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Lloyd C. L. Hollenberg

Publications and source records attributed to Lloyd C. L. Hollenberg.

143 records · Page 8Linked to original sources
arXiv2005

Quantum information transport to multiple receivers

The importance of transporting quantum information and entanglement with high fidelity cannot be overemphasized. We present a scheme based on adiabatic passage that allows for transportation of a qubit, operator measurements and entanglement, using a 1-D array of quantum sites with a single sender (Alice) and multiple receivers (Bobs). Alice need not know which Bob is the receiver, and if several Bobs try to receive the signal, they obtain a superposition state which can be used to realize two-qubit operator measurements for the generation of maximally entangled states.

quant-ph↗
arXiv2005

Coherent electronic transfer in quantum dot systems using adiabatic passage

We describe a scheme for using an all-electrical, rapid, adiabatic population transfer between two spatially separated dots in a triple-quantum dot system. The electron spends no time in the middle dot and does not change its energy during the transfer process. Although a coherent population transfer method, this scheme may well prove useful in incoherent electronic computation (for example quantum-dot cellular automata) where it may provide a coherent advantage to an otherwise incoherent device. It can also be thought of as a limiting case of type II quantum computing, where sufficient coherence exists for a single gate operation, but not for the preservation of superpositions after the operation. We extend our analysis to the case of many intervening dots and address the issue of transporting quantum information through a multi-dot system.

cond-mat.other↗
arXiv2005

Electrical readout of a spin qubit without double occupancy

We identify a novel mechanism to read out a single solid-state electron spin using an all-electrical spin-to-charge conversion in a closed system. Our scheme uses three donors and two electron spins, one spin is the qubit, the other is a reference. The population in the third, originally ionized, donor is monitored with an electrometer. Energy-dependent tunnelling of the reference spin to the ionized donor is used to determine the state of the qubit. In contrast to previous methods [e.g., B.E. Kane, Nature (London), \textbf{393}, 133 (1998)] we avoid double electron occupancy of any site within the system, thereby eliminating the possibility of unwanted electron loss from the system. The single spin readout scheme described here is applicable to both electron and nuclear spin based quantum computer architectures.

cond-mat.other↗
arXiv2005

Multiplayer quantum Minority game with decoherence

A quantum version of the Minority game for an arbitrary number of agents is considered. It is known that when the number of agents is odd, quantizing the game produces no advantage to the players, but for an even number of agents new Nash equilibria appear that have no classical analogue and have improved payoffs. We study the effect on the Nash equilibrium payoff of various forms of decoherence. As the number of players increases the multipartite GHZ state becomes increasingly fragile, as indicated by the smaller error probability required to reduce the Nash equilibrium payoff to the classical level.

quant-ph↗
arXiv2005

Identifying an Experimental Two-State Hamiltonian to Arbitrary Accuracy

Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on these parameters. This method requires only one measurement basis and the ability to initialise the system in some arbitrary state which is not an eigenstate of the Hamiltonian in question. The scaling of the uncertainty is studied for large numbers of measurements and found to be proportional to one on the square-root of the number of measurements.

quant-ph↗
arXiv2005

Quantum-Dot Cellular Automata using Buried Dopants

The use of buried dopants to construct quantum-dot cellular automata is investigated as an alternative to conventional electronic devices for information transport and elementary computation. This provides a limit in terms of miniaturisation for this type of system as each potential well is formed by a single dopant atom. As an example, phosphorous donors in silicon are found to have good energy level separation with incoherent switching times of the order of microseconds. However, we also illustrate the possibility of ultra-fast quantum coherent switching via adiabatic evolution. The switching speeds are numerically calculated and found to be 10's of picoseconds or less for a single cell. The effect of decoherence is also simulated in the form of a dephasing process and limits are estimated for operation with finite dephasing. The advantages and limitations of this scheme over the more conventional quantum-dot based scheme are discussed. The use of a buried donor cellular automata system is also discussed as an architecture for testing several aspects of buried donor based quantum computing schemes.

cond-mat.mes-hall↗
arXiv2005

Analysis and Geometric Optimization of Single Electron Transistors for Read-Out in Solid-State Quantum Computing

The single electron transistor (SET) offers unparalled opportunities as a nano-scale electrometer, capable of measuring sub-electron charge variations. SETs have been proposed for read-out schema in solid-state quantum computing where quantum information processing outcomes depend on the location of a single electron on nearby quantum dots. In this paper we investigate various geometries of a SET in order to maximize the device's sensitivity to charge transfer between quantum dots. Through the use of finite element modeling we model the materials and geometries of an Al/Al2O3 SET measuring the state of quantum dots in the Si substrate beneath. The investigation is motivated by the quest to build a scalable quantum computer, though the methodology used is primarily that of circuit theory. As such we provide useful techniques for any electronic device operating at the classical/quantum interface.

cond-mat.mes-hall↗
arXiv2004

Error Rate of the Kane Quantum Computer CNOT Gate in the Presence of Dephasing

We study the error rate of CNOT operations in the Kane solid state quantum computer architecture. A spin Hamiltonian is used to describe the system. Dephasing is included as exponential decay of the off diagonal elements of the system's density matrix. Using available spin echo decay data, the CNOT error rate is estimated at approsimately 10^{-3}.

quant-ph↗
arXiv2004

Scalability of Shor's algorithm with a limited set of rotation gates

Typical circuit implementations of Shor's algorithm involve controlled rotation gates of magnitude $π/2^{2L}$ where $L$ is the binary length of the integer N to be factored. Such gates cannot be implemented exactly using existing fault-tolerant techniques. Approximating a given controlled $π/2^{d}$ rotation gate to within $δ=O(1/2^{d})$ currently requires both a number of qubits and number of fault-tolerant gates that grows polynomially with $d$. In this paper we show that this additional growth in space and time complexity would severely limit the applicability of Shor's algorithm to large integers. Consequently, we study in detail the effect of using only controlled rotation gates with $d$ less than or equal to some $d_{\rm max}$. It is found that integers up to length $L_{\rm max} = O(4^{d_{\rm max}})$ can be factored without significant performance penalty implying that the cumbersome techniques of fault-tolerant computation only need to be used to create controlled rotation gates of magnitude $π/64$ if integers thousands of bits long are desired factored. Explicit fault-tolerant constructions of such gates are also discussed.

quant-ph↗
arXiv2004

Implementation of Shor's Algorithm on a Linear Nearest Neighbour Qubit Array

Shor's algorithm, which given appropriate hardware can factorise an integer $N$ in a time polynomial in its binary length $L$, has arguable spurred the race to build a practical quantum computer. Several different quantum circuits implementing Shor's algorithm have been designed, but each tacitly assumes that arbitrary pairs of qubits within the computer can be interacted. While some quantum computer architectures possess this property, many promising proposals are best suited to realising a single line of qubits with nearest neighbour interactions only. In light of this, we present a circuit implementing Shor's factorisation algorithm designed for such a linear nearest neighbour architecture. Despite the interaction restrictions, the circuit requires just $2L+4$ qubits and to first order requires $8L^{4}$ gates arranged in a circuit of depth $32L^{3}$ -- identical to first order to that possible using an architecture that can interact arbitrary pairs of qubits.

quant-ph↗
arXiv2003

Quantum Error Correction on Linear Nearest Neighbor Qubit Arrays

A minimal depth quantum circuit implementing 5-qubit quantum error correction in a manner optimized for a linear nearest neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that incorporate the necessary swap operations. Simulations of the circuit's performance when subjected to discrete and continuous errors are presented. The relationship between the error rate of a physical qubit and that of a logical qubit is investigated with emphasis on determining the concatenated error correction threshold.

quant-ph↗
arXiv2003

Maximizing the Hilbert space for a finite number of distinguishable quantum states

We consider a quantum system with a finite number of distinguishable quantum states, which may be partitioned freely by a number of quantum particles, assumed to be maximally entangled. We show that if we partition the system into a number of qudits, then the Hilbert space dimension is maximized when each quantum particle is allowed to represent a qudit of order $e$. We demonstrate that the dimensionality of an entangled system, constrained by the total number quantum states, partitioned so as to maximize the number of qutrits will always exceed the dimensionality of other qudit partitioning. We then show that if we relax the requirement of partitioning the system into qudits, but instead let the particles exist in any given state, that the Hilbert space dimension is greatly increased.

quant-ph↗
arXiv2001

Reaching the continuum limit in lattice gauge theory - without a computer

The scaling slope of the anti-symmetric mass gap M of compact U(1)_{2+1} lattice gauge theory is obtained analytically in the Hamiltonian formalism using the plaquette expansion. Based on the first four moments of the Hamiltonian with respect to a one-plaquette mean field state the results demonstrate clear scaling of M at and beyond the transition from strong to weak coupling. The scaling parameters determined agree well with the range of numerical determinations available.

hep-lat↗
arXiv2001

Analytic calculation of the mass gap in U(1)_{2+1} lattice gauge theory

An analytic calculation of the photon mass gap M of compact U(1)_{2+1} in the Hamiltonian formalism is performed utilizing the first four Hamiltonian moments with respect to a one-plaquette mean field state in the plaquette expansion method. Scaling of M is clearly evident at and beyond the transition from strong to weak coupling. The scaling behaviour agrees well with the range of results from numerical calculations.

hep-lat↗
arXiv2000

Fast Quantum Search Algorithms in Protein Sequence Comparison - Quantum Biocomputing

Quantum search algorithms are considered in the context of protein sequence comparison in biocomputing. Given a sample protein sequence of length m (i.e m residues), the problem considered is to find an optimal match in a large database containing N residues. Initially, Grover's quantum search algorithm is applied to a simple illustrative case - namely where the database forms a complete set of states over the 2^m basis states of a m qubit register, and thus is known to contain the exact sequence of interest. This example demonstrates explicitly the typical O(sqrt{N}) speedup on the classical O(N) requirements. An algorithm is then presented for the (more realistic) case where the database may contain repeat sequences, and may not necessarily contain an exact match to the sample sequence. In terms of minimizing the Hamming distance between the sample sequence and the database subsequences the algorithm finds an optimal alignment, in O(sqrt{N}) steps, by employing an extension of Grover's algorithm, due to Boyer, Brassard, Hoyer and Tapp for the case when the number of matches is not a priori known.

quant-ph↗
arXiv1996

Analytic Solution for the Ground State Energy of the Extensive Many-Body Problem

A closed form expression for the ground state energy density of the general extensive many-body problem is given in terms of the Lanczos tri-diagonal form of the Hamiltonian. Given the general expressions of the diagonal and off-diagonal elements of the Hamiltonian Lanczos matrix, $α_n(N)$ and $β_n(N)$, asymptotic forms $α(z)$ and $β(z)$ can be defined in terms of a new parameter $z\equiv n/N$ ($n$ is the Lanczos iteration and $N$ is the size of the system). By application of theorems on the zeros of orthogonal polynomials we find the ground-state energy density in the bulk limit to be given in general by ${\cal E}_0 = {\rm inf}\,\left[α(z) - 2\,β(z)\right]$.

cond-mat↗