Thomas G. Draper

Bio: Thomas G. Draper is an academic researcher from University of Maryland, College Park. The author has contributed to research in topics: Quantum computer & Adder. The author has an hindex of 5, co-authored 7 publications receiving 769 citations.

A new quantum ripple-carry addition circuit

Abstract: We present a new linear-depth ripple-carry quantum addition circuit. Previous addition circuits required linearly many ancillary qubits; our new adder uses only a single ancillary qubit. Also, our circuit has lower depth and fewer gates than previous ripple-carry adders.

A logarithmic-depth quantum carry-lookahead adder

Abstract: We present an efficient addition circuit, borrowing techniques from classical carry-lookahead arithmetic. Our quantum carry-lookahead (QCLA) adder accepts two n-bitnumbers and adds them in O(log n) depth using O(n) ancillary qubits. We present bothin-place and out-of-place versions, as well as versions that add modulo 2n and modulo2n - 1. Previously, the linear-depth ripple-carry addition circuit has been the methodof choice. Our work reduces the cost of addition dramatically with only a slight increasein the number of required qubits. The QCLA adder can be used within current modularmultiplication circuits to reduce substantially the run-time of Shor's algorithm.

Addition on a Quantum Computer

Abstract: A new method for computing sums on a quantum computer is introduced This technique uses the quantum Fourier transform and reduces the number of qubits necessary for addition by removing the need for temporary carry bits This approach also allows the addition of a classical number to a quantum superposition without encoding the classical number in the quantum register This method also allows for massive parallelization in its execution

A logarithmic-depth quantum carry-lookahead adder

Abstract: We present an efficient addition circuit, borrowing techniques from the classical carry-lookahead arithmetic circuit. Our quantum carry-lookahead (QCLA) adder accepts two n-bit numbers and adds them in O(log n) depth using O(n) ancillary qubits. We present both in-place and out-of-place versions, as well as versions that add modulo 2^n and modulo 2^n - 1. Previously, the linear-depth ripple-carry addition circuit has been the method of choice. Our work reduces the cost of addition dramatically with only a slight increase in the number of required qubits. The QCLA adder can be used within current modular multiplication circuits to reduce substantially the run-time of Shor's algorithm.

Nonlinear complexity of boolean permutations

Abstract: We introduce the concept of nonlinear complexity, where the complexity of a function is determined by the number of nonlinear building blocks required for construction. We group functions by linear equivalence, and induce a complexity hierarchy for the affine equivalent double cosets. We prove multiple invariants of double cosets over the affine general linear group, and develop a specialized double coset equivalence test. This is used to classify the 16! permutations over 4 bits into 302 equivalence classes, which have a maximal nonlinear depth of 6. In addition, we present a new complexity class defined in terms of nonlinearity.

Surface codes: Towards practical large-scale quantum computation

Abstract: This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to stabilizers acting on a two-dimensional array of physical qubits, on which we implement the surface code. We next describe how logical qubits are formed in the surface code array and give numerical estimates of their fault tolerance. We outline how logical qubits are physically moved on the array, how qubit braid transformations are constructed, and how a braid between two logical qubits is equivalent to a controlled-not. We then describe the single-qubit Hadamard, Ŝ and T operators, completing the set of required gates for a universal quantum computer. We conclude by briefly discussing physical implementations of the surface code. We include a number of Appendices in which we provide supplementary information to the main text. © 2012 American Physical Society.

Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects

Abstract: The practical construction of scalable quantum-computer hardware capable of executing nontrivial quantum algorithms will require the juxtaposition of different types of quantum systems. We analyze a modular ion trap quantum-computer architecture with a hierarchy of interactions that can scale to very large numbers of qubits. Local entangling quantum gates between qubit memories within a single register are accomplished using natural interactions between the qubits, and entanglement between separate registers is completed via a probabilistic photonic interface between qubits in different registers, even over large distances. We show that this architecture can be made fault tolerant, and demonstrate its viability for fault-tolerant execution of modest size quantum circuits.

A new quantum ripple-carry addition circuit

Abstract: We present a new linear-depth ripple-carry quantum addition circuit. Previous addition circuits required linearly many ancillary qubits; our new adder uses only a single ancillary qubit. Also, our circuit has lower depth and fewer gates than previous ripple-carry adders.

Open Quantum Assembly Language

Abstract: This document describes a quantum assembly language (QASM) called OpenQASM that is used to implement experiments with low depth quantum circuits. OpenQASM represents universal physical circuits over the CNOT plus SU(2) basis with straight-line code that includes measurement, reset, fast feedback, and gate subroutines. The simple text language can be written by hand or by higher level tools and may be executed on the IBM Q Experience.

Synthesis and optimization of reversible circuits—a survey

Abstract: Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, postsynthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms—search based, cycle based, transformation based, and BDD based—as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.