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A new quantum ripple-carry addition circuit

TL;DR: In this paper, a linear-depth ripple-carry quantum addition circuit with only a single ancillary qubit has been proposed, which has lower depth and fewer gates than previous ripple carry adders.
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.
Citations
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Journal ArticleDOI
TL;DR: The concept of the stabilizer, using two qubits, is introduced, and the single-qubit Hadamard, S and T operators are described, completing the set of required gates for a universal quantum computer.
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.

2,205 citations

Journal ArticleDOI
TL;DR: In this article, a modular ion trap quantum-computer architecture with a hierarchy of interactions that can scale to very large numbers of qubits is presented. But the architecture is not fault-tolerant.
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.

580 citations


Cites background from "A new quantum ripple-carry addition..."

  • ...When only local interactions are available without dedicated buses for entanglement distribution, a quantum ripple-carry adder (QRCA) is the adequate adder of choice [49], for which the execution time goes as O(n)....

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Posted Content
TL;DR: 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 that is used to implement experiments with low depth quantum circuits.
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.

308 citations


Cites background from "A new quantum ripple-carry addition..."

  • ...The ripple-carry adder [29] shown in Fig....

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  • ...Figure 11: Example of a quantum ripple-carry adder from [29]....

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Journal ArticleDOI
TL;DR: This survey reviews algorithmic paradigms—search based, cycle based, transformation based, and BDD based—as well as specific algorithms for reversible synthesis, both exact and heuristic, and outlines key open challenges in synthesis of reversible and quantum logic.
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.

278 citations

Journal ArticleDOI
TL;DR: A polynomial-time algorithm for optimizing quantum circuits that takes the actual implementation of fault-tolerant logical gates into consideration, allowing space-time trade-offs to be easily explored.
Abstract: Most work in quantum circuit optimization has been performed in isolation from the results of quantum fault-tolerance. Here we present a polynomial-time algorithm for optimizing quantum circuits that takes the actual implementation of fault-tolerant logical gates into consideration. Our algorithm resynthesizes quantum circuits composed of Clifford group and T gates, the latter being typically the most costly gate in fault-tolerant models, e.g., those based on the Steane or surface codes, with the purpose of minimizing both T-count and T-depth. A major feature of the algorithm is the ability to resynthesize circuits with ancillae at effectively no additional cost, allowing space-time trade-offs to be easily explored. The tested benchmarks show up to 65.7% reduction in T-count and up to 87.6% reduction in T-depth without ancillae, or 99.7% reduction in T-depth using ancillae.

244 citations

References
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Journal ArticleDOI
TL;DR: This work provides an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation, and shows that the auxiliary memory required to perform this operation in a reversible way grows linearly with the size of the number to be factorized.
Abstract: Quantum computers require quantum arithmetic We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation Quantum modular exponentiation seems to be the most difficult (time and space consuming) part of Shor's quantum factorizing algorithm We show that the auxiliary memory required to perform this operation in a reversible way grows linearly with the size of the number to be factorized \textcopyright{} 1996 The American Physical Society

747 citations


Additional excerpts

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Journal ArticleDOI
TL;DR: This work reduces the cost of addition dramatically with only a slight increase in the number of required qubits, and can be used within current modularmultiplication circuits to reduce substantially the run-time of Shor's algorithm.
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.

241 citations

Posted Content
TL;DR: A new method for computing sums on a quantum computer is introduced that uses the quantum Fourier transform and reduces the number of qubits necessary for addition by removing the need for temporary carry bits.
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

237 citations


"A new quantum ripple-carry addition..." refers background in this paper

  • ...know whether we can add in linear depth with no ancillae and without this restriction on the output bit. It would be interesting to compare the ripple-carry adder of this paper to the transform adder [2]. Both circuits have linear depth. It is unclear which adder would be easier to 7 implement in practice; the answer depends on the relative costs of Toffoli gates and controlled rotations. It is well-k...

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