17 pages, forthcoming in Probing the Meaning and Structure of Quantum Mechanics: Superpositions, Semantics, Dynamics and Identity, D. Aerts, C. de Ronde, H. Freytes and R. Giuntini (Eds.), World Scientific, Singapore, 2015
In this paper we consider the phenomenon of superpositions in quantum mechanics and suggest a way to deal with the idea in a logical setting from a syntactical point of view, that is, as subsumed in the language of the formalism, and not semantically. We restrict the discussion to the propositional level only. Then, after presenting the motivations and a possible world semantics, the formalism is outlined and we also consider within this schema the claim that superpositions may involve contradictions, as in the case of the Schrödinger's cat, which (it is usually said) is both alive and dead. We argue that this claim is a misreading of the quantum case. Finally, we sketch a new form of quantum logic that involves three kinds of negations and present the relationships among them. The paper is a first approach to the subject, introducing some main guidelines to be developed by a `syntactical' logical approach to quantum superpositions.
Large-scale quantum computers will inevitably need quantum error correction to protect information against decoherence. Traditional error correction typically requires many qubits, along with high-efficiency error syndrome measurement and real-time feedback. Autonomous quantum error correction (AQEC) instead uses steady-state bath engineering to perform the correction in a hardware-efficient manner. We realize an AQEC scheme, implemented with only two transmon qubits in a 2D scalable architecture, that actively corrects single-photon loss and passively suppresses low-frequency dephasing using …
A measurement-induced continuous-variable logical gate is able to prepare Schrödinger cat states if the gate uses a non-Gaussian resource state, such as cubic phase state [I. V. Sokolov, Phys. Lett. A 384, 126762 (2020)]. Our scheme provides an alternative to hybrid circuits which use photon subtraction and (or) Fock resource states and photon number detectors. We reveal the conditions under which the gate conditionally prepares quantum superposition of two undistorted "copies" of an arbitrary input state that occupies a finite area in phase space. A detailed analysis of the fidelity between t…
Quantum Error Correction with Superpositions of Squeezed Fock States
RIKEN Center for Quantum Computing, RIKEN（理化学研究所量子计算中心）；Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University（湖南师范大学低维量子结构与量子控制教育部重点实验室、物理系及量子效应与应用协同创新中心）；Quantum Research Institute and Department of Physics, University of Michigan（密歇根大学量子研究所与物理系）
Practical quantum computing requires robust encoding of logical qubits in physical systems to protect fragile quantum information. Currently, the lack of scalability limits the logical encoding in most physical systems, and thus the high scalability of propagating light can be a game changer for realizing a practical quantum computer. However, propagating light also has a drawback: the difficulty of logical encoding due to weak nonlinearity. Here, we propose Gaussian breeding that encodes arbitrary Gottesman-Kitaev-Preskill (GKP) qubits in propagating light. The key idea is the efficient and i…
At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would generate a non-distributive lattice of propositions, and from quantum superpositions, which would entail new rules for quantum disjunctions. While the quantum logic program is not as popular as it once was, a crucial question remains unsettled: what is the relationship between the logical structures of classical and quantum mechanics? In this essay we answer this q…
Quantum Structure in Cognition and the Foundations of Human Reasoning
Center Leo Apostel for Interdisciplinary Studies（利奥·阿波斯泰尔跨学科研究中心）；Brussels Free University（布鲁塞尔自由大学）；University of British Columbia（不列颠哥伦比亚大学）；Instituto de Filosofía y Ciencias de la Complejidad (IFICC)（哲学与复杂性研究所（IFICC））
Demonstration of logical quantum phase estimation for X-ray absorption spectra
Quemix Inc.（Quemix公司）；The University of Tokyo（东京大学）；Honda R&D Co., LTD.（本田研发有限公司）；National Institutes for Quantum Science and Technology (QST)（国立量子科学技术研究院）
Optimization or sampling of arbitrary pairwise Ising models, in a quantum annealing protocol of constrained interaction topology, can be enabled by a minor-embedding procedure. The logical problem of interest is transformed to a physical (device programmable) problem, where one binary variable is represented by a logical qubit consisting of multiple physical qubits. In this paper we discuss tuning of this transformation for the cases of clique, biclique, and cubic lattice problems on the D-Wave 2000Q quantum computer. We demonstrate parameter tuning protocols in spin glasses and channel commun…
Graph kernels are often used in bioinformatics and network applications to measure the similarity between graphs; therefore, they may be used to construct efficient graph classifiers. Many graph kernels have been developed thus far, but to the best of our knowledge there is no existing graph kernel that considers all subgraphs to measure similarity. We propose a novel graph kernel that applies a quantum computer to measure the graph similarity taking all subgraphs into account by fully exploiting the power of quantum superposition to encode every subgraph into a feature. For the construction o…
Formal Modeling and Verification of Grover's Algorithm
Capital Normal University（首都师范大学）；Beijing Key Laboratory of Electronic System Reliability Technology, Capital Normal University（首都师范大学电子系统可靠性技术北京市重点实验室）；School of Mathematical Sciences, Capital Normal University（首都师范大学数学科学学院）；International Science and Technology Cooperation Base of Electronic System Reliability and Mathematical Interdisciplinary, Capital Normal University（首都师范大学电子系统可靠性与数学交叉国际科技合作基地）
Modality, Potentiality and Contradiction in Quantum Mechanics
在[11]中，Newton da Costa与本文作者一起论证了用次协调方法考虑量子叠加的可能性。我们声称，尽管对量子力学（QM）的大多数解释都试图逃避矛盾，但有许多迹象表明，从事这类研究可能是值得的。最近，Arenhart和Krause [1，2，3]提出了几个反对这种方法的论点，并声称，考虑到反对的平方，量子叠加更好地理解为矛盾命题而不是矛盾命题。在[17]中，我们捍卫了量子叠加的次协调方法（PAQS），并提供了支持其发展的论据。本文分析了量子力学中模态、势和矛盾的含义，并进一步论证了为什么PAQS比Arenhart-Krause提出的量子叠加的多样性方法（CAQS）更适合于面对量子技术迫使我们考虑的解释性问题。
Quantum measurement-induced gate based on entanglement with ideal cubic phase state used as a non-Gaussian resource is able to produce Shrödinger cat state in the form of two high fidelity ``copies'' of the target state on phase plane [N.I. Masalaeva, I.V. Sokolov, Phys. Lett. A 424, 127846 (2022)]. In this work we examine the effect of finite initial squeezing of the resource state on the gate performance. We present exact solution for the gate output state and demonstrate that there exists a degree of squeezing, available in experiment, such that the output cat state quality almost does not …
