Probabilistic quantum cloning and identifying machines can be constructed via unitary-reduction processes [Duan and Guo, Phys. Rev. Lett. 80, 4999 (1998)]. Given the cloning (identifying) probabilities, we derive an explicit representation of the unitary evolution and corresponding Hamiltonian to realize probabilistic cloning (identification). The logic networks are obtained by decomposing the unitary representation into universal quantum logic operations. The robustness of the networks is also discussed. Our method is suitable for a $k$-partite system, such as quantum computer, and may be generalized to general state-dependent cloning and identification.
We propose an effective scheme for realizing a long-range quantum state phase-covariant cloning between two qubits in fiber-nanocavity system via an adiabatic passage. Since no cavity (fiber) photons or excited levels of the nitrogen-vacancy (NV) center are populated during the whole process, the scheme is immune to the decay of cavity (fiber) and spontaneous emission of the NV center. The strictly numerical simulation shows that the fidelity is high even in the presence of realistic imperfections.
The quantum mechanical no-cloning theorem for pure states is generalized and transfered to the quantum logics with a conditional probability calculus in a rather abstract, though simple and basic fashion without relying on a tensor product construction or finite dimension as required in other generalizations.
A common way of stating the non-cloning theorem -- one of distinguishing characteristics of quantum theory -- is that one cannot make a copy of an arbitrary unknown quantum state. Even though this theorem is an important part of the ongoing discussion of the nature of a quantum state, the role of the theorem in the logical-algebraic approach to quantum theory has not yet been systematically studied. According to the standard point of view (which is in line with the logical tradition), quantum cloning amounts to two classical rules of inference, namely, monotonicity and idempotency of entailmen…
Resonant dissipation-enabled adiabatic quantum state transfer processes between the polarization degrees of freedom of a single photon wave packet and quantum emitters are discussed. These investigations generalize previous work [N. Trautmann and G. Alber, Phys. Rev. A 93, 053807 (2015)] by taking into account the properties of the spontaneously emitted photon wave packet and of non adiabatic corrections. It is demonstrated that the photonic degrees of freedoms of these adiabatic one-photon quantum state transfer processes can be used for the passive, heralded and deterministic preparation of …
The negatively charged nitrogen-vacancy (NV) center spin in diamond can be used to realize quantum computation and to sense magnetic fields. Its spin triplet consists of three levels labeled with its spin z-components of +1, 0, and -1. Without external field, the +1 and -1 states are degenerate and higher than the 0 state due to the zero-field splitting. By taking the symmetrical and anti-symmetrical superpositions of the +1 and -1 states as our qubit basis, we obtain exact evolution operator of the NV center spin under time-dependent magnetic field by mapping the three-level system on time-de…
This thesis contains contributions to the theory of quantum computation. We first define a new method to efficiently approximate special unitary operators. Specifically, given a special unitary U and a precision ε > 0, we show how to efficiently find a sequence of Clifford+V or Clifford+T operators whose product approximates U up to ε in the operator norm. In the general case, the length of the approximating sequence is asymptotically optimal. If the unitary to approximate is diagonal then our method is optimal: it yields the shortest sequence approximating U up to ε. Next, we introduce a math…
We propose a scheme to realize a multiqubit tunable phase gate in a circuit QED setup where two resonators, each coupling with a qudit, are interconnected to a common qudit (d=4). In this proposal, only two levels of each qudit serve as the logical states and the other two levels are used for the gate realization. The proposal is efficient and simple because only a classical microwave pulse is needed, no matter how many qudits are involved, which significantly reduces experimental difficulty. In a nonresonant case, the tunable phase gate can be achieved readily, while under the resonant condit…
We describe a class of "neighboring-blocks" stabilizer quantum error correction codes and demonstrate that such class of codes can be implemented in a resource-efficient manner using a single ancilla and circular near-neighbor qubit connectivity. We propose an implementation for syndrome-measurement circuits for codes from the class and illustrate its workings for cases of 3-qubit repetition code, Laflamme's 5-qubit code, and Shor's 9-qubit code. For 3-qubit repetition code and Laflamme's 5-qubit code suggested scheme has the property that it uses only native two-qubit CNS gates, which potenti…
Continuous-time quantum walks (CTQWs) on static graphs provide efficient methods for search and sampling as well as a model for universal quantum computation. We consider an extension of CTQWs to the case of dynamic graphs, in which an ordered sequence of graphs governs free evolution of the quantum walk. We then consider how perfect state transfer during the quantum walk can be used to design dynamic graphs that implement a universal set of quantum logic gates. We give explicit examples for a complete logical basis, and we validate implementations using numerical simulations for quantum telep…
To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in p…
High-efficiency quantum information processing is equivalent to the fewest quantum resources and the simplest operations by means of logic qubit gates. Based on the reflection geometry of a single photon interacting with a three-level $Λ$-typle atom-cavity system, we present some refined protocols for realizing controlled-not (CNOT), Fredkin, and Toffoli gates on hybrid systems. The first control qubit of our gates is encoded on a flying photon, and the rest qubits are encoded on the atoms in optical cavity. Moreover, these quantum gates can be extended to the optimal synthesis of multi-qubit …
We propose an efficient scheme to implement a multiplex-controlled phase gate with multiple photonic qubits simultaneously controlling one target photonic qubit based on circuit quantum electrodynamics (QED). For convenience, we denote this multiqubit gate as MCP gate. The gate is realized by using a two-level coupler to couple multiple cavities. The coupler here is a superconducting qubit. This scheme is simple because the gate implementation requires only \textit{one step} of operation. In addition, this scheme is quite general because the two logic states of each photonic qubit can be encod…
We introduce a new class of primitive building blocks for realizing quantum logic elements based on nanoscale magnetization textures called skyrmions. In a skyrmion qubit, information is stored in the quantum degree of helicity, and the logical states can be adjusted by electric and magnetic fields, offering a rich operation regime with high anharmonicity. By exploring a large parameter space, we propose two skyrmion qubit variants depending on their quantized state. We discuss appropriate microwave pulses required to generate single-qubit gates for quantum computing, and skyrmion multiqubit s…
This paper presents a physical mapping tool for quantum circuits, which generates the optimal Universal Logic Block (ULB) that can perform any logical fault-tolerant (FT) quantum operations with the minimum latency. The operation scheduling, placement, and qubit routing problems tackled by the quantum physical mapper are highly dependent on one another. More precisely, the scheduling solution affects the quality of the achievable placement solution due to resource pressures that may be created as a result of operation scheduling whereas the operation placement and qubit routing solutions influ…
Solid-state spin defects are a promising platform for quantum science and technology, having realized demonstrations of a variety of key components for quantum information processing, particularly in the area of quantum networks. An outstanding challenge for building larger-scale quantum systems with solid-state defects is realizing high-fidelity control over multiple defects with nanoscale separations, which is required to realize strong spin-spin interactions for multi-qubit logic and the creation of entangled states. In this work, we experimentally demonstrate an optical frequency-domain mu…
Bosonic Cyclic Codes: Trading Stabilizers for Gaussian Non-Clifford Phase Gates
Cornell University（康奈尔大学）；University of California, Berkeley（加州大学伯克利分校）；University of Maryland（马里兰大学）；NIST/University of Maryland（美国国家标准与技术研究院/马里兰大学）；Université de Sherbrooke（舍布鲁克大学）
Dehmelt and VanDyck's famous 1987 measurement of the electron and positron g-factor is still the most precise g-factor comparison in the lepton sector, and a sensitive test of possible CPT violation. A complementary g-factor comparison between the proton and the antiproton is highly desirable to test CPT symmetry in the baryon sector. Current experiments, based on Dehmelt's continuous Stern-Gerlach effect and the double Penning-trap technique, are making rapid progress. They are, however, extremely difficult to carry out because ground state cooling using cryogenic techniques is virtually impo…
The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven to be extremely challenging in both condensed matter and synthetic quantum systems. Here, we prepare the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measure a topological entanglement entropy near the expected value of $\ln2$, and simulate anyon interferometry to extract the braiding…
We introduce an exactly solvable model of interacting Majorana fermions realizing $Z_{2}$ topological order with a $Z_{2}$ fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid state systems, including topological insulators, nanowires or two-dimensional electron gases, proximitized by $s$-wave superconductors. Our model finds a natural application as a Majorana…
We propose a prime factorizer operated in a framework of quantum annealing (QA). The idea is inverse operation of a multiplier implemented with QA-based Boolean logic circuits. We designed the QA machine on an application-specific-annealing-computing architecture which efficiently increases available hardware budgets at the cost of restricted functionality. The invertible operation of QA logic gates consisting of superconducting flux qubits was confirmed by circuit simulation with classical noise sources. The circuits were implemented and fabricated by using superconducting integrated circuit …
