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.

scholarly journals Quantum Circuit Synthesis Using Projective Simulation

2021 ◽  
Vol 24 (67) ◽  
pp. 90-101
Author(s):  
Otto Menegasso Pires ◽  
Eduardo Inacio Duzzioni ◽  
Jerusa Marchi ◽  
Rafael De Santiago
Keyword(s):  
Quantum Computing ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Optimization Techniques ◽  
Error Tolerance ◽  
Quantum Circuits ◽  
Quantum Decoherence ◽  
Circuit Synthesis ◽  
Circuit Optimization ◽  
Learning Technique

Quantum Computing has been evolving in the last years. Although nowadays quantum algorithms performance has shown superior to their classical counterparts, quantum decoherence and additional auxiliary qubits needed for error tolerance routines have been huge barriers for quantum algorithms efficient use.These restrictions lead us to search for ways to minimize algorithms costs, i.e the number of quantum logical gates and the depth of the circuit. For this, quantum circuit synthesis and quantum circuit optimization techniques are explored.We studied the viability of using Projective Simulation, a reinforcement learning technique, to tackle the problem of quantum circuit synthesis. The agent had the task of creating quantum circuits up to 5 qubits. Our simulations demonstrated that the agent had a good performance but its capacity for learning new circuits decreased as the number of qubits increased.

scholarly journals Quantum circuit optimization using quantum Karnaugh map

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
J.-H. Bae ◽  
Paul M. Alsing ◽  
Doyeol Ahn ◽  
Warner A. Miller
Keyword(s):  
Quantum Computation ◽  
Quantum Algorithms ◽  
Optimization Technique ◽  
Circuit Complexity ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Circuit Optimization ◽  
General Technique ◽  
Small Quantum

Abstract Every quantum algorithm is represented by set of quantum circuits. Any optimization scheme for a quantum algorithm and quantum computation is very important especially in the arena of quantum computation with limited number of qubit resources. Major obstacle to this goal is the large number of elemental quantum gates to build even small quantum circuits. Here, we propose and demonstrate a general technique that significantly reduces the number of elemental gates to build quantum circuits. This is impactful for the design of quantum circuits, and we show below this could reduce the number of gates by 60% and 46% for the four- and five-qubit Toffoli gates, two key quantum circuits, respectively, as compared with simplest known decomposition. Reduced circuit complexity often goes hand-in-hand with higher efficiency and bandwidth. The quantum circuit optimization technique proposed in this work would provide a significant step forward in the optimization of quantum circuits and quantum algorithms, and has the potential for wider application in quantum computation.

scholarly journals ACCELERATION OF QUANTUM ALGORITHMS USING THREE-QUBIT GATES

2004 ◽  
Vol 02 (01) ◽  
pp. 1-10 ◽  
Author(s):  
JUHA J. VARTIAINEN ◽  
ANTTI O. NISKANEN ◽  
MIKIO NAKAHARA ◽  
MARTTI M. SALOMAA
Keyword(s):  
Numerical Optimization ◽  
Control Parameter ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Idle Time ◽  
Quantum Circuits ◽  
Circuit Optimization ◽  
Practical Realization ◽  
Charge Qubit ◽  
The Individual

Quantum-circuit optimization is essential for any practical realization of quantum computation, in order to beat decoherence. We present a scheme for implementing the final stage in the compilation of quantum circuits, i.e. for finding the actual physical realizations of the individual modules in the quantum-gate library. We find that numerical optimization can be efficiently utilized in order to generate the appropriate control-parameter sequences which produce the desired three-qubit modules within the Josephson charge-qubit model. Our work suggests ways in which one can in fact considerably reduce the number of gates required to implement a given quantum circuit, hence diminishing idle time and significantly accelerating the execution of quantum algorithms.

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.

scholarly journals An Innovative Genetic Algorithm for the Quantum Circuit Compilation Problem

2019 ◽  
Vol 33 ◽  
pp. 7707-7714
Author(s):  
Riccardo Rasconi ◽  
Angelo Oddi
Keyword(s):  
Genetic Algorithm ◽  
Nearest Neighbor ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Heuristic Function ◽  
Circuit Realization ◽  
Benchmark Instances ◽  
Technological Limitations ◽  
Selection Of

Quantum Computing represents the next big step towards speed boost in computation, which promises major breakthroughs in several disciplines including Artificial Intelligence. This paper investigates the performance of a genetic algorithm to optimize the realization (compilation) of nearest-neighbor compliant quantum circuits. Currrent technological limitations (e.g., decoherence effect) impose that the overall duration (makespan) of the quantum circuit realization be minimized, and therefore the makespanminimization problem of compiling quantum algorithms on present or future quantum machines is dragging increasing attention in the AI community. In our genetic algorithm, a solution is built utilizing a novel chromosome encoding where each gene controls the iterative selection of a quantum gate to be inserted in the solution, over a lexicographic double-key ranking returned by a heuristic function recently published in the literature.Our algorithm has been tested on a set of quantum circuit benchmark instances of increasing sizes available from the recent literature. We demonstrate that our genetic approach obtains very encouraging results that outperform the solutions obtained in previous research against the same benchmark, succeeding in significantly improving the makespan values for a great number of instances.

scholarly journals Efficient quantum circuits for binary elliptic curve arithmetic: reducing $T$-gate complexity

2013 ◽  
Vol 13 (7&8) ◽  
pp. 631-644
Author(s):  
Brittanney Amento ◽  
Martin Rotteler ◽  
Rainer Steinwalds
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Finite Fields ◽  
Quantum Algorithms ◽  
Substantial Reduction ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Curves Over Finite Fields ◽  
Curve Representation ◽  
Modern Cryptography

Elliptic curves over finite fields ${\mathbb F}_{2^n}$ play a prominent role in modern cryptography. Published quantum algorithms dealing with such curves build on a short Weierstrass form in combination with affine or projective coordinates. In this paper we show that changing the curve representation allows a substantial reduction in the number of $T$-gates needed to implement the curve arithmetic. As a tool, we present a quantum circuit for computing multiplicative inverses in $\mathbb F_{2^n}$ in depth $\bigO(n\log_2 n)$ using a polynomial basis representation, which may be of independent interest.

scholarly journals Efficient and effective quantum compiling for entanglement-based machine learning on IBM Q devices

2018 ◽  
Vol 16 (08) ◽  
pp. 1840006 ◽  
Author(s):  
Davide Ferrari ◽  
Michele Amoretti
Keyword(s):  
Machine Learning ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Entangled States ◽  
Hard Problem ◽  
Practical Applications ◽  
Ghz States ◽  
Quantum Machine Learning ◽  
Uniform Quantum

Quantum compiling means fast, device-aware implementation of quantum algorithms (i.e. quantum circuits, in the quantum circuit model of computation). In this paper, we present a strategy for compiling IBM Q-aware, low-depth quantum circuits that generate Greenberger–Horne–Zeilinger (GHZ) entangled states. The resulting compiler can replace the QISKit compiler for the specific purpose of obtaining improved GHZ circuits. It is well known that GHZ states have several practical applications, including quantum machine learning. We illustrate our experience in implementing and querying a uniform quantum example oracle based on the GHZ circuit, for solving the classically hard problem of learning parity with noise.

scholarly journals On the depth overhead incurred when running quantum algorithms on near-term quantum computers with limited qubit connectivity

2020 ◽  
Vol 20 (9&10) ◽  
pp. 787-806 ◽  
Author(s):  
Steven Herbert
Keyword(s):  
Quantum Algorithms ◽  
Quantum Circuit ◽  
The Other ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Interaction Graph ◽  
Finite Degree ◽  
Near Term

This paper addresses the problem of finding the depth overhead that will be incurred when running quantum circuits on near-term quantum computers. Specifically, it is envisaged that near-term quantum computers will have low qubit connectivity: each qubit will only be able to interact with a subset of the other qubits, a reality typically represented by a qubit interaction graph in which a vertex represents a qubit and an edge represents a possible direct 2-qubit interaction (gate). Thus the depth overhead is unavoidably incurred by introducing swap gates into the quantum circuit to enable general qubit interactions. This paper proves that there exist quantum circuits where a depth overhead in Omega(\log n) must necessarily be incurred when running quantum circuits with n qubits on quantum computers whose qubit interaction graph has finite degree, but that such a logarithmic depth overhead is achievable. The latter is shown by the construction of a 4-regular qubit interaction graph and associated compilation algorithm that can execute any quantum circuit with only a logarithmic depth overhead.

scholarly journals Universal discriminative quantum neural networks

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
H. Chen ◽  
L. Wossnig ◽  
S. Severini ◽  
H. Neven ◽  
M. Mohseni
Keyword(s):  
Machine Learning ◽  
Hybrid Methods ◽  
Quantum Circuit ◽  
Learning Task ◽  
Error Rates ◽  
Quantum Circuits ◽  
Circuit Optimization ◽  
Learning Tasks ◽  
Classical Analogue ◽  
Optimal Values

AbstractRecent results have demonstrated the successful applications of quantum-classical hybrid methods to train quantum circuits for a variety of machine learning tasks. A natural question to ask is consequentially whether we can also train such quantum circuits to discriminate quantum data, i.e., perform classification on data stored in form of quantum states. Although quantum mechanics fundamentally forbids deterministic discrimination of non-orthogonal states, we show in this work that it is possible to train a quantum circuit to discriminate such data with a trade-off between minimizing error rates and inconclusiveness rates of the classification tasks. Our approach achieves at the same time a performance which is close to the theoretically optimal values and a generalization ability to previously unseen quantum data. This generalization power hence distinguishes our work from previous circuit optimization results and furthermore provides an example of a quantum machine learning task that has inherently no classical analogue.

scholarly journals Quantum Gate Pattern Recognition and Circuit Optimization for Scientific Applications

2021 ◽  
Vol 251 ◽  
pp. 03023
Author(s):  
Wonho Jang ◽  
Koji Terashi ◽  
Masahiko Saito ◽  
Christian W. Bauer ◽  
Benjamin Nachman ◽  
...  
Keyword(s):  
High Energy Physics ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Circuit Complexity ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
High Energy ◽  
Circuit Optimization ◽  
Final State ◽  
State Radiation

There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of quantum devices produced over a next decade. We introduce two separate ideas for circuit optimization and combine them in a multi-tiered quantum circuit optimization protocol called AQCEL. The first ingredient is a technique to recognize repeated patterns of quantum gates, opening up the possibility of future hardware optimization. The second ingredient is an approach to reduce circuit complexity by identifying zero- or low-amplitude computational basis states and redundant gates. As a demonstration, AQCEL is deployed on an iterative and effcient quantum algorithm designed to model final state radiation in high energy physics. For this algorithm, our optimization scheme brings a significant reduction in the gate count without losing any accuracy compared to the original circuit. Additionally, we have investigated whether this can be demonstrated on a quantum computer using polynomial resources. Our technique is generic and can be useful for a wide variety of quantum algorithms.

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