# Automated Quantum Circuit Synthesis and Cost Estimation for the Binary Welded Tree Oracle

29 Jun 2017-ACM Journal on Emerging Technologies in Computing Systems (Association for Computing Machinery (ACM))-Vol. 13, Iss: 4, pp 51

TL;DR: This article proposes a solution to automatically generate the circuit for the Oracle for welding using the Quantum Assembly Language, which is a language for describing quantum circuits, and optimize the generated circuit using the Fault-Tolerant Quantum Logic Synthesis tool for any BWT instance.

Abstract: Quantum computing is a new computational paradigm that promises an exponential speed-up over classical algorithms. To develop efficient quantum algorithms for problems of a non-deterministic nature, random walk is one of the most successful concepts employed. In this article, we target both continuous-time and discrete-time random walk in both the classical and quantum regimes. Binary Welded Tree (BWT), or glued tree, is one of the most well-known quantum walk algorithms in the continuous-time domain. Prior work implements quantum walk on the BWT with static welding. In this context, static welding is randomized but case-specific. We propose a solution to automatically generate the circuit for the Oracle for welding. We implement the circuit using the Quantum Assembly Language, which is a language for describing quantum circuits. We then optimize the generated circuit using the Fault-Tolerant Quantum Logic Synthesis tool for any BWT instance. Automatic welding enables us to provide a generalized solution for quantum walk on the BWT.

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04 Apr 2019

TL;DR: In this paper, the authors propose and evaluate backend compiler approaches to map and optimize high-level quantum programs to execute with high reliability on noisy intermediate-scale quantum (NISQ) systems with diverse hardware characteristics.

Abstract: A massive gap exists between current quantum computing (QC) prototypes, and the size and scale required for many proposed QC algorithms. Current QC implementations are prone to noise and variability which affect their reliability, and yet with less than 80 quantum bits (qubits) total, they are too resource-constrained to implement error correction. The term Noisy Intermediate-Scale Quantum (NISQ) refers to these current and near-term systems of 1000 qubits or less. Given NISQ's severe resource constraints, low reliability, and high variability in physical characteristics such as coherence time or error rates, it is of pressing importance to map computations onto them in ways that use resources efficiently and maximize the likelihood of successful runs. This paper proposes and evaluates backend compiler approaches to map and optimize high-level QC programs to execute with high reliability on NISQ systems with diverse hardware characteristics. Our techniques all start from an LLVM intermediate representation of the quantum program (such as would be generated from high-level QC languages like Scaffold) and generate QC executables runnable on the IBM Q public QC machine. We then use this framework to implement and evaluate several optimal and heuristic mapping methods. These methods vary in how they account for the availability of dynamic machine calibration data, the relative importance of various noise parameters, the different possible routing strategies, and the relative importance of compile-time scalability versus runtime success. Using real-system measurements, we show that fine grained spatial and temporal variations in hardware parameters can be exploited to obtain an average 2.9x (and up to 18x) improvement in program success rate over the industry standard IBM Qiskit compiler. Despite small qubit counts, NISQ systems will soon be large enough to demonstrate "quantum supremacy", i.e., an advantage over classical computing. Tools like ours provide significant improvements in program reliability and execution time, and offer high leverage in accelerating progress towards quantum supremacy.

157 citations

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TL;DR: It is shown that fine grained spatial and temporal variations in hardware parameters can be exploited to obtain an average 2.9x (and up to 18x) improvement in program success rate over the industry standard IBM Qiskit compiler.

Abstract: A massive gap exists between current quantum computing (QC) prototypes, and the size and scale required for many proposed QC algorithms. Current QC implementations are prone to noise and variability which affect their reliability, and yet with less than 80 quantum bits (qubits) total, they are too resource-constrained to implement error correction. The term Noisy Intermediate-Scale Quantum (NISQ) refers to these current and near-term systems of 1000 qubits or less. Given NISQ's severe resource constraints, low reliability, and high variability in physical characteristics such as coherence time or error rates, it is of pressing importance to map computations onto them in ways that use resources efficiently and maximize the likelihood of successful runs.
This paper proposes and evaluates backend compiler approaches to map and optimize high-level QC programs to execute with high reliability on NISQ systems with diverse hardware characteristics. Our techniques all start from an LLVM intermediate representation of the quantum program (such as would be generated from high-level QC languages like Scaffold) and generate QC executables runnable on the IBM Q public QC machine. We then use this framework to implement and evaluate several optimal and heuristic mapping methods. These methods vary in how they account for the availability of dynamic machine calibration data, the relative importance of various noise parameters, the different possible routing strategies, and the relative importance of compile-time scalability versus runtime success. Using real-system measurements, we show that fine grained spatial and temporal variations in hardware parameters can be exploited to obtain an average $2.9$x (and up to $18$x) improvement in program success rate over the industry standard IBM Qiskit compiler.

90 citations

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TL;DR: A novel method was proposed to optimize the number of teleportation and to reduce the execution time for generating DQC, and a significant reduction in teleportation cost and execution time was obtained in benchmark circuits.

Abstract: A new approach to reduce the teleportation cost and execution time in Distributed Quantum Circuits (DQCs) was proposed in the present paper. DQCs, a well-known solution, have been applied to solve the problem of maintaining a large number of qubits next to each other. In the distributed quantum system, the qubits are transferred to another subsystem by a quantum protocol like teleportation. Hence, a novel method was proposed to optimize the number of teleportation and to reduce the execution time for generating DQC. To this end, first, the quantum circuit was reordered according to the qubits placement to improve the computational execution time, and then the quantum circuit was modeled as a graph. Finally, we combined the genetic algorithm (GA) and the modified tabu search algorithm (MTS) to partition the graph model in order to obtain a distributed quantum circuit aimed at reducing the number of teleportation costs. A significant reduction in teleportation cost (TC) and execution time (ET) was obtained in benchmark circuits. In particular, we performed a more accurate optimization than the previous approaches, and the proposed approach yielded the best results for several benchmark circuits.

6 citations

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TL;DR: In this article , a collaborative metaverse-based a-la-carte framework for Tertiary Education is proposed, which is a technologically driven educational metaverse environment involving loosely coupled building blocks.

Abstract: The paper aims to propose a futuristic educational and learning framework called CO-MATE (Collaborative Metaverse-based A-La-Carte Framework for Tertiary Education). The architectural framework of CO-MATE was conceptualized in a four-layered approach which depicts various infrastructure and service layer functionalities. CO-MATE is a technologically driven educational metaverse environment involving loosely coupled building blocks to provide an a-la-carte model for platform designers. For this, the authors had undertaken a systematic mapping study of the pre/post-COVID period to review the application of various emerging technologies. Further, the paper also discusses the core attributes and component offerings of CO-MATE for a technology-driven and automated immersive-learning environment and exemplifies the same through various use cases.

4 citations

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TL;DR: In this article, a two-qubit gate in surface code is implemented as a virtual "pipe" in space-time called a braiding path, and the path should be carefully routed to avoid congestion.

Abstract: Quantum computers can solve problems that are intractable using the most powerful classical computer. However, qubits are fickle and error prone. It is necessary to actively correct errors in the execution of a quantum circuit. Quantum error correction (QEC) codes are developed to enable fault-tolerant quantum computing. With QEC, one logical circuit is converted into an encoded circuit. Most studies on quantum circuit compilation focus on NISQ devices which have 10-100 qubits and are not fault-tolerant. In this paper, we focus on the compilation for fault-tolerant quantum hardware. In particular, we focus on optimizing communication parallelism for the surface code based QEC. The execution of surface code circuits involves non-trivial geometric manipulation of a large lattice of entangled physical qubits. A two-qubit gate in surface code is implemented as a virtual “pipe” in space-time called a braiding path. The braiding paths should be carefully routed to avoid congestion. Communication between qubits is considered the major bottleneck as it involves scheduling and searching for simultaneous paths between qubits. We provide a framework for efficiently scheduling braiding paths. We discover that for quantum programs with a local parallelism pattern, our framework guarantees an optimal solution, while the previous greedy-heuristic-based solution cannot. Moreover, we propose an extension to the local parallelism analysis framework to address the communication bottleneck. Our framework achieves orders of magnitude improvement after addressing the communication bottleneck.

1 citations

##### References

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Bell Labs

^{1}TL;DR: Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored are given.

Abstract: A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a cost in computation time of at most a polynomial factor: It is not clear whether this is still true when quantum mechanics is taken into consideration. Several researchers, starting with David Deutsch, have developed models for quantum mechanical computers and have investigated their computational properties. This paper gives Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored. These two problems are generally considered hard on a classical computer and have been used as the basis of several proposed cryptosystems. We thus give the first examples of quantum cryptanalysis. >

5,655 citations

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Bell Labs

^{1}TL;DR: In this paper, it was shown that a quantum mechanical computer can solve integer factorization problem in a finite power of O(log n) time, where n is the number of elements in a given integer.

Abstract: were proposed in the early 1980’s [Benioff80] and shown to be at least as powerful as classical computers an important but not surprising result, since classical computers, at the deepest level, ultimately follow the laws of quantum mechanics. The description of quantum mechanical computers was formalized in the late 80’s and early 90’s [Deutsch85][BB92] [BV93] [Yao93] and they were shown to be more powerful than classical computers on various specialized problems. In early 1994, [Shor94] demonstrated that a quantum mechanical computer could efficiently solve a well-known problem for which there was no known efficient algorithm using classical computers. This is the problem of integer factorization, i.e. testing whether or not a given integer, N, is prime, in a time which is a finite power of o (logN) . ----------------------------------------------

5,636 citations

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TL;DR: In this paper, a universal set of one-and two-quantum-bit gates for quantum computation using the spin states of coupled single-electron quantum dots is proposed, and the desired operations are effected by the gating of the tunneling barrier between neighboring dots.

Abstract: We propose an implementation of a universal set of one- and two-quantum-bit gates for quantum computation using the spin states of coupled single-electron quantum dots. Desired operations are effected by the gating of the tunneling barrier between neighboring dots. Several measures of the gate quality are computed within a recently derived spin master equation incorporating decoherence caused by a prototypical magnetic environment. Dot-array experiments that would provide an initial demonstration of the desired nonequilibrium spin dynamics are proposed.

5,395 citations

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01 Jan 2001

TL;DR: Estimates on the important parameters of access time, commute time, cover time and mixing time are discussed and recent algorithmic applications of random walks are sketched, in particular to the problem of sampling.

Abstract: Various aspects of the theory of random walks on graphs are surveyed In particular, estimates on the important parameters of access time, commute time, cover time and mixing time are discussed Connections with the eigenvalues of graphs and with electrical networks, and the use of these connections in the study of random walks is described We also sketch recent algorithmic applications of random walks, in particular to the problem of sampling

1,548 citations

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TL;DR: The concept of quantum random walk is introduced, and it is shown that due to quantum interference effects the average path length can be much larger than the maximum allowed path in the corresponding classical random walk.

Abstract: We introduce the concept of quantum random walk, and show that due to quantum interference effects the average path length can be much larger than the maximum allowed path in the corresponding classical random walk A quantum-optics application is described

1,304 citations

### "Automated Quantum Circuit Synthesis..." refers background or methods in this paper

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