Concepts of Quantum Computers

Armond Duwell

My dissertation consists of two independent parts. Part one of my dissertation examines concepts of quantum information. I clarify three very different concepts of information and assess their implications for understanding quantum mechanics. First I clarify the concept of information due to Shannon, and its relation to physical theories. Using the Shannon concept, I examine two purportedly new concepts of quantum information. I argue that a fundamental philosophical mistake is made regarding these concepts. Advocates of these new concepts do not properly distinguish between the properties of information due to the physical medium it is stored in from the properties of information per se. This distinction is crucial for developing a new concept to help us understand quantum mechanics and evaluating its merits. Part two of my dissertation examines explanations of the efficiency that quantum computers enjoy over classical computers for some computational tasks, and the relationship between explanations of efficiency and interpretations of quantum mechanics. I examine the so-called quantum parallelism thesis, that quantum computers can perform many computations in a single step, a feat thought not to be possible on classical computers. The truth of this thesis is not obvious, and contested by some. I develop a set of general criteria for computation that any computing device must satisfy. I use these criteria to demonstrate that the quantum parallelism thesis is true. As an application of these general criteria for computation I articulate three distinct concepts of parallelism and demonstrate that classical computers can compute in parallel as well. This demonstrates that the truth of the quantum parallelism thesis alone does not provide a complete explanation of the efficiency of quantum computers. I supplement the quantum parallelism thesis to provide a complete explanation. Finally, I address the claim that only the many-worlds interpretation of quantum mechanics can underwrite the truth of the quantum parallelism thesis. The general criteria for computation provide support for the quantum parallelism thesis independent of any interpretation of quantum mechanics.

Daowen Qiu

Manusha Karunathilaka, Shaolun Ruan, Lin-Ping Yuan +5 more

Quantum computing has shown great potential to revolutionize traditional computing and can provide an exponential speedup for a wide range of possible applications, attracting various stakeholders. However, understanding fundamental quantum computing concepts remains a significant challenge for novices because of their abstract and counterintuitive nature. Thus, we propose an analogy-based characterization framework to construct the mental mapping between quantum computing concepts and daily objects, informed by in-depth expert interviews and a literature review, covering key quantum concepts and characteristics like number of qubits, output state duality, quantum concept type, and probability quantification. Then, we developed an AR-based prototype system, Intuit, using situated analytics to explain quantum concepts through daily objects and phenomena (e.g., rotating coins, paper cutters). We thoroughly evaluated our approach through in-depth user and expert interviews. The Results demonstrate the effectiveness and usability of Intuit in helping learners understand abstract concepts in an intuitive and engaging manner.

David Deutsch, ARTUR K. EKERT, Richard Jozsa +3 more

Weisi Tang, Xin Luo

Matrix theory play a fundamental role in classical and quantum computing. Among this paper, we study the fundamental concepts of some matrices including unitary matrix and Hermitian matrix, which may convert some initial qubits into various kinds of qubits. We also explore the fundamental concept of eigenvalues. Furthermore, we input the concept of product vectors. Finally we use above-mentioned concepts examing the entanglement witness for verifying the entanglement in quantum computing and circuits.

G. P. Berman, Gary D. Doolen, Ronnie Mainieri +1 more