giant nonlinearities capable of entangling pairs of photons, and (iii) reliable single-photon detectors. In addition, an optical quantum computer would need a robust reversible photon storage device. Here we discuss several related techniques, based on the coherent manipulation of atomic ensembles in the regime of electromagnetically induced transparency, that are capable of implementing all of the above prerequisites for deterministic optical quantum computation with single photons.

Certain algorithms for quantum computers are able to outperform their classical counterparts. In 1994, Peter Shor came up with a quantum algorithm that calculates the prime factors of a large number vastly more efficiently than a classical computer. For general scalability of such algorithms, hardware, quantum error correction, and the algorithmic realization itself need to be extensible. Here we present the realization of a scalable Shor algorithm, as proposed by Kitaev. We factor the number 15 by effectively employing and controlling seven qubits and four "cache qubits" and by implementing generalized arithmetic operations, known as modular multipliers. This algorithm has been realized scalably within an ion-trap quantum computer and returns the correct factors with a confidence level exceeding 99%.

The main purpose of this review is to deal with questions related to the nature of quantum information and particularly with quantum entanglement as an important component of quantum information and computing. We will not discuss here quantum computer algorithms, like the algorithm by Shor, or their advantages and disadvantages. We only cover the material that lies at the foundations of quantum information and computing and epistemological questions. We attempt to connect the famous debate between Einstein and Bohr on quantum entanglement to some of the latest work on qubits and quantum computing and to the mathematical theorems that form the basis of these discussions, particularly the theorem of Bell. We present a critical analysis of this material and hope that this will give the reader a better understanding of what can be said with certainty about the nature of quantum information.

SUMMARY Quantum computing has attracted considerable attention in recent years because it promises speedups that conventional supercomputers cannot offer, at least for some applications. Though existing quantum computers (QCs) are, in most cases, still too small to solve significant problems, their future impact on domain sciences is already being explored now. Within this context, we present a quantum computing concept for 1-D elastic wave propagation in heterogeneous media with two components: a theoretical formulation and an implementation on a real QC. The method rests on a finite-difference approximation, followed by a sparsity-preserving transformation of the discrete elastic wave equation to a Schrödinger equation, which can be simulated directly on a gate-based QC. An implementation on an error-free quantum simulator verifies our approach and forms the basis of numerical experiments with small problems on the real QC IBM Brisbane. The latter produce simulation results that qualitatively agree with the error-free version but are contaminated by quantum decoherence and noise effects. Complementing the discrete transformation to the Schrödinger equation by a continuous version allows the replacement of finite differences by other spatial discretization schemes, such as the spectral-element method. Anticipating the emergence of error-corrected quantum chips, we analyse the computational complexity of the best quantum simulation algorithms for future QCs. This analysis suggests that our quantum computing approach may lead to wavefield simulations that run exponentially faster than simulations on classical computers.

Recent improvements in control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure problems and idealized model Hamiltonians, the highly relevant problem of directly solving a complex correlated material appears to require a prohibitive amount of resources. Here, we show that by using a hybrid quantum-classical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer. In our approach, the quantum computer solves a small effective quantum impurity problem that is self-consistently determined via a feedback loop between the quantum and classical computation. Use of a quantum computer enables much larger and more accurate simulations than with any known classical algorithm, and will allow many open questions in quantum materials to be resolved once a small quantum computer with around one hundred logical qubits becomes available.

Quantum computers perform computations exploiting quantum mechanics to a possible advantage, allowing us to prepare and manipulate states that do not have a classical equivalent. In particular, phenomena like superposition and entanglement may enable quantum computers to outperform their classical counterparts in certain applications. Implementing these useful quantum algorithms is contingent upon building accurate quantum hardware that is not affected by noise. Environmental noise decreases coherence time of qubits, meaning that qubits do not stay in a desired state long enough to carry out a complex computation. To that end, harnessing the full power of quantum computers necessitate characterization of noise sources and how they impact a given quantum system. Often times, T1and T2 are used to quantify noise. In this project, we provide an approach as to how T1 and T2 values are calculated and simulated for quantum systems. In addition, we compare simulated values of T1 and T2 with those of real quantum computer’s measurements. IBMQ Experience, an open source software allowing users to simulate and use real quantum hardware, is used. QuTip, a Python-based toolbox offering quantum simulation tools for open quantum systems, is also used.

Computer science will be radically transformed if ongoing efforts to build large-scale quantum computers eventually succeed and if the properties of these computers meet optimistic expectations. Nevertheless, computer scientists still lack a thorough understanding of the power of quantum computing, and it is not always clear how best to utilize the power that is understood. This dilemma exists because quantum algorithms are difficult to grasp and even more difficult to write. Despite large-scale international efforts, only a few important quantum algorithms are documented, leaving many essential questions about the potential of quantum algorithms unanswered. These unsolved problems are ideal challenges for the application of automatic programming technologies. Genetic programming techniques, in particular, have already produced several new quantum algorithms and it is reasonable to expect further discoveries in the future. These methods will help researchers to discover how additional practical problems can be solved using quantum computers, and they will also help to guide theoretical work on both the power and limits of quantum computing. This tutorial will provide an introduction to quantum computing and an introduction to the use of evolutionary computation for automatic quantum computer programming. No background in physics or in evolutionary computation will be assumed. While the primary focus of the tutorial will be on general concepts, specific results will also be presented, including human-competitive results produced by genetic programming. Follow-up material is available from the presenter's book, Automatic Quantum Computer Programming: A Genetic Programming Approach, published by Springer and Kluwer Academic Publishers.

This paper explores the impact of quantum computing on modern information security technologies, especially the threat to traditional encryption methods. The parallel processing capability of quantum computing and Shor algorithm make traditional encryption methods face the risk of being cracked. To address this challenge, this paper introduces novel cryptographic methods based on quantum computing, including quantum walking (QW) and quantum entanglement based cryptographic schemes, as well as quantum attack-resistant cryptographic algorithms (PQC). The computing principles, advantages and disadvantages of NTRUEncrypt and Lattice-based encryption algorithms are discussed in detail, and the application and prospect of these new encryption methods in information security are analyzed.

An application of an evolutionary approach to hardware design is presented. A genetic algorithm was developed to discover good designs for quantum computer algorithms. The algorithms are expressed as quantum operator sequences applied in a circuit model. The circuits discovered are configurations of special purpose quantum computers. We have been exploring the evolution of algorithms as alternative configurations of hardware. By simulation it is established that the circuits will correctly compute a small collection of basic, low-level functions. Experiments produced designs for primitive quantum computers that evaluate logical or arithmetic functions with a total of twelve or fewer inputs and outputs.

A quantum computation algorithm is demonstrated using single photons and linear optics. Quantum registers are realized by modes and polarization of photons, and the unitary transformations for them are implemented with linear optics. For each quantum computation, the answer to the Deutsch Jozsa problem for any 4 bit digit is given by a single-photon detection signal with a small error rate. The origin of the error is also studied and categorized according to the sources: systematic errors of quantum gates, phase relaxation, amplitude dumping, and misreadout. It is suspected that a demonstration of 11 qubits using linear optics anda single photon with less than a 20 % error rate is achievable by the technique used in the experiment. As a further objective, an idea to construct controlled-NOT gate using quantum phase gate (QPG) given by Chuang et. al., is introduced and experiments on the QPGs are also reviewed.

Quantum Machine Learning (QML) is a new phraseology in the world today. With various upcoming Artificial Intelligence (AI) technologies, everyday data scientists and corporate around the world are trying to harness its power. QML borrows concepts of Quantum Computing and QML algorithms enhance the existing Machine Learning (ML) algorithms by processing datasets more efficiently. Quantum Computers are a powering force driving QML algorithms that boosts computational power and helps analyse data. QML algorithms can be applied in sectors involving number crunching, pattern identification and so on. In the existing world, QML can be a game-changer for organizations that work on identifying product correlations and customer behaviour in a brief time. This paper discusses studies related to principles of Quantum Mechanics, Quantum Computing and QML algorithm. Additionally, it explores opportunities and challenges faced in the field of QML. Lastly, the paper talks about QML applications and compares various available QML toolkits from the market. Future direction and exhaustive survey of papers from various spectrums related to Quantum Computing is presented in this paper.

Since a quantum computational system is a generalization of a classical computational system, its computational power should be greater or equal than that of the classical system. In spite of that the computational power of 1-way quantum finite automata has been shown to be smaller than that of their classical counterpart. I argue that this paradox lies on the ground that the currently accepted definition of quantum automaton neglects the concept of quantum reversibility. In this article I review the role that reversibility plays into quantum computing and I propose a new model of 1-way quantum finite automata whose computational power is at least equal to that of classical automata.

Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in which a quantum state plays the role of a proof (also called a certificate or witness), and is checked by a polynomial-time quantum computation. For some problems, the fact that a quantum proof state could be a superposition over exponentially many classical states appears to offer computational advantages over classical proof strings. In the interactive proof system setting, one may consider a verifier and one or more provers that exchange and process quantum information rather than classical information during an interaction for a given input string, giving rise to quantum complexity classes such as QIP, QSZK, and QMIP* that represent natural quantum analogues of IP, SZK, and MIP. While quantum interactive proof systems inherit some properties from their classical counterparts, they also possess distinct and uniquely quantum features that lead to an interesting landscape of complexity classes based on variants of this model. In this survey we provide an overview of many of the known results concerning quantum proofs, computational models based on this concept, and properties of the complexity classes they define. In particular, we discuss non-interactive proofs and the complexity class QMA, single-prover quantum interactive proof systems and the complexity class QIP, statistical zero-knowledge quantum interactive proof systems and the complexity class \class{QSZK}, and multiprover interactive proof systems and the complexity classes QMIP, QMIP*, and MIP*.

We theoretically present a method to realize a deterministic photon-photon (SWAP)^{1/2} gate using a three-level lambda system interacting with single photons in reflection geometry. The lambda system is used completely passively as a temporary memory for a photonic qubit; the initial state of the lambda system may be arbitrary, and active control by auxiliary fields is unnecessary throughout the gate operations. These distinct merits make this entangling gate suitable for deterministic and scalable quantum computation.

We propose a novel confinement method of photons, temporal trapping, to circumvent the tradeoff between optical confinement and loss in nonlinear photonics, showing a potential route to all-optical strong coupling and deterministic optical quantum computation.