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

IEEE Transactions on Quantum Engineering

Preparing Dicke States on a Quantum Computer

Chandra Sekhar Mukherjee, Subhamoy Maitra, Vineet Gaurav, Dibyendu Roy

Published Jan 1, 2020• 38 citations
Publisher

Abstract

Exact requirement of controlled NOT (CNOT) and single-qubit gates to implement a quantum algorithm in a given architecture is one of the central problems in this computational paradigm. In this article, we take a tutorial approach in explaining the preparation of Dicke states (|Dkn〉) using concise realizations of partially defined unitary transformations. We show how to efficiently implement the state-of-the-art deterministic Dicke state preparation circuits and in turn optimize them in terms of CNOT and single-qubit gate counts. We explain theoretical ideas in reducing the gate counts and observe how these improvements are reflected in actual implementation of the circuits. To emphasize the advantages, we describe the circuit for preparing |D24〉 on the “ibmqx2” machine of the IBM quantum experience (QX) service. Our approach shows that the error induced due to noise in the system is lesser in comparison to the existing works. We conclude by describing the CNOT map of the generic |Dkn〉 preparation circuit and analyze different ways of distributing the CNOT gates in the circuit and its effect on the induced error in the Noisy Intermediate Scale Quantum environment.

DOI
10.1109/tqe.2020.3041479

Related papers

On Actual Preparation of Dicke State on a Quantum Computer

Chandra Sekhar Mukherjee, Subhamoy Maitra, Vineet Gaurav +1 more

The exact number of CNOT and single qubit gates needed to implement a Quantum Algorithm in a given architecture is one of the central problems of Quantum Computation. In this work we study the importance of concise realizations of Partially defined Unitary Transformations for better circuit construction using the case study of Dicke State Preparation. The Dicke States $(\left|D^n_k \right>)$ are an important class of entangled states with uses in many branches of Quantum Information. In this regard we provide the most efficient Deterministic Dicke State Preparation Circuit in terms of CNOT and single qubit gate counts in comparison to existing literature. We further observe that our improvements also reduce architectural constraints of the circuits. We implement the circuit for preparing $\left| D^4_2 \right>$ on the "ibmqx2" machine of the IBM QX service and observe that the error induced due to noise in the system is lesser in comparison to the existing circuit descriptions. We conclude by describing the CNOT map of the generic $\left| D^n_k \right>$ preparation circuit and analyze different ways of distributing the CNOT gates in the circuit and its affect on the induced error.

arXiv:2007.01681•Jul 3, 2020•4 citations

Quantum State Preparation Using an Exact CNOT Synthesis Formulation

Hanyu Wang, Jason Cong, Giovanni De Micheli

Minimizing the use of CNOT gates in quantum state preparation is a crucial step in quantum compilation, as they introduce coupling constraints and more noise than single-qubit gates. Reducing the number of CNOT gates can lead to more efficient and accurate quantum computations. However, the attainment of optimal solutions is hindered by the complexity of modeling superposition and entanglement. In this paper, we propose an effective state preparation algorithm using an exact CNOT synthesis formulation. Our method represents a milestone as the first design automation algorithm to surpass manual design, reducing the best CNOT count to prepare a Dicke state by 2x. For general states with up to 20 qubits, our method reduces the CNOT count by 9% and 32% for dense and sparse states, respectively, on average, compared to the latest algorithms.

arXiv:2401.01009•Design, Automation, and Test in Europe•Mar 25, 2024•5 citations

Quantum circuit synthesis on noisy intermediate-scale quantum devices

Shuai Yang, Guojing Tian, Jialin Zhang +1 more

In the near future of the noisy intermediate-scale quantum (NISQ) era, almost all quantum computing devices will be restricted to a specific fixed qubits connectivity architecture. Thus, the synthesis of quantum circuits with limited connectivity is urgent. We design quantum circuit synthesis algorithms for basic and essential synthesis problems, such as quantum state preparation, general unitary synthesis, and quantum isometries. For any architecture, the controlled not (cnot) count is at most 5/3 times the state-of-the-art result on complete-graph architecture. For some specific architectures, such as square-grid ones, the ratio is reduced to 1.126. The numerical simulation result is confirmatory of theoretical conclusions. Our algorithms significantly reduce by more than $50%$ additional cnot count compared to mapping algorithms. These algorithms help to implement the larger-scale algorithm in the physics device. Our results illustrate that well-designed synthesis algorithms can mitigate the problem of limited qubit connectivity in the NISQ era and may suggest the design of large-scale quantum devices.

Physical Review A•Jan 2, 2024•7 citations

Improved Mapping of Quantum Circuits to IBM QX Architectures

Abhoy Kole, Stefan Hillmich, Kamalika Datta +2 more

Quantum computers are becoming a reality today due to the rapid progress made by researchers in the last years. In the process of building quantum computers, IBM has developed several versions-starting from 5-qubit architectures like IBM QX2 and IBM QX4 to larger 16- or 20-qubit architectures. These architectures support arbitrary rotations of a single qubit and a controlled negation (CNOT) involving two qubits. The two qubit operations come with added coupling-map restrictions that only allow specific physical qubits to be the control and target qubits of the operation. In order to execute a quantum circuit on the IBM QX architecture, CNOT gates must satisfy the so-called coupling constraints of the architecture. Previous works addressed this issue with the objective of reducing the number of gates and the circuit depth. However, in this article, we show that further improvements are possible. To this end, we present a general approach for further improving the number of gate operations and depth of the mapped circuit. The proposed approach encompasses the selection of physical qubits, determining initial and local permutations efficiently to obtain the final circuit mapped to the given IBM QX architecture. Through experiments, improvements are observed over existing methods in terms of the number of gates and circuit depth.

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems•Dec 27, 2019•39 citations

Efficient Realizations of CNOT gates in IBM’s Quantum Computers

Alexandre A. A. de Almeida, Gerhard W. Dueck, Alexandre César Rodrigues da Silva

IBM's quantum computers implement gates from Clifford +T gate library. All single qubit gates are implemented, but only a subset of the possible CNOT are provided. It is well known that the functionally of the missing gates can be achieved by a sequence of gates. The sequence of gates is based on SWAP gates. Up to seven elementary gates are required to implement a SWAP gate. In this paper we show how the same effect can be achieved with fewer gates. To show the potential of the proposed transformations, an example is presented where a reduction of 44% in the gate count and a 26% reduction in the number of levels for IBM's QX5 computer is achieved. An algorithm that is considered state of the art, is used for the comparison.

International Symposium on Embedded Computing and System Design (ISED)•Dec 1, 2018•6 citations

Efficient Boolean Methods for Preparing Uniform Quantum States

Fereshte Mozafari, Heinz Riener, Mathias Soeken +1 more

As each quantum algorithm requires a specific initial quantum state, quantum state preparation is an important task in quantum computing. The preparation of quantum states is performed by a quantum circuit consisting of controlled-NOT (CNOT) and single-qubit gates. Known algorithms to prepare arbitrary$n$-qubit quantum states create quantum circuits in$O(2^n)$runtime and use$O(2^n)$CNOTs, which are more expensive than single-qubit gates in NISQ architectures. To reduce runtime and the number of CNOTs, we simplify the problem by considering an important family of quantum states, which areuniform quantum states(UQSs). We map UQSs to Boolean functions and propose aUQS preparation(UQSP) method. Preparing UQSs using Boolean functions allows us to utilize different representations of Boolean functions. We utilize decision diagrams to reduce runtime and enable preparation for a larger number of qubits where the state-of-the-art methods are not applicable. To further reduce the number of CNOTs, we utilize variable reordering and functional dependencies among the variables. Our state preparation method requires an exponential number of CNOTs in the worst case but it reduces CNOTs significantly for practical benchmarks. Moreover, our method generates an exact representation of quantum states without using free-qubits. We compare our algorithm with QisKit. The comparison shows that our UQSP method is capable to reduce the average number of CNOTs by 75.31% for the practical benchmarks. The runtime is almost reduced by a factor of 2.

IEEE Transactions on Quantum Engineering•Jan 1, 2021•17 citations
Exact requirement of controlled NOT (CNOT) and single-qubit gates to implement a quantum algorithm in a given architecture is one of the central problems in this computational paradigm. In this article, we take a tutorial approach in explaining the preparation of Dicke states (|Dkn〉) using concise realizations of partially defined unitary transformations. We show how to efficiently implement the state-of-the-art deterministic Dicke state preparation circuits and in turn optimize them in terms of CNOT and single-qubit gate counts. We explain theoretical ideas in reducing the gate counts and observe how these improvements are reflected in actual implementation of the circuits. To emphasize the advantages, we describe the circuit for preparing |D24〉 on the “ibmqx2” machine of the IBM quantum experience (QX) service. Our approach shows that the error induced due to noise in the system is lesser in comparison to the existing works. We conclude by describing the CNOT map of the generic |Dkn〉 preparation circuit and analyze different ways of distributing the CNOT gates in the circuit and its effect on the induced error in the Noisy Intermediate Scale Quantum environment.
The exact number of CNOT and single qubit gates needed to implement a Quantum Algorithm in a given architecture is one of the central problems of Quantum Computation. In this work we study the importance of concise realizations of Partially defined Unitary Transformations for better circuit construction using the case study of Dicke State Preparation. The Dicke States (∣Dkn>)(\left|D^n_k \right>)(∣Dkn​⟩) are an important class of entangled states with uses in many branches of Quantum Information. In this regard we provide the most efficient Deterministic Dicke State Preparation Circuit in terms of CNOT and single qubit gate counts in comparison to existing literature. We further observe that our improvements also reduce architectural constraints of the circuits. We implement the circuit for preparing ∣D24>\left| D^4_2 \right>​D24​⟩ on the "ibmqx2" machine of the IBM QX service and observe that the error induced due to noise in the system is lesser in comparison to the existing circuit descriptions. We conclude by describing the CNOT map of the generic ∣Dkn>\left| D^n_k \right>∣Dkn​⟩ preparation circuit and analyze different ways of distributing the CNOT gates in the circuit and its affect on the induced error.
Minimizing the use of CNOT gates in quantum state preparation is a crucial step in quantum compilation, as they introduce coupling constraints and more noise than single-qubit gates. Reducing the number of CNOT gates can lead to more efficient and accurate quantum computations. However, the attainment of optimal solutions is hindered by the complexity of modeling superposition and entanglement. In this paper, we propose an effective state preparation algorithm using an exact CNOT synthesis formulation. Our method represents a milestone as the first design automation algorithm to surpass manual design, reducing the best CNOT count to prepare a Dicke state by 2x. For general states with up to 20 qubits, our method reduces the CNOT count by 9% and 32% for dense and sparse states, respectively, on average, compared to the latest algorithms.
In the near future of the noisy intermediate-scale quantum (NISQ) era, almost all quantum computing devices will be restricted to a specific fixed qubits connectivity architecture. Thus, the synthesis of quantum circuits with limited connectivity is urgent. We design quantum circuit synthesis algorithms for basic and essential synthesis problems, such as quantum state preparation, general unitary synthesis, and quantum isometries. For any architecture, the controlled not (cnot) count is at most 5/3 times the state-of-the-art result on complete-graph architecture. For some specific architectures, such as square-grid ones, the ratio is reduced to 1.126. The numerical simulation result is confirmatory of theoretical conclusions. Our algorithms significantly reduce by more than 5050%50 additional cnot count compared to mapping algorithms. These algorithms help to implement the larger-scale algorithm in the physics device. Our results illustrate that well-designed synthesis algorithms can mitigate the problem of limited qubit connectivity in the NISQ era and may suggest the design of large-scale quantum devices.
Quantum computers are becoming a reality today due to the rapid progress made by researchers in the last years. In the process of building quantum computers, IBM has developed several versions-starting from 5-qubit architectures like IBM QX2 and IBM QX4 to larger 16- or 20-qubit architectures. These architectures support arbitrary rotations of a single qubit and a controlled negation (CNOT) involving two qubits. The two qubit operations come with added coupling-map restrictions that only allow specific physical qubits to be the control and target qubits of the operation. In order to execute a quantum circuit on the IBM QX architecture, CNOT gates must satisfy the so-called coupling constraints of the architecture. Previous works addressed this issue with the objective of reducing the number of gates and the circuit depth. However, in this article, we show that further improvements are possible. To this end, we present a general approach for further improving the number of gate operations and depth of the mapped circuit. The proposed approach encompasses the selection of physical qubits, determining initial and local permutations efficiently to obtain the final circuit mapped to the given IBM QX architecture. Through experiments, improvements are observed over existing methods in terms of the number of gates and circuit depth.
IBM's quantum computers implement gates from Clifford +T gate library. All single qubit gates are implemented, but only a subset of the possible CNOT are provided. It is well known that the functionally of the missing gates can be achieved by a sequence of gates. The sequence of gates is based on SWAP gates. Up to seven elementary gates are required to implement a SWAP gate. In this paper we show how the same effect can be achieved with fewer gates. To show the potential of the proposed transformations, an example is presented where a reduction of 44% in the gate count and a 26% reduction in the number of levels for IBM's QX5 computer is achieved. An algorithm that is considered state of the art, is used for the comparison.
As each quantum algorithm requires a specific initial quantum state, quantum state preparation is an important task in quantum computing. The preparation of quantum states is performed by a quantum circuit consisting of controlled-NOT (CNOT) and single-qubit gates. Known algorithms to prepare arbitrarynnn-qubit quantum states create quantum circuits inO(2n)O(2^n)O(2n)runtime and useO(2n)O(2^n)O(2n)CNOTs, which are more expensive than single-qubit gates in NISQ architectures. To reduce runtime and the number of CNOTs, we simplify the problem by considering an important family of quantum states, which areuniform quantum states(UQSs). We map UQSs to Boolean functions and propose aUQS preparation(UQSP) method. Preparing UQSs using Boolean functions allows us to utilize different representations of Boolean functions. We utilize decision diagrams to reduce runtime and enable preparation for a larger number of qubits where the state-of-the-art methods are not applicable. To further reduce the number of CNOTs, we utilize variable reordering and functional dependencies among the variables. Our state preparation method requires an exponential number of CNOTs in the worst case but it reduces CNOTs significantly for practical benchmarks. Moreover, our method generates an exact representation of quantum states without using free-qubits. We compare our algorithm with QisKit. The comparison shows that our UQSP method is capable to reduce the average number of CNOTs by 75.31% for the practical benchmarks. The runtime is almost reduced by a factor of 2.