Probing chaos by magic monotones

The Wigner function formalism has played a pivotal role in examining the nonclassical aspects of quantum states and their classical simulatability. Nevertheless, its application in qubit systems faces limitations due to negativity induced by Clifford gates. In this Letter, we propose a novel classical simulation method for qubit Clifford circuits based on the framed Wigner function, an extended form of the Wigner function with an additional phase degree of freedom. In our framework, Clifford gates do not induce negativity by switching to a suitable frame; thereby, a wide class of nonstabilizer states can be represented positively. By leveraging this technique, we show that some marginal outcomes of Clifford circuits with nonstabilizer state inputs can be efficiently sampled at polynomial time and memory costs. We develop a graph-theoretical approach to identify classically simulatable marginal outcomes and apply it to log-depth random Clifford circuits. We also present the outcome probability estimation scheme using the framed Wigner function and discuss its precision. Our approach opens new avenues for utilizing quasiprobabilities to explore classically simulatable quantum circuits.

Stabilizer operations (SO) occupy a prominent role in fault-tolerant quantum computing. They are defined operationally by the use of Clifford gates, Pauli measurements, and classical control. These operations can be efficiently simulated on a classical computer, a result which is known as the Gottesman–Knill theorem. However, an additional supply of magic states is enough to promote them to a universal, fault-tolerant model for quantum computing. To quantify the needed resources in terms of magic states, a resource theory of magic has been developed. SO are considered free within this theory; however, they are not the most general class of free operations. From an axiomatic point of view, these are the completely stabilizer-preserving (CSP) channels, defined as those that preserve the convex hull of stabilizer states. It has been an open problem to decide whether these two definitions lead to the same class of operations. In this work, we answer this question in the negative, by constructing an explicit counter-example. This indicates that recently proposed stabilizer-based simulation techniques of CSP maps are strictly more powerful than Gottesman–Knill-like methods. The result is analogous to a well-known fact in entanglement theory, namely, that there is a gap between the operationally defined class of local operations and classical communication and the axiomatically defined class of separable channels.

As quantum computing development advances closer toward achieving fault-tolerant error-corrected realisation, debates on applications, impacts, risks, and benefits of quantum computing are timely and due. While there is awareness of the potential power and complexity of quantum computers, there has been relatively little attention on the social impacts and ethical implications of this technology. In grappling with the social impacts of quantum computing, some stakeholders have turned to applied ethics, specifically (classical) computer and Artificial Intelligence (AI) ethics, for guidance. While computer and AI ethics are useful starting points for evaluating the ethical issues posed by quantum computing, uncritically applying existing sets of ethical principles risks overlooking how quantum computing differs from these technologies. We argue that borrowing of ethical principles and guidelines from AI and computing is inappropriate for several reasons: (1) quantum computing, classical computing, and AI are different technologies with significant material differences; (2) unlike AI and classical computers which have become established, quantum computing is an emerging technology, which has implications on the levels of accessibility and immediate impact in society; and (3) there are significant differences in the way AI and quantum computing have been developed and by whom. We also briefly summarise some of the unique risks and societ al impacts posed by quantum computing. We posit that these reasons support the argument for a new sub-field of quantum computing ethics, which would allow a relevant scholarship to develop and provide guidance as quantum computing technology continues to mature.

In the world of computation, the invention of Computers has reduced human effort for accomplishing task. Depending on the type, size and nature of the work the computers are manufactured in different magnitudes. As the technology grows, it facilitated to manufacture high performing, high throughput, and high memory Classical computers. Classical computers store any information in the form of bits in the memory device, which can be either 1 or 0 (binary system) and all the processing will be done in the same logic i.e., high voltage/low voltage. Because of this logic the classical computers solve some problems by using more resources. Quantum computer are the next level computers which uses quantum theory principles for solving problems. The quantum computer uses Qubit as basic unit which uses principles of quantum computing such as superposition and entanglement, which gives qubit, the efficiency of exhibiting many logical states at a time. This paper shows a comparative study on classical and quantum computers and illustrates various problems in classical computers and respective solutions with use of quantum computers.

Exploring the trade-off between computational power and energy efficiency: An analysis of the evolution of quantum computing and its relation to classical computing

When visualised as an operation on the Bloch sphere, the qubit\n"pi-over-eight" gate corresponds to one-eighth of a complete rotation about the\nvertical axis. This simple gate often plays an important role in quantum\ninformation theory, typically in situations for which Pauli and Clifford gates\nare insufficient. Most notably, when it supplements the set of Clifford gates\nthen universal quantum computation can be achieved. The "pi-over-eight" gate is\nthe simplest example of an operation from the third level of the Clifford\nhierarchy (i.e., it maps Pauli operations to Clifford operations under\nconjugation). Here we derive explicit expressions for all qudit (d-level, where\nd is prime) versions of this gate and analyze the resulting group structure\nthat is generated by these diagonal gates. This group structure differs\ndepending on whether the dimensionality of the qudit is two, three or greater\nthan three. We then discuss the geometrical relationship of these gates (and\nassociated states) with respect to Clifford gates and stabilizer states. We\npresent evidence that these gates are maximally robust to depolarizing and\nphase damping noise, in complete analogy with the qubit case. Motivated by this\nand other similarities we conjecture that these gates could be useful for the\ntask of qudit magic-state distillation and, by extension, fault-tolerant\nquantum computing. Very recent, independent work by Campbell, Anwar and Browne\nconfirms the correctness of this intuition, and we build upon their work to\ncharacterize noise regimes for which noisy implementations of these gates can\n(or provably cannot) supplement Clifford gates to enable universal quantum\ncomputation.\n

A Busy March Meeting Is Brewing in Seattle

During recent years, quantum computers have received increasing attention, primarily due to their ability to significantly increase computational performance for specific problems. Computational performance could be improved for mathematical optimization by quantum annealers. This special type of quantum computer can solve quadratic unconstrained binary optimization problems. However, multi-energy systems optimization commonly involves integer and continuous decision variables. Due to their mixed-integer problem structure, quantum annealers cannot be directly used for multi-energy system optimization.To solve multi-energy system optimization problems, we present a hybrid Benders decomposition approach combining optimization on quantum and classical computers. In our approach, the quantum computer solves the master problem, which involves only the integer variables from the original energy system optimization problem. The subproblem includes the continuous variables and is solved by a classical computer. For better performance, we apply improvement techniques to the Benders decomposition. We test the approach on a case study to design a cost-optimal multi-energy system. While we provide a proof of concept that our Benders decomposition approach is applicable for the design of multi-energy systems, the computational time is still higher than for approaches using classical computers only. We therefore estimate the potential improvement of our approach to be expected for larger and fault-tolerant quantum computers.

According to the Gottesman-Knill theorem, quantum algorithms which utilise only the operations belonging to a certain restricted set are efficiently simulable classically. Since some of the operations in this set generate entangled states, it is commonly concluded that entanglement is insufficient to enable quantum computers to outperform classical computers. I argue in this paper that this conclusion is misleading. First, the statement of the theorem (that the particular set of quantum operations in question can be simulated using a classical computer) is, on reflection, already evident when we consider Bell's and related inequalities in the context of a discussion of computational machines. This, in turn, helps us to understand that the appropriate conclusion to draw from the Gottesman-Knill theorem is not that entanglement is insufficient to enable a quantum performance advantage, but rather that if we limit ourselves to the operations referred to in the Gottesman-Knill theorem, we will not have used the resources provided by an entangled quantum system to their full potential.

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.

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 …

Quantum computing is an extremely promising research combining theoretical and experimental quantum physics, mathematics, quantum information theory and computer science. Classical simulation of quantum computations will cover part of the gap between the theoretical mathematical formulation of quantum mechanics and the realization of quantum computers. One of the most important problems in “quantum computer science” is the development of new symbolic languages for quantum computing and the adaptation of existing symbolic languages for classical computing to quantum algorithms. The present paper is devoted to the adaptation of the Mathematica symbolic language to known quantum algorithms and corresponding simulation on the classical computer. Concretely we shall represent in the Mathematica symbolic language Simon’s algorithm, the Deutsch-Josza algorithm, Grover’s algorithm, Shor’s algorithm and quantum error-correcting codes. We shall see that the same framework can be used for all these algorithms. This framework will contain the characteristic property of the symbolic language representation of quantum computing and it will be a straightforward matter to include this framework in future algorithms.KeywordsDeutsch-Josza algorithmGrover’s algorithmQuantum computingQuantum error-correctingShor’s algorithmSimon’s algorithmSimulation of quantum algorithms

Quantum computers have the potential to create important new opportunities for ongoing essential research on gauge theories. They can provide simulations that are unattainable on classical computers such as sign-problem afflicted models or time evolutions. In this work, we variationally prepare the low-lying eigenstates of a non-Abelian gauge theory with dynamically coupled matter on a quantum computer. This enables the observation of hadrons and the calculation of their associated masses. The SU(2) gauge group considered here represents an important first step towards ultimately studying quantum chromodynamics, the theory that describes the properties of protons, neutrons and other hadrons. Our calculations on an IBM superconducting platform utilize a variational quantum eigensolver to study both meson and baryon states, hadrons which have never been seen in a non-Abelian simulation on a quantum computer. We develop a hybrid resource-efficient approach by combining classical and quantum computing, that not only allows the study of an SU(2) gauge theory with dynamical matter fields on present-day quantum hardware, but further lays out the premises for future quantum simulations that will address currently unanswered questions in particle and nuclear physics.

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.

Quantum machine learning [QML] is a new formulation on quantum hardware platform will try to achieve more enhanced data analysis and prediction which classical computer will not be able to generate. Classical computers are having computational limitations in terms of large volume data processing. Quantum machine are not to replace classical machines but quantum computers will solve operational difficulties of classical machines in terms of computational time. Quantum machine learning accelerates the supervised, unsupervised, and reinforcement learning methods. Classical ML methods such as SVM, PCA, Clustering, Neural networks are giving promising results but classical machines are inadequate to perform certain computations. Proposed Quantum machine learning would result in complex and weird patterns. Quantum support vector machine(QSVM) is a method used in supervised learning for classification and regression. QSVM uses high-dimensional feature space possibly on infinite dimension called as enhanced feature space for generating hyperplane. This hyperplane will classify non-linear and complex data on multiclass domain to achieve improved accuracy in less computational time. This paper investigates various strategies for quantum enhanced machine learning algorithm in supervised learning method. KeywordsQuantum computingMachine learningQubitQuantum machine learningSupport vector machine