Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Asia and South Pacific Design Automation Conference (ASP-DAC)

Synthesis of quantum logic circuits

Vivek Shende, Stephen S. Bullock, Igor L. Markov

Published Jul 19, 2005• 46 citations
Publisher

Abstract

The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits to the attention of the EDA community (Iwama et al., 2002; Shende et al., 2003; Bullock and Markov, 2003; Shende et al., 2004; Hung et al., 2004). We discuss efficient circuits to initialize quantum registers and implement generic quantum computations. Our techniques yield circuits that are twice as small as the best previously published technique. Moreover, a theoretical lower bound shows that our new circuits can be improved by at most a factor of two. Further, the circuits grow by at most a factor of nine under severe architectural restrictions.

DOI
10.1109/aspdac.2005.1466172

Related papers

Synthesis of quantum-logic circuits

Vivek Shende, Stephen S. Bullock, Igor L. Markov

The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits (Proc. R. Soc. Lond. A, Math. Phys. Sci., vol. 425, p. 73, 1989) to the attention of the electronic design automation community (Proc. 40th ACM/IEEE Design Automation Conf., 2003), (Phys. Rev. A, At. Mol. Opt. Phy., vol. 68, p. 012318, 2003), (Proc. 41st Design Automation Conf., 2004), (Proc. 39th Design Automation Conf., 2002), (Proc. Design, Automation, and Test Eur., 2004), (Phys. Rev. A, At. Mol. Opt. Phy., vol. 69, p. 062321, 2004), (IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 22, p. 710, 2003). Efficient quantum-logic circuits that perform two tasks are discussed: 1) implementing generic quantum computations, and 2) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the state space of an n-qubit register is not finite and contains exponential superpositions of classical bitstrings. The proposed circuits are asymptotically optimal for respective tasks and improve earlier published results by at least a factor of 2. The circuits for generic quantum computation constructed by the algorithms are the most efficient known today in terms of the number of most expensive gates [quantum controlled-NOTs (CNOTs)]. They are based on an analog of the Shannon decomposition of Boolean functions and a new circuit block, called quantum multiplexor (QMUX), which generalizes several known constructions. A theoretical lower bound implies that the circuits cannot be improved by more than a factor of 2. It is additionally shown how to accommodate the severe architectural limitation of using only nearest neighbor gates, which is representative of current implementation technologies. This increases the number of gates by almost an order of magnitude, but preserves the asymptotic optimality of gate counts.

arXiv:quant-ph/0406176•IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems•May 12, 2006•678 citations

Logic Synthesis for Quantum State Generation

Philipp Niemann, Rhitam Datta, Robert Wille

Quantum computation established itself as a promising emerging technology and, hence, attracted considerable attention in the domain of computer-aided-design (CAD). However, quantum mechanical phenomena such as superposition, phase shifts, or entanglement lead to a logic model which poses serious challenges to the development of a proper design flow for quantum circuits. Consequently, researchers addressed synthesis of quantum circuits not as a single design step, but considered sub-tasks such as synthesis of Boolean components or synthesis of restricted subsets of quantum functionality. Generating a particularly desired quantum state is another of these sub-tasks. However, logic synthesis of quantum circuits accomplishing that has hardly been considered yet. In this work, we propose a generic method which automatically synthesizes a quantum circuit generating any desired quantum state from an initially given basis state. The proposed method allows for both, a theoretical determination of upper bounds as well as an experimental evaluation of the number of quantum gates needed for this important design step.

IEEE International Symposium on Multiple-Valued Logic (ISMVL)•May 1, 2016•31 citations

Primer on the Design and Construction of Quantum Circuits

Edgard Muñoz‐Coreas, Israel Koiku

Quantum algorithms promise up to a superpolynomial factor speedup in computational tasks compared to their classical counterparts. Quantum computers are now approaching sizes where quantum algorithms can be demonstrated. As a result, the implementation of algorithms as quantum circuits has become an important research topic. In this work, we provide an overview of quantum computation and the design of quantum circuits. Properties unique to quantum computation are outlined. We introduce how a quantum algorithm is translated into a circuit and show measures used to assess the performance of quantum circuits.

IEEE MetroCon•Nov 13, 2024•0 citations

Smaller two-qubit circuits for quantum communication and computation

Vivek Shende, Igor L. Markov, Stephen S. Bullock

We show how to implement an arbitrary two-qubit unitary operation using any of several quantum gate libraries with small a priori upper bounds on gate counts. In analogy to library-less logic synthesis, we consider circuits and gates in terms of the underlying model of quantum computation, and do not assume any particular technology. As increasing the number of qubits can be prohibitively expensive, we assume throughout that no extra qubits are available for temporary storage. Using quantum circuit identities, we improve an earlier lower bound of 17 elementary gates by Bullock and Markov to 18, and their upper bound of 23 elementary gates to 18. We also improve upon the generic circuit with six CNOT gates by Zhang et al. (our circuit uses three), and that by Vidal and Dawson with 11 basic gates (we use 10). We study the performance of our synthesis procedures on two-qubit operators that are useful in quantum algorithms and communication protocols. With additional work, we find small circuits and improve upon previously known circuits in some cases.

Design, Automation, and Test in Europe•Feb 16, 2004•14 citations

Smaller two-qubit circuits for quantum communication and computation

Vivek Shende, Igor L. Markov, Stephen S. Bullock

We show how to implement an arbitrary two-qubit unitary operation using any of several quantum gate libraries with small a priori upper bounds on gate counts. In analogy to library-less logic synthesis, we consider circuits and gates in terms of the underlying model of quantum computation, and do not assume any particular technology. As increasing the number of qubits can be prohibitively expensive, we assume throughout that no extra qubits are available for temporary storage. Using quantum circuit identities, we improve an earlier lower bound of 17 elementary gates by Bullock and Markov to 18, and their upper bound of 23 elementary gates to 18. We also improve upon the generic circuit with six CNOT gates by Zhang et al. (our circuit uses three), and that by Vidal and Dawson with 11 basic gates (we use 10). We study the performance of our synthesis procedures on two-qubit operators that are useful in quantum algorithms and communication protocols. With additional work, we find small circuits and improve upon previously known circuits in some cases.

Design, Automation, and Test in Europe•Jul 20, 2004•22 citations

An Efficient Method for Generating Matrices of Quantum Logic Circuits

Zhiqiang Li, Jiajia Hu, Xi Wu +3 more

Lecture notes in computer science•Jan 1, 2020•0 citations
The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits to the attention of the EDA community (Iwama et al., 2002; Shende et al., 2003; Bullock and Markov, 2003; Shende et al., 2004; Hung et al., 2004). We discuss efficient circuits to initialize quantum registers and implement generic quantum computations. Our techniques yield circuits that are twice as small as the best previously published technique. Moreover, a theoretical lower bound shows that our new circuits can be improved by at most a factor of two. Further, the circuits grow by at most a factor of nine under severe architectural restrictions.
The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits (Proc. R. Soc. Lond. A, Math. Phys. Sci., vol. 425, p. 73, 1989) to the attention of the electronic design automation community (Proc. 40th ACM/IEEE Design Automation Conf., 2003), (Phys. Rev. A, At. Mol. Opt. Phy., vol. 68, p. 012318, 2003), (Proc. 41st Design Automation Conf., 2004), (Proc. 39th Design Automation Conf., 2002), (Proc. Design, Automation, and Test Eur., 2004), (Phys. Rev. A, At. Mol. Opt. Phy., vol. 69, p. 062321, 2004), (IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 22, p. 710, 2003). Efficient quantum-logic circuits that perform two tasks are discussed: 1) implementing generic quantum computations, and 2) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the state space of an n-qubit register is not finite and contains exponential superpositions of classical bitstrings. The proposed circuits are asymptotically optimal for respective tasks and improve earlier published results by at least a factor of 2. The circuits for generic quantum computation constructed by the algorithms are the most efficient known today in terms of the number of most expensive gates [quantum controlled-NOTs (CNOTs)]. They are based on an analog of the Shannon decomposition of Boolean functions and a new circuit block, called quantum multiplexor (QMUX), which generalizes several known constructions. A theoretical lower bound implies that the circuits cannot be improved by more than a factor of 2. It is additionally shown how to accommodate the severe architectural limitation of using only nearest neighbor gates, which is representative of current implementation technologies. This increases the number of gates by almost an order of magnitude, but preserves the asymptotic optimality of gate counts.
Quantum computation established itself as a promising emerging technology and, hence, attracted considerable attention in the domain of computer-aided-design (CAD). However, quantum mechanical phenomena such as superposition, phase shifts, or entanglement lead to a logic model which poses serious challenges to the development of a proper design flow for quantum circuits. Consequently, researchers addressed synthesis of quantum circuits not as a single design step, but considered sub-tasks such as synthesis of Boolean components or synthesis of restricted subsets of quantum functionality. Generating a particularly desired quantum state is another of these sub-tasks. However, logic synthesis of quantum circuits accomplishing that has hardly been considered yet. In this work, we propose a generic method which automatically synthesizes a quantum circuit generating any desired quantum state from an initially given basis state. The proposed method allows for both, a theoretical determination of upper bounds as well as an experimental evaluation of the number of quantum gates needed for this important design step.
Quantum algorithms promise up to a superpolynomial factor speedup in computational tasks compared to their classical counterparts. Quantum computers are now approaching sizes where quantum algorithms can be demonstrated. As a result, the implementation of algorithms as quantum circuits has become an important research topic. In this work, we provide an overview of quantum computation and the design of quantum circuits. Properties unique to quantum computation are outlined. We introduce how a quantum algorithm is translated into a circuit and show measures used to assess the performance of quantum circuits.
We show how to implement an arbitrary two-qubit unitary operation using any of several quantum gate libraries with small a priori upper bounds on gate counts. In analogy to library-less logic synthesis, we consider circuits and gates in terms of the underlying model of quantum computation, and do not assume any particular technology. As increasing the number of qubits can be prohibitively expensive, we assume throughout that no extra qubits are available for temporary storage. Using quantum circuit identities, we improve an earlier lower bound of 17 elementary gates by Bullock and Markov to 18, and their upper bound of 23 elementary gates to 18. We also improve upon the generic circuit with six CNOT gates by Zhang et al. (our circuit uses three), and that by Vidal and Dawson with 11 basic gates (we use 10). We study the performance of our synthesis procedures on two-qubit operators that are useful in quantum algorithms and communication protocols. With additional work, we find small circuits and improve upon previously known circuits in some cases.
We show how to implement an arbitrary two-qubit unitary operation using any of several quantum gate libraries with small a priori upper bounds on gate counts. In analogy to library-less logic synthesis, we consider circuits and gates in terms of the underlying model of quantum computation, and do not assume any particular technology. As increasing the number of qubits can be prohibitively expensive, we assume throughout that no extra qubits are available for temporary storage. Using quantum circuit identities, we improve an earlier lower bound of 17 elementary gates by Bullock and Markov to 18, and their upper bound of 23 elementary gates to 18. We also improve upon the generic circuit with six CNOT gates by Zhang et al. (our circuit uses three), and that by Vidal and Dawson with 11 basic gates (we use 10). We study the performance of our synthesis procedures on two-qubit operators that are useful in quantum algorithms and communication protocols. With additional work, we find small circuits and improve upon previously known circuits in some cases.