• In ancient times, kitchens were often located outside the main living quarters of a home. They were typically small, with an open hearth for cooking and a few basic utensils.
• During the Middle Ages, kitchens began to be built inside castles and manor houses. These kitchens were much larger and more complex than earlier versions, with multiple hearths, ovens, and cooking utensils.
• During the Renaissance, kitchens continued to become more elaborate, with the development of specialized cooking tools and the introduction of new cooking techniques. The kitchen also became a central gathering place for the household.
• With the onset of the Industrial Revolution, kitchens began to incorporate new technologies, such as gas stoves and refrigeration. As more people moved into cities, smaller kitchens became the norm.
• In the 20th century, the design and functionality of kitchens continued to evolve. The introduction of electricity and new materials, such as stainless steel, allowed for more efficient and hygienic kitchens. Open-plan kitchens, where the kitchen is integrated with the living and dining areas, also became popular.
Two universes mosey down the street
Connected by love and a leash and nothing else.
Mostly I look at lamplight through the leaves
While he mooches along with tail up and snout down,
Getting a secret knowledge through the nose
Almost entirely hidden from my sight.
We stand while he’s enraptured by a bush
Till I can’t stand our standing any longer
And haul on the leash to bring him away.
He lives in the moment, which is good for him,
But when I see a stone wall, I think of Greece,
The sort of place he’d have a lot to say about—
The sniffable pots and broken statues,
The seas, the Ionic evenings all in a row.
But he just gives a yelp and comes running over
To smell my palm, and what can I do but
Smile and bend down to give him a hello?
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Department of Computer Science, University of Victoria, Victoria, Canada
Abstract: Quantum computing is an emerging field that can revolutionize our ability to solve problems and enable breakthroughs in many areas including optimization, machine learning, chemistry, and drug design. With the increasing computational power of quantum computers and the proliferation of quantum development kits, the demand for a skilled workforce in quantum computing increases significantly. The theory of quantum computing lies at the crossroads of quantum physics, mathematics, and computer science. The field of quantum computing has matured and can now be explored by all students. While today, quantum computers and simulators are readily accessible and programmable over the internet, quantum computing education is just ramping up.
This paper describes our experiences in organizing and delivering quantum computing workshops for high-school students with little or no experience in the abovementioned fields. We introduce students to the world of quantum computing in innovative ways, such as newly designed “unplugged” activities for teaching basic quantum computing concepts. Overall, we take a programmatic approach and introduce students to the IBM Q Experience using Qiskit and Jupyter notebooks. Our experiences and findings suggest that basic quantum computing concepts are palatable for high-school students, and-due to significant differences between classical and quantum computing-early exposure to quantum computing is a valuable addition to the set of problem-solving and computing skills that high-schoolers obtain before entering university.
Dirac Bra-Ket notation, also known simply as bra-ket notation, is a standard mathematical notation used extensively in quantum mechanics and quantum computing. It was introduced by Paul Dirac and provides a convenient and powerful framework for describing quantum states and their evolution. Here are several ways in which Dirac Bra-Ket notation is important in quantum computing:
Representation of Quantum States:
Kets (|ψ⟩): Quantum states are typically represented as kets, denoted by |ψ⟩. This notation simplifies the representation of complex vectors in a Hilbert space.
Bras (⟨ψ|): The corresponding dual vectors, or bras, are denoted by ⟨ψ|. These are the complex conjugate transpose of the kets.
Inner Product:
The inner product of two states |ψ⟩ and |φ⟩ is written as ⟨ψ|φ⟩. This notation succinctly captures the concept of the probability amplitude, which is fundamental to quantum mechanics and quantum computing.
Outer Product:
The outer product, written as |ψ⟩⟨φ|, represents a linear operator that can be used to construct projection operators and density matrices, which are crucial in quantum algorithms and quantum information theory.
Operators and Measurements:
Quantum operators, such as Hamiltonians and measurement operators, can be conveniently expressed using bra-ket notation. For example, an operator A^\hat{A}A^ acting on a state |ψ⟩ can be written as A^∣ψ⟩\hat{A}|ψ⟩A^∣ψ⟩.
Measurement probabilities are often expressed in terms of bras and kets, e.g., the probability of measuring a state |ψ⟩ in the basis state |φ⟩ is |⟨φ|ψ⟩|².
Tensor Products:
In quantum computing, systems are often composed of multiple qubits, which are represented by tensor products of individual qubit states. Bra-ket notation elegantly handles these tensor products, e.g., |ψ⟩⊗|φ⟩.
Quantum Gates and Circuits:
Quantum gates, which perform operations on qubits, can be represented using unitary operators in bra-ket notation. For example, the action of a gate U on a qubit state |ψ⟩ is written as U|ψ⟩.
Simplifying Complex Expressions:
Bra-ket notation simplifies the manipulation of complex expressions involving quantum states and operators, making it easier to derive results and understand the behavior of quantum systems.
Formalism for Quantum Algorithms:
Many quantum algorithms, such as the Quantum Fourier Transform (QFT) and Grover’s search algorithm, are conveniently expressed and analyzed using bra-ket notation, providing clarity and insight into their functioning.
In summary, Dirac Bra-Ket notation is essential in quantum computing for its ability to provide a clear and concise way to describe and manipulate quantum states, operators, and the evolution of quantum systems. It is a powerful tool that underpins much of the theory and practice in the field.
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