Exact two-qubit universal quantum circuit

We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly simulates arbitrary two-qubit operations in SU(4). Each block in this circuit is given in a closed form solution. We also provide a uniform upper bound of the applications of the given entangling gates, and find that exactly half of all the controlled-unitary gates satisfy the same upper bound as the CNOT gate. These results allow for the efficient implementation of operations in SU(4) required for both quantum computation and quantum simulation.     

A quantum encryption scheme using d-level systems

Using the generalized Bell states and quantum gates, we introduce a quantum encryption scheme of d-level states （qudits）. The scheme can detect and correct arbitrary transmission errors using only local operations and classical communications between the communicators. In addition, the entanglement key used to encrypt can be recycled. The protocol is informationally secure, because the output state is a totally mixed one for every input state p.     

Nonadiabatic geometric quantum computation protected by dynamical decoupling via the XXZ Hamiltonian

Nonadiabatic geometric quantum computation protected by dynamical decoupling combines the robustness of nonadiabatic geometric gates and the decoherence-resilience feature of dynamical decoupling. Solid-state systems provide an appealing candidate for the realization of nonadiabatic geometric quantum computation protected dynamical decoupling since the solid-state qubits are easily embedded in electronic circuits and scaled up to large registers. In this paper, we put forward a scheme of nonadiabatic geometric quantum computation protected by dynamical decoupling via the XXZ Hamiltonian, which not only combines the merits of nonadiabatic geometric gates and dynamical decoupling but also can be realized in a number of solid-state systems, such as superconducting circuits and quantum dots.     

Practical scheme for quantum computation with any two-qubit entangling gate

Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not, are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. We present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this result for systems of arbitrary finite dimension has been provided by Brylinski and Brylinski; however, their proof relies on a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical.     

Optimal conversion of nonlocal unitary operations

We study when a nonlocal unitary operation acting on two d-level systems can probabilistically simulate another one when arbitrary local operations and classical communication are allowed. We provide necessary and sufficient conditions for the simulation to be possible. Probabilistic interconvertability is used to define an equivalence relation between gates. We show that this relation induces a finite number of classes that we identify. In the case of two qubits, two classes of nonlocal operations exist. We show how the representatives of these classes, CNOT and SWAP, can be deterministically converted into any operation of its class and calculate the optimal probability of the reverse process.     

Quantum teleportation of optical quantum gates

We show that a universal set of gates for quantum computation with optics can be quantum teleported through the use of EPR entangled states, homodyne detection, and linear optics and squeezing operations conditioned on measurement outcomes. This scheme may be used for fault-tolerant quantum computation in any optical scheme (qubit or continuous-variable). The teleportation of nondeterministic nonlinear gates employed in linear optics quantum computation is discussed.     

Knill-laflamme-milburn linear optics quantum computation as a measurement-based computation

We show that the Knill Lafllame Milburn method of quantum computation with linear optics gates can be interpreted as a one-way, measurement-based quantum computation of the type introduced by Briegel and Raussendorf. We also show that the permanent state of n n-dimensional systems is a universal state for quantum computation.     

利用非稳定子态容错实现密集旋转操作

Non-Clifford操作不能在量子纠错码上自然横向实现, 但可通过辅助量子态和在量子纠错码上能横向实现的Clifford操作来容错实现, 从而取得容错量子计算的通用性. 非平庸的单量子比特操作是Non-Clifford操作, 可以分解为绕z轴和绕x轴非平庸旋转操作的组合. 本文首先介绍了利用非稳定子态容错实现绕z轴和绕x轴旋转的操作, 进而设计线路利用魔幻态容错制备非稳定子态集, 最后讨论了运用制备的非稳定子态集模拟任意非平庸单量子比特操作的问题. 与之前工作相比, 制备非稳定子态的线路得到简化, 成功概率提高, 且在高精度模拟任意单量子比特操作时所消耗的非稳定子态数目减少了50%. 关键词： 容错量子计算 非稳定子态 魔幻态 Clifford操作     

A Scheme for Simulation of Quantum Gates byAbelian Anyons

Anyons can be used to realize quantum computation, because they are two-level systems in two dimensions. In this paper, we propose a scheme to simulate single-qubit gates and CNOT gate using Abelian anyons in the Kitaev model. Two pairs of anyons (six spins) are used to realize single-qubit gates, while ten spins are needed for the CNOT gate. Based on these quantum gates, we show how to realize the Grover algorithm in a two-qubit system.     

Universality of black hole quantum computing

By analyzing the key properties of black holes from the point of view of quantum information, we derive a model‐independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. We analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft‐enough in order not to offset the basic properties of the system. We derive model‐independent bounds on some crucial time‐scales, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. We show that for black hole type quantum computers all these time‐scales are of the order of the black hole half‐life time. Furthermore, we construct explicitly a set of Hamiltonians that generates a universal set of quantum gates for the black hole type computer. We find that the gates work at maximal energy efficiency. Furthermore, we establish a fundamental bound on the complexity of quantum circuits encoded on these systems, and characterize the unitary operations that are implementable. It becomes apparent that the computational power is very limited due to the fact that the black hole life‐time is of the same order of the gate operation time. As a consequence, it is impossible to retrieve its information, within the life‐time of a black hole, by externally coupling to the black hole qubits. However, we show that, in principle, coupling to some of the internal degrees of freedom allows acquiring knowledge about the micro‐state. Still, due to the trivial complexity of operations that can be performed, there is no time advantage over the collection of Hawking radiation and subsequent decoding.     

Universal quantum computation with qudits

Quantum circuit model has been widely explored for various quantum applications such as Shors algorithm and Grovers searching algorithm. Most of previous algorithms are based on the qubit systems. Herein a proposal for a universal circuit is given based on the qudit system, which is larger and can store more information. In order to prove its universality for quantum applications, an explicit set of one-qudit and two-qudit gates is provided for the universal qudit computation. The one-qudit gates are general rotation for each two-dimensional subspace while the two-qudit gates are their controlled extensions. In comparison to previous quantum qudit logical gates, each primitive qudit gate is only dependent on two free parameters and may be easily implemented. In experimental implementation, multilevel ions with the linear ion trap model are used to build the qudit systems and use the coupling of neighbored levels for qudit gates. The controlled qudit gates may be realized with the interactions of internal and external coordinates of the ion.     

Noncyclic nonadiabatic holonomic quantum gates via shortcuts to adiabaticity

High-fidelity quantum gates are essential for large-scale quantum computation. However, any quantum manipulation will inevitably affected by noises, systematic errors and decoherence effects, which lead to infidelity of a target quantum task. Therefore, implementing high-fidelity, robust and fast quantum gates is highly desired. Here, we propose a fast and robust scheme to construct high-fidelity holonomic quantum gates for universal quantum computation based on resonant interaction of three-level quantum systems via shortcuts to adiabaticity. In our proposal, the target Hamiltonian to induce noncyclic non-Abelian geometric phases can be inversely engineered with less evolution time and demanding experimentally, leading to high-fidelity quantum gates in a simple setup. Besides, our scheme is readily realizable in physical system currently pursued for implementation of quantum computation. Therefore, our proposal represents a promising way towards fault-tolerant geometric quantum computation.     

几何量子计算

实现可集成的量子计算的关键步骤是实现保真度足够高的一组普适量子逻辑门，最近几年发展的几何量子计算使用几何位相来实现量子逻辑门，其特点是利用几何位相的整体几何性质来避免某些局域的无规噪声的影响，从而实现较高保真度的量子门，文章先简要介绍常规几何量子逻辑门的概念，然后重点介绍最近提出的非常规几何量子计算：量子计算中使用的逻辑门的总位相既包含有几何位相，又包含有动力学位相，但它仅依赖于一些几何特征，而且，对于任意的量子位输入态，在量子门操作过程中积累的位相要么是零，要么是仅依赖几何特征的位相。     

Efficient decomposition of quantum gates

Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit which is optimal in the sense of fully controlled single-qubit gates and yet is equivalent with the multiqubit gate. In the second step of the optimization, superfluous control bits are eliminated, which eventually results in a smaller total number of the elementary gates. In our scheme the number of controlled NOT gates is O(4(n)) which coincides with the theoretical lower bound.     

Implementation of universal quantum gates based on nonadiabatic geometric phases

We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this set of gates is designed for Josephson junctions and for NMR systems. Interestingly, we find that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions. A remarkable feature of the present nonadiabatic geometric gates is that there is no intrinsic limitation on the operation time.     

Quaternary Quantum/Reversible Half-Adder,Full-Adder,Parallel Adder and Parallel Adder/Subtractor Circuits

Multiple valued quantum logic is a promising research area in quantum computing technology having several advantages over binary quantum logic. Adder circuits as well as subtractor circuits are the major components of various computational units in computers and other complex computational systems. In this paper, we propose a quaternary quantum reversible half-adder circuit using quaternary 1-qudit gates, 2-qudit Feynman and Muthukrishnan-Stroud gates. Then we propose a quaternary quantum reversible full adder and a quaternary quantum parallel adder circuit. In addition, we propose a quaternary quantum reversible parallel adder/subtractor circuit. The proposed designs are compared with existing designs and improvements in terms of hardware complexity, quantum cost, number of constant inputs and garbage outputs are reported.

     

Efficient Construction of High-Dimensional Cluster State

We present a scheme for efficiently constructing high-dimensional cluster state using probabilistic entangling quantum gates. It is shown that the required computational overhead scales efficiently both with lip and n even if all the entangling quantum gates only succeed with an arbitrary small probability, where p is the success probability of the entangling quantum gate and n is the number of qubits in the computation.     

Universal quantum computation through control of spin-orbit coupling

We propose a method for quantum computation which uses control of spin-orbit coupling in a linear array of single electron quantum dots. Quantum gates are carried out by pulsing the exchange interaction between neighboring electron spins, including the anisotropic corrections due to spin-orbit coupling. Control over these corrections, even if limited, is sufficient for universal quantum computation over qubits encoded into pairs of electron spins. The number of voltage pulses required to carry out either single-qubit rotations or controlled-Not gates scales as the inverse of a dimensionless measure of the degree of control of spin-orbit coupling.     

Efficient Quantum Circuit for Encoding and Decoding of the [[8,3,5]] Stabilizer Code

A general protocol for constructing a complete efficient encoding and decoding quantum circuit of the [[8,3,5]] stabilizer code is proposed. The [[8,3,5]] stabilizer code is an eight-qubit code that protects a three-qubit state with up to one error, which is very important for quantum information processing. Single-qubit operations, two-qubit controlled gates and Toffoli gates are required in the proposed circuit. The current protocol can be generalized to all quantum stabilizer codes satisfying quantum Hamming bound, and implemented in some quantum systems.