Fermionic Quantum Computation

We define a model of quantum computation with local fermionic modes (LFMs)—sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m LFMs and the Hilbert space of m qubits, simulation of one fermionic gate takes O(m) qubit gates and vice versa. We show that using different encodings, the simulation cost can be reduced to O(log m) and a constant, respectively. Nearest neighbors fermionic gates on a graph of bounded degree can be simulated at a constant cost. A universal set of fermionic gates is found. We also study computation with Majorana fermions which are basically halves of LFMs. Some connection to qubit quantum codes is made.     

An Unsharp Logic from Quantum Computation

Logical gates studied in quantum computation suggest a natural logical abstraction that gives rise to a new form of unsharp quantum logic. We study the logical connectives corresponding to the following gates: the Toffoli gate, the NOT and the $\sqrt {NOT} $ (which admit of natural physical models). This leads to a semantic characterization of a logic that we call quantum computational logic (QCL).     

High-Fidelity and Low-Cost Hyperparallel Quantum Gates for Photon Systems via Λ-Type Systems

Quantum gates designed with minimized resources overhead have a crucial role in quantum information processing. Here, based on the degrees of freedom (DoFs) of photons and Λ-type atom systems, two high-fidelity and low-cost protocols are presented for realizing polarization-spatial hyperparallel controlled-not (CNOT) and Toffoli gates on photon systems with only two and four two-qubit polarization–polarization swap (P-P-SWAP) gates in each DoF, respectively. Moreover, the quantum gates can be extended feasibly to construct 2m-target-qubit hyperparallel CNOT and 2n-control-qubit Toffoli gates required only 4m and 4n P-P-SWAP gates on $(m+1)$- and $(n+1)$-photon systems, respectively, which dramatically lower the costs and bridge the divide between the theoretical lower bounds and the current optimal syntheses for the photonic quantum computing. Further, the unique auxiliary atom of these quantum gates can be regarded as a temporary quantum memory that requires no initialization and measurement, and is reused within the coherence time, as the state of the atom remains unchanged after the hyperparallel quantum computing.     

Quantum Tasks Using Symmetric Cluster States

The cluster state has its feasibility for universal quantum computations. In this paper, we show that one symmetric cluster state can be used for the teleportation of an arbitrary two-qubit state deterministically. The one takes use of generalized Bell basis measurement while the other is completed using a general projective measurement from constructed orthogonal measurement basis and the Pauli flip measurement. Moreover, this state can also be utilized for remotely preparation of a restricted two qubit state within two different quantum network topologies, the controlled and jointed forms. Finally its capability for dense coding is investigated and shown n+3 classical bits transmissions by sending only n+1 qubits.     

Quantum Circuit Synthesis using a New Quantum Logic Gate Library of NCV Quantum Gates

Since Controlled-Square-Root-of-NOT (CV, CV^?) gates are not permutative quantum gates, many existing methods cannot effectively synthesize optimal 3-qubit circuits directly using the NOT, CNOT, Controlled-Square-Root-of-NOT quantum gate library (NCV), and the key of effective methods is the mapping of NCV gates to four-valued quantum gates. Firstly, we use NCV gates to create the new quantum logic gate library, which can be directly used to get the solutions with smaller quantum costs efficiently. Further, we present a novel generic method which quickly and directly constructs this new optimal quantum logic gate library using CNOT and Controlled-Square-Root-of-NOT gates. Finally, we present several encouraging experiments using these new permutative gates, and give a careful analysis of the method, which introduces a new idea to quantum circuit synthesis.     

A (<Emphasis Type="Italic">t</Emphasis>,<Emphasis Type="Italic">n</Emphasis>)-Threshold Scheme of Multi-party Quantum Group Signature with Irregular Quantum Fourier Transform

A novel (t,n)-threshold scheme for the multi-party quantum group signature is proposed based on the irregular quantum Fourier transform, in which every t-qubit quantum message needs n participants to generate the quantum group signature. All the quantum operation gates in the quantum circuit can be distributed and arranged randomly in the irregular QFT algorithm, which can increase the von Neumann entropy of the signed quantum message and the randomicity of the quantum signature generation significantly. The generation and verification of the quantum group signature can be both performed in quantum circuits with the parallel algorithm. Security analysis shows that an available and legal quantum (t,n)-threshold group signature can be achieved.     

Quantum computation with programmable connections between gates

A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e.g. in achieving the programmability of permutations of N different unitary channels with 1 use instead of N uses per channel. For this task, a new elemental resource is needed, the quantum switch, which can be programmed to switch the order of two channels with a single use of each one.     

Quantum computers on multiatomic ensembles in quantum electrodynamic cavity

Schemes for the construction of quantum computers on multiatomic ensembles in quantum electrodynamic cavity are considered. With that, both encoding of physical qubits on each separate multiatomic ensemble and logical encoding of qubits on the pairs of ensembles are introduced. Possible constructions of swapping (SWAP, \(\sqrt {SWAP} \)) and controlled swapping gates (CSWAP) are analyzed. Mechanism of collective blockade and dynamical elimination procedure are proposed for realization of these gates. The comparison of the scheme solutions is carried out for the construction of quantum computer at using of physical and logical qubits.     

Multiple multicontrol unitary operations: Implementation and applications

The efficient implementation of computational tasks is critical to quantum computations. In quantum circuits, multicontrol unitary operations are important components. Here, we present an extremely efficient and direct approach to multiple multicontrol unitary operations without decomposition to CNOT and single-photon gates. With the proposed approach, the necessary two-photon operations could be reduced from O(n³) with the traditional decomposition approach to O(n), which will greatly relax the requirements and make large-scale quantum computation feasible. Moreover, we propose the potential application to the (n-k)-uniform hypergraph state.     

Partial Boolean Functions With Exact Quantum Query Complexity One

We provide two sufficient and necessary conditions to characterize any n-bit partial Boolean function with exact quantum query complexity 1. Using the first characterization, we present all n-bit partial Boolean functions that depend on n bits and can be computed exactly by a 1-query quantum algorithm. Due to the second characterization, we construct a function F that maps any n-bit partial Boolean function to some integer, and if an n-bit partial Boolean function f depends on k bits and can be computed exactly by a 1-query quantum algorithm, then F(f) is non-positive. In addition, we show that the number of all n-bit partial Boolean functions that depend on k bits and can be computed exactly by a 1-query quantum algorithm is not bigger than an upper bound depending on n and k. Most importantly, the upper bound is far less than the number of all n-bit partial Boolean functions for all efficiently big n.     

Quantum Gates and Quantum Algorithms with Clifford Algebra Technique

We use the Clifford algebra technique (J. Math. Phys. 43:5782, 2002; J. Math. Phys. 44:4817, 2003), that is nilpotents and projectors which are binomials of the Clifford algebra objects γ ^a with the property {γ ^a ,γ ^b }₊=2η ^ab , for representing quantum gates and quantum algorithms needed in quantum computers in a simple and an elegant way. We identify n-qubits with the spinor representations of the group SO(1,3) for a system of n spinors. Representations are expressed in terms of products of projectors and nilpotents; we pay attention also on the nonrelativistic limit. An algorithm for extracting a particular information out of a general superposition of 2 ⁿ qubit states is presented. It reproduces for a particular choice of the initial state the Grover’s algorithm (Proc. 28th Annual ACM Symp. Theory Comput. 212, 1996).     

Quantum maps

We quantize area-preserving maps M of the phase plane q, p by devising a unitary operator $\text{U}$ transforming states | φ_n〉 into | φ_n+1〉. The result is a system with one degree of freedom q on which to study the quantum implications of generic classical motion, including stochasticity. We derive exact expressions for the equation iterating wavefunctions ψ_n(q), the propagator for Wigner functions W_n(q,p), the eigenstates of the discrete analog of the quantum harmonic oscillator, and general complex Gaussian wave packets iterated by a $\text{U}$ derived from a linear M. For | ψ_n〉 associated with curves $\text{L}$_n in q, p, we derive a semiclassical theory for evolving states and stationary states, analogous to the familiar WKB method. This theory breaks down when $\text{L}$_n gets so complicated as to develop convolutions of area ? or smaller. Such complication is generic; its principal morphotologies are“whorls” and “tendrils,” associated respectively with elliptic and hyperbolic fixed points of M. Under $\text{U}$, ψ_n(q) eventually transforms into a new sort of wave that no longer perceives the details of $\text{L}$_n. For all regimes, however, the smoothed | ψ_n(q)|² appears semiclassically appears to be given accurately by the smoothed projection of $\text{L}$_n onto the q axis, both smoothings being over a de Broglie wavelength. The classical, quantum, and semiclassical theory is illustrated by computations on the discrete quartic oscillator map. We display for the first time stochastic wavefunctions, dominated by dense clusters of caustics and characterized by multiple scales of oscillation.     

Initializing the Amplitude Distribution of a Quantum State

To date, quantum computational algorithms have operated on a superposition of all basis states of a quantum system. Typically, this is because it is assumed that some function f is known and implementable as a unitary evolution. However, what if only some points of the function f are known? It then becomes important to be able to encode only the knowledge that we have about f. This paper presents an algorithm that requires a polynomial number of elementary operations for initializing a quantum system to represent only the m known points of a function f.     

On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers

We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is related to the evaluation of the Jones and Tutte polynomials. We consider the connection between the weight enumerator polynomial from coding theory and Z and exploit the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in order to obtain the weight enumerator for a certain class of linear codes. In this way we demonstrate that for a certain class of sparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCC_ε) graphs, quantum computers provide a polynomial speed up in the difference between the number of edges and vertices of the graph, and an exponential speed up in q, over the best classical algorithms known to date.     

Remote Implementation of Multi-qubit Quantum Phase Gates

Based on Wu et al.’s original idea (Phys. Lett. A 372:2802, 2008), we propose a scheme to remotely implement multi-qubit quantum phase gates. With the assistance of entanglement swapping, classical communication and quantum repeater, multi-qubit quantum phase gates can be realized perfectly nearly. It is emphasized that our proposal can overcome the limitation that error probability scales exponentially with the length of the channel during the realization of the gates.     

A Dynamics for Discrete Quantum Gravity

This paper is based on the causal set approach to discrete quantum gravity. We first describe a classical sequential growth process (CSGP) in which the universe grows one element at a time in discrete steps. At each step the process has the form of a causal set (causet) and the “completed” universe is given by a path through a discretely growing chain of causets. We then quantize the CSGP by forming a Hilbert space H on the set of paths. The quantum dynamics is governed by a sequence of positive operators ρ _n on H that satisfy normalization and consistency conditions. The pair (H,{ρ _n }) is called a quantum sequential growth process (QSGP). We next discuss a concrete realization of a QSGP in terms of a natural quantum action. This gives an amplitude process related to the “sum over histories” approach to quantum mechanics. Finally, we briefly discuss a discrete form of Einstein’s field equation and speculate how this may be employed to compare the present framework with classical general relativity theory.     

Quantum Zeno effect: Quantum shuffling and Markovianity

The behavior displayed by a quantum system when it is perturbed by a series of von Neumann measurements along time is analyzed. Because of the similarity between this general process with giving a deck of playing cards a shuffle, here it is referred to as quantum shuffling, showing that the quantum Zeno and anti-Zeno effects emerge naturally as two time limits. Within this framework, a connection between the gradual transition from anti-Zeno to Zeno behavior and the appearance of an underlying Markovian dynamics is found. Accordingly, although a priori it might result counterintuitive, the quantum Zeno effect corresponds to a dynamical regime where any trace of knowledge on how the unperturbed system should evolve initially is wiped out (very rapid shuffling). This would explain why the system apparently does not evolve or decay for a relatively long time, although it eventually undergoes an exponential decay. By means of a simple working model, conditions characterizing the shuffling dynamics have been determined, which can be of help to understand and to devise quantum control mechanisms in a number of processes from the atomic, molecular and optical physics.     

Quantum efficiency and responsivity of InSb photodiodes utilizing the Moss-Burstein effect

In this work a detailed analysis of the quantum efficiency of InSb n⁺-p photodetectors produced by liquid phase epitaxy is given, in the case when the n⁺ region is doped to such a level that the Moss-Burstein effect plays an important role. Our starting point was the theoretically determined coefficient of intrinsic absorption and derived expressions for the generated photocurrent in the n⁺ region, depletion layer and p-phase of the photodetector. The results are presented in the form of graphical dependence of the quantum efficiency on the wavelength, with the electron concentration in the n⁺ layer as a parameter.     

Bidirectional Quantum Teleportation of a Class of <Emphasis Type="Italic">n</Emphasis>-Qubit States by Using (2<Emphasis Type="Italic">n</Emphasis> + <Emphasis Type="Bold">2</Emphasis>)-Qubit Entangled States as Quantum Channel

A new protocol of bidirectional quantum teleportation (BQT) is proposed in which the users can transmit a class of n-qubit state to each other simultaneously, by using (2n + 2)-qubit entangled states as quantum channel. The state of the art approaches can only transmit two-qubit states in each round. This scheme is based on control-not operation, single-qubit measurements and appropriate single-qubit unitary operations. It is shown that the protocol is secure in preparation phase.     

Optimal Concentration Inequalities for Dynamical Systems

For dynamical systems modeled by a Young tower with exponential tails, we prove an exponential concentration inequality for all separately Lipschitz observables of n variables. When tails are polynomial, we prove polynomial concentration inequalities. Those inequalities are optimal. We give some applications of such inequalities to specific systems and specific observables.