scholarly journals Clifford Circuit Optimization with Templates and Symbolic Pauli Gates

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 580
Author(s):  
Sergey Bravyi ◽  
Ruslan Shaydulin ◽  
Shaohan Hu ◽  
Dmitri Maslov
Keyword(s):  
Template Matching ◽  
Optimization Method ◽  
Quantum Circuit ◽  
Finite Subgroup ◽  
Small Subset ◽  
Circuit Optimization ◽  
Gate Count ◽  
Clifford Group ◽  
Qubit Gate ◽  
Quantum Error

The Clifford group is a finite subgroup of the unitary group generated by the Hadamard, the CNOT, and the Phase gates. This group plays a prominent role in quantum error correction, randomized benchmarking protocols, and the study of entanglement. Here we consider the problem of finding a short quantum circuit implementing a given Clifford group element. Our methods aim to minimize the entangling gate count assuming all-to-all qubit connectivity. First, we consider circuit optimization based on template matching and design Clifford-specific templates that leverage the ability to factor out Pauli and SWAP gates. Second, we introduce a symbolic peephole optimization method. It works by projecting the full circuit onto a small subset of qubits and optimally recompiling the projected subcircuit via dynamic programming. CNOT gates coupling the chosen subset of qubits with the remaining qubits are expressed using symbolic Pauli gates. Software implementation of these methods finds circuits that are only 0.2% away from optimal for 6 qubits and reduces the two-qubit gate count in circuits with up to 64 qubits by 64.7% on average, compared with the Aaronson-Gottesman canonical form.

Realization and Optimization of Quantum Equivalent Circuits of Reversible Combinational Circuits

2020 ◽  
Vol 17 (5) ◽  
pp. 2080-2084
Author(s):  
A. Kamaraj ◽  
P. Marichamy ◽  
K. P. Kaviyashri
Keyword(s):  
Energy Dissipation ◽  
Functional Expression ◽  
Quantum Circuit ◽  
Vlsi Circuits ◽  
Quantum Cost ◽  
Combinational Circuits ◽  
Gate Structure ◽  
Gate Count ◽  
Garbage Output ◽  
Qubit Gate

Energy dissipation is the important constrain in the design and implementation of VLSI circuits. Usage of Reversible logic circuit is the best solution for lower energy dissipation. In this paper, basic reversible gates and some existing gates and KMD gates are realized using the Quantum Equivalent structure and the Controlled-V and V+ gate structure from their functional expression. Using the qubit gate reduction procedure of quantum circuit, the quantum cost and number of primitive gates of the functional expression are deduced. After synthesizing the Quantum Cost (QC), Gate count (GC), Garbage Output (GO), number of gates, constant inputs are compared with the non-optimized circuit. The quantum circuit and controlled V and V+ structure are realized in RCViewer+ tool using .tfc (“Toffoli-Fredkin Cascade”) code.

scholarly journals Connectivity matrix model of quantum circuits and its application to distributed quantum circuit optimization

2021 ◽  
Vol 20 (7) ◽  
Author(s):  
Ismail Ghodsollahee ◽  
Zohreh Davarzani ◽  
Mariam Zomorodi ◽  
Paweł Pławiak ◽  
Monireh Houshmand ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Connectivity Matrix ◽  
Circuit Optimization ◽  
Novel Approach ◽  
The Matrix ◽  
Minimum Number ◽  
Two Phases

AbstractAs quantum computation grows, the number of qubits involved in a given quantum computer increases. But due to the physical limitations in the number of qubits of a single quantum device, the computation should be performed in a distributed system. In this paper, a new model of quantum computation based on the matrix representation of quantum circuits is proposed. Then, using this model, we propose a novel approach for reducing the number of teleportations in a distributed quantum circuit. The proposed method consists of two phases: the pre-processing phase and the optimization phase. In the pre-processing phase, it considers the bi-partitioning of quantum circuits by Non-Dominated Sorting Genetic Algorithm (NSGA-III) to minimize the number of global gates and to distribute the quantum circuit into two balanced parts with equal number of qubits and minimum number of global gates. In the optimization phase, two heuristics named Heuristic I and Heuristic II are proposed to optimize the number of teleportations according to the partitioning obtained from the pre-processing phase. Finally, the proposed approach is evaluated on many benchmark quantum circuits. The results of these evaluations show an average of 22.16% improvement in the teleportation cost of the proposed approach compared to the existing works in the literature.

An optimal measurement method for spatial distribution of radio frequency identification multi-tag based on image analysis and PSO

2019 ◽  
Vol 41 (12) ◽  
pp. 3331-3339
Author(s):  
Xiaolei Yu ◽  
Yujun Zhou ◽  
Zhenlu Liu ◽  
Zhimin Zhao
Keyword(s):  
Neural Network ◽  
Image Analysis ◽  
Radio Frequency ◽  
Radio Frequency Identification ◽  
Template Matching ◽  
Detection System ◽  
Optimization Method ◽  
Frequency Identification ◽  
Edge Detection Method ◽  
Reading Distance

In this paper, a multi-tag optimization method based on image analysis and particle swarm optimization (PSO) neural network is proposed to verify the effect of radio frequency identification (RFID) multi-tag distribution on the performance of the system. A RFID tag detection system is proposed with two charge coupled device (CCD). This system can automatically focus on the tag according to its position, so it can obtain the image information more accurately by template matching and edge detection method. Therefore, the spatial structure of multi-tag and the corresponding reading distance can be obtained for training. Because of its excellent performance in multi-objective optimization, the PSO neural network is used to train and predict multi-tag distribution at the maximum reading distance. Compared with other neural networks, PSO is more accurate and its uptime is shorter for RFID multi-tag analysis.

scholarly journals Generation of Realistic Virtual Garments on Recovery Human Model

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Yuxiang Zhu ◽  
Yanjun Peng
Keyword(s):  
Human Body ◽  
Template Matching ◽  
Measurement Techniques ◽  
Measurement Data ◽  
Optimization Method ◽  
Human Model ◽  
Spatial Transformation ◽  
Single Image ◽  
Virtual Character ◽  
Fem Model

Displaying a variety of fabrics on a customized character could help customers choose which fabric is more suitable for themselves and help customers choose clothing. However, it is not an easy task to show realistic garment on customized virtual character. As a result, we propose a stable finite element method (FEM) model which is stable to approximate stretching behaviors. At first, we measure four kinds of cloth materials with measurement techniques to research elastic deformations in real cloth samples. Then, we use the parameter optimization method by fitting the model with measurement data. For promoting the display of realistic fabrics, we recover 3D human in shape and pose from a single image automatically. Human body datasets are constructed at first. Then, CNN-based image retrieval in shape and skeleton-based template matching method in pose are combined for 3D human model recovery. To enrich human body details, we synthesize the human body and 3D face with spatial transformation. We compared our proposed method of recovering 3D human from a single image with the state-of-the-art methods, and the experimental results show that the proposed method allows the recovered virtual human to put on garment with different fabrics and significantly improves the fidelity of virtual garment.

scholarly journals Strawberry Fields: A Software Platform for Photonic Quantum Computing

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 129 ◽  
Author(s):  
Nathan Killoran ◽  
Josh Izaac ◽  
Nicolás Quesada ◽  
Ville Bergholm ◽  
Matthew Amy ◽  
...  
Keyword(s):  
Quantum Computer ◽  
Quantum Circuit ◽  
Continuous Variable ◽  
Quantum Computers ◽  
Circuit Optimization ◽  
Hamiltonian Simulation ◽  
Quantum Programming ◽  
Quantum Polynomial ◽  
Main Components ◽  
Near Future

We introduce Strawberry Fields, an open-source quantum programming architecture for light-based quantum computers, and detail its key features. Built in Python, Strawberry Fields is a full-stack library for design, simulation, optimization, and quantum machine learning of continuous-variable circuits. The platform consists of three main components: (i) an API for quantum programming based on an easy-to-use language named Blackbird; (ii) a suite of three virtual quantum computer backends, built in NumPy and TensorFlow, each targeting specialized uses; and (iii) an engine which can compile Blackbird programs on various backends, including the three built-in simulators, and - in the near future - photonic quantum information processors. The library also contains examples of several paradigmatic algorithms, including teleportation, (Gaussian) boson sampling, instantaneous quantum polynomial, Hamiltonian simulation, and variational quantum circuit optimization.

scholarly journals The surface code with a twist

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 2 ◽  
Author(s):  
Theodore J. Yoder ◽  
Isaac H. Kim
Keyword(s):  
Quantum Error Correction ◽  
New Variety ◽  
Near Surface ◽  
Topological Quantum ◽  
Clifford Group ◽  
Logical Qubits ◽  
Surface Code ◽  
Quantum Error ◽  
Qubit Efficiency ◽  
Logical Qubit

The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new variety called twists have made it possible to implement the full Clifford group without state distillation. Here we investigate a patch-based encoding involving a modified twist. In our modified formulation, the resulting codes, called triangle codes for the shape of their planar layout, have only weight-four checks and relatively simple syndrome extraction circuits that maintain a high, near surface-code-level threshold. They also use 25% fewer physical qubits per logical qubit than the surface code. Moreover, benefiting from the twist, we can implement all Clifford gates by lattice surgery without the need for state distillation. By a surgical transformation to the surface code, we also develop a scheme of doing all Clifford gates on surface code patches in an atypical planar layout, though with less qubit efficiency than the triangle code. Finally, we remark that logical qubits encoded in triangle codes are naturally amenable to logical tomography, and the smallest triangle code can demonstrate high-pseudothreshold fault-tolerance to depolarizing noise using just 13 physical qubits.

A Quantum Circuit Optimization Framework Based on Pattern Matching

SPIN ◽  
2021 ◽  
Author(s):  
Mingyu Chen ◽  
Yu Zhang ◽  
Yongshang Li
Keyword(s):  
Pattern Matching ◽  
Quantum Algorithms ◽  
General Pattern ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Circuit Optimization ◽  
Coherent Noise ◽  
Pattern Description ◽  
Algorithm Framework ◽  
Machine Readable

In the NISQ era, quantum computers have insufficient qubits to support quantum error correction, which can only perform shallow quantum algorithms under noisy conditions. Aiming to improve the fidelity of quantum circuits, it is necessary to reduce the circuit depth as much as possible to mitigate the coherent noise. To address the issue, we propose PaF , a Pattern matching-based quantum circuit rewriting algorithm Framework to optimize quantum circuits. The algorithm framework finds all sub-circuits satisfied in the input quantum circuit according to the given external pattern description, then replaces them with better circuit implementations. To extend the capabilities of PaF , a general pattern description format is proposed to make rewriting patterns in existing work become machine-readable. In order to evaluate the effectiveness of PaF , we employ the BIGD benchmarks in QUEKO benchmark suite to test the performance and the result shows that PaF provides a maximal speedup of [Formula: see text] by using few patterns.

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