Experimental realization of universal geometric quantum gates with solid-state spins.

Geometric phase is a promising element to induce high-fidelity and robust quantum operations due to its built-in noise-resilience feature. Unfortunately, its practical applications are usually circumscribed by requiring complex interactions among multiple levels/qubits and the longer gate-time than the corresponding dynamical ones. Here, we propose a general framework of geometric quantum computation with the integration of the time-optimal control technique, where the shortest smooth geometric path is found to realize accelerated geometric quantum gates, and thus greatly decreases the gate errors induced by both the decoherence effect and operational imperfections. Meanwhile, we faithfully implement our idea on a scalable platform of a two-dimensional superconducting transmon-qubit lattice, with simple and experimental accessible interactions. In addition, numerical simulations show that our implemented geometric gates possess higher fidelities and stronger robustness, which outperform the best performance of the corresponding dynamical ones. Therefore, our scheme provides a promising alternative way towards scalable fault-tolerant solid-state quantum computation.

The first quantum revolution provided a microscopic understanding of nature and underpinned the development of transistors, originally made in germanium. The following assembly of silicon transistors into integrated circuits triggered the digital age, which completely changed our daily life. We are now in the midst of the second quantum revolution, in which quantum matter is engineered to develop disruptive technologies beyond the reach of classical understanding. Quantum computing is considered by many the man on the moon goal of such second quantum revolution. How will we get there? In this talk I will discuss, from a materials perspective, how we are turning everyday silicon into the quantum computing wonder material by using quantum dots defined electrostatically in SiGe heterostructures. Group-IV semiconductors Si and Ge offer several advantages for the realization of spin quantum bits. Si and Ge can be isotopically purified into a nuclear spin free materials, which allows long spin coherence time. A quantum dot defined by metallic gates in a strained Si/SiGe heterostructure can trap a single electron, such that the electron spin can be operated as a quantum bit, the elementary unit of quantum computation. Quantum dots in Si/SiGe heterostructure are promising because bear similarities from a materials and integration perspective to the transistors used in advanced semiconductor manufacturing. Advanced quantum control in Si qubits allows to run quantum algorithms on two qubit processors. Strong spin-photon coupling has been achieved in Si, a first step towards realizing large networks of quantum dot based spin qubit registers.[1] Additionally, SiGe heterostructures allows us to explore high mobility holes in strained Ge as a complementary option for fast quantum hardware due to the different band structure properties of Ge compared to Si. Recently, gate-controlled stable quantum dots were demonstrated in planar Ge, a first step towards Ge hole qubits.[2] However, to deploy a qubit into high volume manufacturing in a quantum computer requires stringent control over substrate uniformity and quality. In this talk we will focus on carrier mobility and energetic valley splittings in SiGe heterostructures, which are two key electrical metrics of substrate quality relevant for qubits. To ensure rapid progress in quantum wells development we have implemented fast feedback loops from materials growth, to innovative heterostructure field effect transistor fabrication, and low temperature characterization. In this direction we show progress in developing a cryogenic platform for high-throughput magnetotransport measurements. [1] N. Samkharadze, G. Zheng, N. Kalhor, D. Brousse, A. Sammak, U. C. Mendes, A. Blais, G. Scappucci, and L. M. K. Vandersypen, Science , eaar4054 (2018). [2] N. W. Hendrickx, D.P. Franke, A. Sammak, M. Kouwenhoven, D. Sabbagh, L. Yeoh, R. Li, M. L. V. Tagliaferri, M. Virgilio, G. Capellini, G. Scappucci, M. Veldhorst, arXiv:1801.08869 (2018)

The nonadiabatic geometric quantum computation is promising as it is robust against certain types of local noises. However, its experimental implementation is challenging due to the need of complex control on multi-level and/or multiple quantum systems. Here, we propose to implement it on a two-dimensional square superconducting qubit lattice. In the construction of our geometric quantum gates, we only use the simplest and experimentally accessible control over the qubit states of the involved quantum systems, without introducing any auxiliary state. Specifically, our scheme is achieved by parametrically tunable all-resonant interaction, which leads to high-fidelity quantum gates. Meanwhile, this simple implementation can be conveniently generalized to a composite scenario, which can further suppress the systematic error during the gate operations. In addition, universal nonadiabatic geometric quantum gates in decoherence-free subspace can also be realized based on the tunable coupling between only two transmon qubits, without consulting to multiple qubits and only using two physical qubits to encode a logical qubit. Therefore, our proposal provides a promising way of high-fidelity geometric manipulation for robust solid-state quantum computation.

Recent devices, using hundreds of superconducting quantum bits, claim to perform quantum computing. However, it is not an easy task to determine and quantify the degree of quantum coherence and control used by these devices. Namely, it is a difficult task to know with certainty whether or not a given device (e.g., the D-Wave One or D-Wave Two) is a quantum computer. Such a verification of quantum computing would be more accessible if we already had some kind of working quantum computer, to be able to compare the outputs of these various computing devices. Moreover, the verification process itself could strongly depend on whether the tested device is a standard (gate-based) or, e.g., an adiabatic quantum computer. Here we do not propose a technical solution to this quantum-computing “verification problem”, but rather outline the problem in a way which would help both specialists and non-experts to see the scale of this difficult task, and indicate some possible paths towards its solution.

Because in IBM’s quantum computers, they only provide quantum gates of single quantum bit and two quantum bits, quantum gates of three quantum bits and many quantum bits must manually be decomposed into quantum gates of single quantum bit and two quantum bits. A good quantum algorithm of solving any given problem with the size of the input of n bits must have a constant successful probability of measuring its answer(s) that is close to one as soon as possible. In this chapter, we first illustrate how to decompose quantum gates of three quantum bits and many quantum bits into quantum gates of single quantum bit and two quantum bits. Next, we introduce how to write quantum programs with version 2.0 of Open QASM to implement decomposition among various kinds of quantum gates. A quantum search algorithm that is sometimes known as Grover’s algorithm to find an item in unsorted databases with 2n items that satisfies any given condition can give a quadratic speed-up and is the best one known. Hence, we then describe how to write quantum programs with version 2.0 of Open QASM to implement the quantum search algorithm in order to solve various applications.

The classical computer is restricted by Moore's law and other factors into the development bottleneck, quantum computer by virtue of its natural acceleration advantage into the field of vision. Quantum computing can achieve the acceleration effect compared with classical computing in many fields. In the field of integer decomposition, Shor algorithm can be solved in polynomial time, which breaks the security of RSA public key cryptosystem. However, the quantum bits (logn + 2, where n is the integer to be decomposed) required by Shor algorithm are difficult to be realized on today's quantum computers. Therefore, the hybrid quantum algorithm model of "classical + quantum (Grover algorithm)" is tried to realize the decomposition of large integers. In this paper, based on the previous hybrid quantum algorithm model, considering that the continuous accumulation of errors in the circuit of the quantum algorithm will lead to the failure of the algorithm as the depth increases, part of the circuit of the quantum algorithm oracle is optimized to reduce the consumption of the depth, quantum gate and quantum bit in the circuit of the quantum algorithm, so as to make it easier to run on the actual quantum computer. By running the optimized quantum circuit on the back end of the simulator of IBM Q quantum cloud platform, and trying to add thermal relaxation and depolarization noises to the circuit, the influence of different noises on the circuit under different iterations was explored.

Quantum computing is a multidisciplinary field at the intersectionof quantum physics, computer science, and mathematics, aiming to har-ness quantum mechanical phenomena for computational advantage. Thisarticle provides a comprehensive review of both the foundational princi-ples and advanced theoretical models of quantum computing. We beginwith the basic framework of quantum computation, introducing the con-cept of qubits as two-level quantum systems, the linear algebra of Hilbertspaces, Dirac’s bra–ket notation, and the postulates of quantum mechan-ics (state superposition, unitary evolution, and projective measurement).We then discuss quantum logic gates and circuits, highlighting how clas-sical reversible computation principles extend to universal quantum gatesets. Next, we survey key quantum algorithms (from Shor’s factoring toGrover’s searching and beyond) and the complexity-theoretic implicationsof quantum computers, contrasting the class BQP with classical complex-ity classes. We cover the theoretical foundations of quantum error cor-rection and fault tolerance, explaining how quantum information can beprotected from decoherence using redundancy and how fault-tolerant pro-tocols can, in principle, allow scalable quantum computation despite noisyhardware. We then explore advanced models and paradigms of quantumcomputation, including measurement-based quantum computing (one-wayquantum computing), topological quantum computation with anyons, adi-abatic quantum computing and quantum annealing, continuous-variablequantum computing, and related approaches. We also provide an overviewof quantum information theory as it relates to computation, discussingentanglement, quantum entropy, and information-theoretic limits like theHolevo bound. Finally, we review the leading physical implementations(quantum hardware models) of quantum computers—trapped ions, super-conducting circuits, photonic systems, solid-state spin qubits, and oth-ers—outlining the challenges and achievements of each approach.

In this paper we will investigate the action of holonomic and topological quantum gates on different classes of four qubit states. In particular, we review the construction of holonomic quantum gate based on geometric phase and topological quantum gate based on braid group. Then, we investigate the entanglement properties of three different classes of four‐qubit states based on geometric invariants. The result shows that entanglement properties of the two most generic classes of four‐qubit states can be controlled by holonomic and topological quantum gate..

Classic computing can take credit for technology ranging from mobile phones to supercomputers. But in recent years, a budding counterpart to these conventional devices has emerged: quantum computers. Whereas classic computing sometimes fails to solve complex calculations, such as factoring hundred-digit numbers, quantum computing holds the potential to easily tackle such problems. The field of quantum computing has attracted researchers, such as National Academy of Sciences member Christopher Monroe. An experimental atomic physicist at the University of Maryland and fellow of the Joint Quantum Institute and the Joint Center for Quantum Information and Computer Science in Maryland, Monroe uses lasers to exploit atomic particles to study complex computational problems. Monroe spoke to PNAS about how quantum computing might evolve. Christopher Monroe. > PNAS:Can you describe some of the basic mechanics of quantum computing? > Monroe:It all comes down to the superposition principle, in which a quantum system can exist in multiple states at the same time. Consider the fundamental unit of information: the bit. A bit is binary information that can be a 0 or a 1. A quantum bit, or qubit, can be in a superposition of both 0 and 1 as long as it’s isolated and unobserved. A single qubit is pretty trivial, but when you put many qubits together, there become exponentially many possibilities. > > Let’s consider 300 qubits. That’s an interesting number because the number of possible configurations, 2300, is more than the number of particles in the universe. You could never simulate what happens with 300 qubits on a classical machine; there’s not enough stuff in the universe to do it. The magic with quantum is the power of exponential growth: every time you add a qubit, you double the number of configurations. > > But to control these qubits and exploit this massive storage, we …

Geometric phases in superconducting nanocircuits

Fundamental transformations in the basic logic of computing are few and far between. Since the invention of digital computers in the early 1940s, the logic underlying computation has remained the same, even as computing hardware evolved from vacuum tubes to silicon transistors. With the advent of quantum computation, a fundamental transformation is near. Quantum computation is based on a different type of logic: rather than being in one of the two states of a classical bit, a quantum bit or qubit can be in a superposition of two states simultaneously. Operations and measurements on these qubits obey the constraints of quantum mechanics. It is now understood that quantum computers have great power in principle to go beyond classical computers, but that not every application is well suited to implementation on quantum computers. For reasons explained in more detail in the Introduction, scientific problems in chemical and materials sciences are uniquely suited to take advantage of quantum computing in the relatively near future. Indeed, quantum computing offers the best hope to solve many of the most important and difficult problems in this field. For example, quantum materials, such as superconductors and complex magnetic materials, show novel kinds of ordered phases that are natural from the point of view of quantum mechanics but difficult to access via computation on classical computers. Quantum sensors based on solid materials are already widely used but could be greatly improved with insight from quantum computations, as could materials for information technologies. Quantum chemical dynamics is another example of a problem that is intrinsically well suited to studies on quantum computers. Applications of quantum chemical dynamics include catalysis, artificial photosynthesis, and other industrially important processes. Quantum computers exist in the laboratory and are beginning to exceed 50 qubits, which is roughly the size beyond which their behavior cannot be predicted or emulated on present-day classical supercomputers. While a quantum computer of 50 qubits is almost certainly not powerful enough to tackle the major scientific challenges in chemical and materials sciences, some of these major challenges start to become accessible with a few hundred qubits if error rates can be kept small. This roundtable was convened to ask how emerging quantum computers can be applied to major scientific problems in chemical and materials sciences, in light of Basic Energy Sciences’s leading role in these fields and the Department of Energy’s leading role in high-performance scientific computation more generally. The main outcome of the roundtable was a consensus that there are scientific problems of great importance on which emerging quantum computers have the potential for disruptive impact, and where comparable progress is unlikely to occur by other means.

This paper proposes a design of a coplanar waveguide resonator (CPWR) to integrate two distant superconducting qubits which is a function required for a quantum information system. In this CPWR, the states of one of the super conducting qubits can be moved to and recovered from the other qubit by microwave resonator photons. The superconducting qubits are relatively straightforward to fabricate from materials such as aluminium using electron beam lithography. The superconducting qubits, which are typically a few hundred micrometres in size, are well suited to perform fast quantum logic gate operations. The CPWR highly couples the two qubits through the tightly confined oscillating magnetic field of the resonator microwave photons. It is shown that, in the proposed CPW resonator structure, the microwave photons can mediate coupling between two distant superconducting qubits (21 mm apart) to realize quantum logic gates.

Since its inception by Richard Feynman in 1982, quantum computing has provided an intriguing opportunity to advance computational capabilities over classical computing. Classical computers use bits to process information in terms of zeros and ones. Quantum computers use the complex world of quantum mechanics to carry out calculations using qubits (the quantum analog of a classical bit). The qubit can be in a superposition of the zero and one state simultaneously unlike a classical bit. The true power of quantum computing comes from the complexity of entanglement between many qubits. When entanglement is realized, quantum algorithms for problems such as factoring numbers and solving linear algebra problems show exponential speed-up relative to any known classical algorithm. Linear algebra problems are of particular interest in engineering application for solving problems that use finite element and finite difference methods. Here, we explore quantum linear algebra problems where we design and implement a quantum circuit that can be tested on IBM’s quantum computing hardware. A set of quantum gates are assimilated into a circuit and implemented on the IBM Q system to demonstrate its algorithm capabilities and its measurement methodology.

Decoherence in quantum bit circuits is presently a major limitation to their use for quantum computing purposes. We present experiments, inspired from NMR, that characterise decoherence in a particular superconducting quantum bit circuit, the quantronium. We introduce a general framework for the analysis of decoherence, based on the spectral densities of the noise sources coupled to the qubit. Analysis of our measurements within this framework indicates a simple model for the noise sources acting on the qubit. We discuss various methods to fight decoherence.

Experimental results on both serial and parallel double quantum dots are presented. The quantum dots are realized in the two-dimensional electron gas of an AlGaAs/GaAs heterostructure. By varying the inter-dot tunnel barriers, double quantum dots are tuned from the weak coupling limit to the strong coupling case. In serial double quantum dots, bonding and anti-bonding molecular states are probed by both direct tunneling and photon-assisted tunneling spectroscopy. In parallel double quantum dots, a coherent transport through the whole structure is verified through Aharonov-Bohm oscillations in the magnetotransport data. Furthermore, coherent molecular states are read out by a cotunneling current. Finally, a scheme for preparing and measuring a solid-state quantum bit is discussed. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)