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arXiv:0903.0748 · International Journal of Quantum Information

CIRCUIT DESIGN FOR A MEASUREMENT-BASED QUANTUM CARRY-LOOKAHEAD ADDER

Agung Trisetyarso, Rodney Van Meter

Published Aug 1, 2010• 23 citations
arXivHTMLPDF

Abstract

We present the design and evaluation of a quantum carry-lookahead adder (QCLA) using measurement-based quantum computation (MBQC), called MBQCLA. QCLA was originally designed for an abstract, concurrent architecture supporting long-distance communication, but most realistic architectures heavily constrain communication distances. The quantum carry-lookahead adder is faster than a quantum ripple-carry adder; QCLA has logarithmic depth while ripple adders have linear depth. MBQCLA utilizes MBQC's ability to transfer quantum states in unit time to accelerate addition. MBQCLA breaks the latency limit of addition circuits in nearest neighbor-only architectures: compared to the Θ(n) limit on circuit depth for linear nearest-neighbor architectures, it can reach Θ(log n) depth. MBQCLA is an order of magnitude faster than a ripple-carry adder when adding registers longer than 100 qubits, but requires a cluster state that is an order of magnitude larger. The cluster state resources can be classified as computation and communication; for the unoptimized form, ≈ 88% of the resources are used for communication. Hand optimization of horizontal communication costs results in a ≈ 12% reduction in spatial resources for the in-place MBQCLA circuit. For comparison, a graph state quantum carry-lookahead adder (GSQCLA) uses only ≈ 9% of the spatial resources of the MBQCLA.

DOI
10.1142/s0219749910006496

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We present the design and evaluation of a quantum carry-lookahead adder (QCLA) using measurement-based quantum computation (MBQC), called MBQCLA. QCLA was originally designed for an abstract, concurrent architecture supporting long-distance communication, but most realistic architectures heavily constrain communication distances. The quantum carry-lookahead adder is faster than a quantum ripple-carry adder; QCLA has logarithmic depth while ripple adders have linear depth. MBQCLA utilizes MBQC's ability to transfer quantum states in unit time to accelerate addition. MBQCLA breaks the latency limit of addition circuits in nearest neighbor-only architectures: compared to the Θ(n) limit on circuit depth for linear nearest-neighbor architectures, it can reach Θ(log n) depth. MBQCLA is an order of magnitude faster than a ripple-carry adder when adding registers longer than 100 qubits, but requires a cluster state that is an order of magnitude larger. The cluster state resources can be classified as computation and communication; for the unoptimized form, ≈ 88% of the resources are used for communication. Hand optimization of horizontal communication costs results in a ≈ 12% reduction in spatial resources for the in-place MBQCLA circuit. For comparison, a graph state quantum carry-lookahead adder (GSQCLA) uses only ≈ 9% of the spatial resources of the MBQCLA.
We present the design of a quantum carry-lookahead adder using measurement-based quantum computation. QCLA utilizes MBQC`s ability to transfer quantum states in unit time to accelerate addition. The quantum carry-lookahead adder (QCLA) is faster than a quantum ripple-carry adder; QCLA has logarithmic depth while ripple adders have linear depth. QCLA is an order of magnitude faster than a ripple-carry adder when adding registers longer than 100 qubits but requires a cluster state that is an order of magnitude larger. Hand optimization results in a ≈\approx≈ 26% reduction in spatial resources for the circuit.
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.
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.
Quantum circuits of arithmetic operations such as addition are needed to implement quantum algorithms in hardware. Quantum circuits based on Clifford+T gates are used as they can be made tolerant to noise. The tradeoff of gaining fault tolerance from using Clifford+T gates and error correcting codes is the high implementation overhead of the T gate. As a result, the T-count performance measure has become important in quantum circuit design. Due to noise, the risk for errors in a quantum circuit computation increases as the number of gate layers (or depth) in the circuit increases. As a result, low depth circuits such as quantum carry lookahead adders (QCLA)s have caught the attention of researchers. This work presents two QCLA designs each optimized with emphasis on T-count or qubit cost respectively. In-place and out-of-place versions of each design are shown. The proposed QCLAs are compared against the existing works in terms of T-count. The proposed QCLAs for out-of-place addition achieve average T gate savings of 54.34%54.34 \%54.34% and 37.21%37.21 \%37.21%, respectively. The proposed QCLAs for in-place addition achieve average T gate savings of 72.11%72.11 \%72.11% and 35.87%35.87 \%35.87%