Quantum challenge2021 Ex1
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This document discusses two solutions for constructing a Toffoli gate using only the native gates of IBM Quantum systems (CX, RZ, SX, X). The first solution constructs control-control rotation gates to flip the phase when both control qubits are 1. The second solution decomposes the Toffoli gate into a circuit α that is transpiled into the native gates. Both solutions are shown to produce the correct unitary matrix for a Toffoli gate when run on the unitary simulator.
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Combinational logic circuit by umakant bhaskar gohatre
Combinational logic circuit by umakant bhaskar gohatreSmt. Indira Gandhi College of Engineering, Navi Mumbai, Mumbai
The document describes the design of a serial-to-parallel converter using a Moore finite state machine approach. It begins with an informal description of the desired functionality. It then determines that a Moore machine model is appropriate since the outputs depend only on the current state, not the inputs. The design process involves constructing a state table and state diagram with 4 states - Reset (S0), Load 1st bit (S1), Load 2nd bit (S2), Load 3rd bit (S3), and Load 4th bit (S4). The state diagram fully specifies the state transitions and outputs for this serial-to-parallel conversion Moore finite state machine.Section based hex cell routing algorithm (sbhcr)
A Hex-Cell network topology can be constructed using units of hexagon cells. It has been introduced in the literature as interconnection network suitable for large parallel computers, which can connect large number of nodes with three links per node. Although this topology exhibits attractive characteristics such as embeddability, symmetry, regularity, strong resilience, and simple routing, the previously suggested routing algorithms suffer from the high number of logical operations and the need for readdressing of nodes every time a new level is add to the network. This negatively impacts the performance of the network as it increases the execution time of these algorithms. In this paper we propose an improved optimal point to point routing algorithm for Hex-Cell network. The algorithm is based on dividing the Hex-Cell topology into six divisions, hence the name Section Based Hex-Cell Routing (SBHCR). The SBHCR algorithm is simple and preserves the advantage of the addressing scheme proposed for the Hex-Cell network. It does not depend on the depth of the network topology which leads to overcome the issue of readdressing of nodes every time a new level is added. Evaluation against two previously suggested routing algorithms has shown the superiority of SBHCR in term of less logical operations.
Implementation of low power divider techniques using
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Implementation of low power divider techniques using radix
This document summarizes a research paper on implementing low power divider techniques using radix-8 division. It describes the design of a radix-8 divider that aims to reduce energy dissipation without penalizing latency. The algorithm and implementation of the divider are explained. Several low power techniques are then applied, including switching off inactive blocks, retiming the recurrence, reducing transitions in multiplexers, changing the redundant representation, partitioning the selection function, and modifying the conversion and rounding process. Applying these techniques can reduce energy dissipation by up to 70% compared to a standard implementation. The performance of the radix-8 divider is also compared to a radix-4 divider and one using overlapped radix-2 stages.
Hardware Description Language
Hardware Description Language (HDL) is used to describe digital systems in a textual format similar to a programming language. HDL represents both the structure and behavior of hardware at different levels of abstraction. It can be used for documentation, simulation to verify design functionality, and synthesis to automate hardware design processes. The two most common HDLs are VHDL and Verilog.
slide8.ppt
This document provides an introduction to hardware description languages (HDLs). It discusses that HDLs describe digital systems in a textual form similar to programming languages, but are specifically used for describing hardware structures and behaviors. The main uses of HDLs are to provide an alternative to schematics and as a documentation language to represent digital systems in a format readable by both humans and computers. There are two main HDLs - VHDL and Verilog. HDLs allow modeling at different levels of abstraction from gate-level to behavioral.
Low complexity design of non binary ldpc decoder using extended min-sum algor...
This document summarizes a research paper on reducing the computational complexity of non-binary LDPC decoders using an extended min-sum algorithm. It introduces low-density parity check codes and non-binary LDPC codes. It then describes an extended min-sum decoding algorithm and proposes two modifications to the parity check matrix - a lower diagonal matrix and a doubly diagonal matrix - to reduce complexity while maintaining performance. Simulation results on code lengths of 504 and 648 bits show the doubly diagonal matrix achieves the best bit error rate. Analysis finds the lower diagonal matrix has the lowest computational complexity of the approaches.
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Combinational logic circuit by umakant bhaskar gohatre
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Implementation of low power divider techniques using
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Implementation of low power divider techniques using radix
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
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Quantum challenge2021 Ex1
- 2. 今回使う重要な回路
- 3. ①回路の分解~transpile~ 以下の回路を用いると既存の回路を任意のゲートのみを使った回路で 表現することができる。 In [1]: from qiskit.compiler import transpile transpile(qc, basis_gates=['sx','rz', 'cx','x'], optimization_level=3).draw() この回路で使いたいゲートを指定 0から3までのlevelがあり数字が大きいほど 少ないゲートでまとめることができる 既存の回路の名前をここで指定 ※以降[transpiler]とおく
- 4. ②行列表示・係数表示 その回路の状態を以下の回路を用いて行列の状態にする In [2]: backend = Aer.get_backend('unitary_simulator') job = execute(qc, backend) result = job.result() print(result.get_unitary(qc, decimals=3).○○) ここを realにすると実数部分の行列を表せる imagにすると虚数部分の行列を表せる ※以降[unitary_simulator]とおく
- 5. 解法①
- 6. 行列表示・係数表示 𝑐𝑐𝑥 = 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 𝑐𝑐𝑥 = 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 ⑴ QuantumChallengeの 解説上の表記 ⑵ unitary_simulatorでの表記 ⑴の行列は上から|000>,|001>,|010>… ⑵の行列は上から|000>,|100>,|110>… というように対応するため行列の表記に差が生じる。
- 10. 『－』の符号の影響で、 この回路は以下のような行列と なってしまう QiskitChallenge Q.1 を に置き変えると、 よって〇(|110>が入力)のときだけ さらに符号が反転する回路を作る ただし、この表記方法はunitary_simulatorでの表記である。 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 −1 0 0 0 0 0
- 11. 回路の作成とその行列
- 12. 回路①の行列 ただし、この表記方法はunitary_simulatorでの表記である。 𝑈0 = 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 −1 0 0 0 0 0 CCXゲートの働きを再現するため、 〇(|110>が入力)のときだけ符号が 反転する回路を作る
- 13. 回路②の行列 ただし、この表記方法はunitary_simulatorでの表記である。 ここでは|111>のときに符号が反転しているが、 |110>が入力のときだけ符号が反転する回路を 作る必要があるので… 𝑈1 = 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 −1
- 14. 回路③の行列 ただし、この表記方法はunitary_simulatorでの表記である。 回路②の両側にXゲートを置いたことで、 |110>が入力のときだけ符号が反転する 回路を作ることができた。 これを回路①と組み合わせると 𝑈2 = 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 −1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1
- 15. 以下の回路の行列 𝑐𝑐𝑥 = 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 ただし、この表記方法はunitary_simulatorでの表記である。 ①,②の回路よりq0,q1が|1＞のときのみ反転する
- 17. 使えるゲートのみに修正① transpilerを用いる In [1]: from qiskit.compiler import transpile transpile(qc, basis_gates=['sx','rz', 'cx','x'], optimization_level=3).draw() CRy(𝜋/2) CRy(−𝜋/2) CRy(𝜋/2) … …
- 18. 使えるゲートのみに修正② transpilerを用いる CP(−𝜋/2) CP(𝜋/2) CP(𝜋/2) In [1]: from qiskit.compiler import transpile transpile(qc, basis_gates=['sx','rz', 'cx','x'], optimization_level=3).draw()
- 19. よってtranspilerを用いることで最終的に回路は以下のようになる QiskitChallenge Q.1 transpilerを用いる In [1]: from qiskit.compiler import transpile transpile(qc, basis_gates=['sx','rz', 'cx','x'], optimization_level=3).draw()
- 20. この回路を示す行列 [unitary_simulator]を使ってこの回路の行列を表すと… In [2]: backend = Aer.get_backend('unitary_simulator') job = execute(qc, backend) result = job.result() print(result.get_unitary(qc, decimals=3).real) よってCCXゲートの行列と一致するのでこの回路は CCXゲートを表すことができている
- 21. 解法②
- 23. この回路を示す行列 [unitary_simulator]を使ってこの回路の行列を表すと… In [2]: backend = Aer.get_backend('unitary_simulator') job = execute(qc, backend) result = job.result() print(result.get_unitary(qc, decimals=3).real) よってCCXゲートの行列と一致するのでこの回路は CCXゲートを表すことができている