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Translation Techniques Between Quantum Circuit Architectures
"... Abstract. We consider techniques for translating quantum circuits between various architectures. Specifically, we are interested in generic techniques for translating a parallelized quantum circuit between two given architectures which give tight asymptotic bounds on the increase in circuit depth. W ..."
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Abstract. We consider techniques for translating quantum circuits between various architectures. Specifically, we are interested in generic techniques for translating a parallelized quantum circuit between two given architectures which give tight asymptotic bounds on the increase in circuit depth. We approach the problem using a graphtheoretic model for physical circuit architectures. The architectures considered include the complete graph Kn, the twodimensional and threedimensional square lattices, the cycle, and the graph of a line, which gives rise to the wellstudied Linear Nearest Neighbour (LNN) circuit architecture model. We present results for translating circuits between these architectures, including a generic technique for translating circuits from arbitrary architectures to the LNN architecture. 1
Computation at a Distance
, 2007
"... We consider a model of computation motivated by possible limitations on quantum computers. We have a linear array of n wires, and we may perform operations only on pairs of adjacent wires. Our goal is to build a circuits that perform specified operations spanning all n wires. We show that the natura ..."
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We consider a model of computation motivated by possible limitations on quantum computers. We have a linear array of n wires, and we may perform operations only on pairs of adjacent wires. Our goal is to build a circuits that perform specified operations spanning all n wires. We show that the natural lower bound of n − 1 on circuit depth is nearly tight for a variety of problems, and we prove linear upper bounds for additional problems. In particular, using only gates adding a wire (mod 2) into an adjacent wire, we can realize any linear operation in GLn(2) as a circuit of depth 5n. We show that some linear operations require depth at least 2n + 1. 1
On the Design and Optimization of a Quantum PolynomialTime Attack on Elliptic Curve Cryptography
, 710
"... Abstract. We consider a quantum polynomialtime algorithm which solves the discrete logarithm problem for points on elliptic curves over GF(2 m). We improve over earlier algorithms by constructing an efficient circuit for multiplying elements of binary finite fields and by representing elliptic curv ..."
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Abstract. We consider a quantum polynomialtime algorithm which solves the discrete logarithm problem for points on elliptic curves over GF(2 m). We improve over earlier algorithms by constructing an efficient circuit for multiplying elements of binary finite fields and by representing elliptic curve points using a technique based on projective coordinates. The depth of our proposed implementation is O(m 2), which is an improvement over the previous bound of O(m 3). 1
Microcoded Architectures for IonTrap Quantum Computers
"... In this paper we present the first ever systematic design space exploration of microcoded software fault tolerant iontrap quantum computers. This exploration reveals the critical importance of a welltuned microcode for providing high performance and ensuring system reliability. In addition, we find ..."
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In this paper we present the first ever systematic design space exploration of microcoded software fault tolerant iontrap quantum computers. This exploration reveals the critical importance of a welltuned microcode for providing high performance and ensuring system reliability. In addition, we find that, despite recent advances in the reliability of quantum memory, the impact of errors due to stored quantum data is now, and will continue to be, a major source of systemic error. Finally, our exploration reveals a single design which out performs all others we considered in run time, fidelity and area. For completeness our design space exploration includes designs from prior work [13] and we find a novel design that is 1 2 the size, 3 times as fast, and an order of magnitude more reliable. 1. Introduction & Prior
Synthesis of Reversible Functions Beyond Gate Count and Quantum Cost
"... Abstract—Many synthesis approaches for reversible and quantum logic have been proposed so far. However, most of them generate circuits with respect to simple metrics, i.e. gate count or quantum cost. On the other hand, to physically realize reversible and quantum hardware, additional constraints exi ..."
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Abstract—Many synthesis approaches for reversible and quantum logic have been proposed so far. However, most of them generate circuits with respect to simple metrics, i.e. gate count or quantum cost. On the other hand, to physically realize reversible and quantum hardware, additional constraints exist. In this paper, we describe cost metrics beyond gate count and quantum cost that should be considered while synthesizing reversible and quantum logic for the respective target technologies. We show that the evaluation of a synthesis approach may differ if additional costs are applied. In addition, a new cost metric, namely Nearest Neighbor Cost (NNC) which is imposed by realistic physical quantum architectures, is considered in detail. We discuss how existing synthesis flows can be extended to generate optimal circuits with respect to NNC while still keeping the quantum cost small. I.
c ○ Rinton Press A 2D NEARESTNEIGHBOR QUANTUM ARCHITECTURE FOR FACTORING IN POLYLOGARITHMIC DEPTH
, 2012
"... We present a 2D nearestneighbor quantum architecture for Shor’s algorithm to factor an nbit number in O(log 3 n) depth. Our implementation uses parallel phase estimation, constantdepth fanout and teleportation, and constantdepth carrysave modular addition. We derive upper bounds on the circuit ..."
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We present a 2D nearestneighbor quantum architecture for Shor’s algorithm to factor an nbit number in O(log 3 n) depth. Our implementation uses parallel phase estimation, constantdepth fanout and teleportation, and constantdepth carrysave modular addition. We derive upper bounds on the circuit resources of our architecture under a new 2D model which allows a classical controller and parallel, communicating modules. We provide a comparison to all previous nearestneighbor factoring implementations. Our circuit results in an exponential improvement in nearestneighbor circuit depth at the cost of a polynomial increase in circuit size and width.
ConstantFactor Optimization of Quantum Adders on 2D Quantum Architectures
"... Abstract. Quantum arithmetic circuits have practical applications in various quantum algorithms. In this paper, we address quantum addition on 2dimensional nearestneighbor architectures based on the work presented by Choi and Van Meter (JETC 2012). To this end, we propose new circuit structures fo ..."
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Abstract. Quantum arithmetic circuits have practical applications in various quantum algorithms. In this paper, we address quantum addition on 2dimensional nearestneighbor architectures based on the work presented by Choi and Van Meter (JETC 2012). To this end, we propose new circuit structures for some basic blocks in the adder, and reduce communication overhead by concurrent optimization of consecutive blocks and also by parallel execution of expensive Toffoli gates. The proposed optimizations reduce total depth from 140 √ n+k1 to 92 √ n+k2 for constants k1, k2 and affect the computation fidelity considerably.
Optimization of Quantum Circuits for Interaction Distance in Linear Nearest Neighbor Architectures
"... Optimization of the interaction distance between qubits to map a quantum circuit into onedimensional quantum architectures is addressed. The problem is formulated as the Minimum Linear Arrangement (MinLA) problem. To achieve this, an interaction graph is constructed for a given circuit, and multipl ..."
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Optimization of the interaction distance between qubits to map a quantum circuit into onedimensional quantum architectures is addressed. The problem is formulated as the Minimum Linear Arrangement (MinLA) problem. To achieve this, an interaction graph is constructed for a given circuit, and multiple instances of the MinLA problem for selected subcircuits of the initial circuit are formulated and solved. In addition, a lookahead technique is applied to improve the cost of the proposed solution which examines different subcircuit candidates. Experiments on quantum circuits for quantum Fourier transform and reversible benchmarks show the effectiveness of the approach.