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

Quantum Information and Computation

Universal quantum computing in linear nearest neighbor architectures

Preethika Kumar, Steven R. Skinner

Published Mar 1, 2011• 6 citations
Publisher

Abstract

We introduce a scheme for realizing universal quantum computing in a linear nearest neighbor architecture with fixed couplings. We first show how to realize a controlled-NOT gate operation between two adjacent qubits without having to isolate the two qubits from qubits adjacent to them. The gate operation is implemented by applying two consecutive pulses of equal duration, but varying amplitudes, on the target qubit. Since only a single control parameter is required in implementing our scheme, it is very efficient. We next show how our scheme can be used to realize single qubit rotations and two-qubit controlled-unitary operations. As most proposals for solid state implementations of a quantum computer use a one-dimensional line of qubits, the schemes presented here will be extremely useful.

DOI
10.26421/qic11.3-4-8

Related papers

Nearest-neighbor architecture to overcome effects of qubit precessions in gate operations

Preethika Kumar, S.R. Skinner, Sahar Daraeizadeh

We design a nearest-neighbor architectural layout that uses fixed positive and negative couplings between qubits, to overcome the effects of relative phases due to qubit precessions, both during idle times and gate operations. The scheme uses decoherence-free subspaces, and we show how to realize gate operations on these encoded qubits. The main advantage of our scheme is that most gate operations are realized by only varying a single control parameter, which greatly reduces the circuit complexity. Moreover, the scheme is robust against phase errors occurring as a result of finite rise and fall times due to non-ideal pulses.

IEEE Congress on Evolutionary Computation (CEC)•Jun 1, 2011•1 citation

Simplified approach to implementing controlled-unitary operations in a two-qubit system

Preethika Kumar, S.R. Skinner

We introduce a scheme for realizing arbitrary controlled-unitary operations in a two-qubit system. If the $2\ifmmode\times\else\texttimes\fi{}2$ unitary matrix is special unitary (has unit determinant), the controlled-unitary gate operation can be realized in a single pulse operation. The pulse in our scheme will constitute varying one of the parameters of the system between an arbitrarily maximum and a ``calculated'' minimum value. This parameter will constitute the variable parameter of the system while the other parameters, which include the coupling between the two qubits, will be treated as fixed parameters. The values of the parameters are what we solve for using our approach in order to realize an arbitrary controlled-unitary operation. We further show that the computational complexity of the operation is no greater than that required for a controlled-NOT (CNOT) gate. Since conventional schemes realize a controlled-unitary operation by breaking it into a sequence of single-qubit and CNOT gate operations, our method is an improvement because we not only require less time duration, but also fewer control lines to implement the same operation. To demonstrate improvement over other schemes, we show, as examples, how two controlled-unitary operations, one being the controlled-Hadamard gate, can be realized in a single pulse operation using our scheme. Furthermore, our method can be applied to a wide range of coupling schemes and can be used to realize gate operations between two qubits coupled via Ising, Heisenberg, and anisotropic interactions.

arXiv:1202.2053•Physical Review A•Aug 30, 2007•11 citations

Switchable Next-Nearest-Neighbor Coupling for Controlled Two-Qubit Operations

Peng Zhao, Peng Xu, Dong Lan +3 more

Minimizing gate depth is important for extending the computational power of a noisy quantum processor, and native multiqubit gates could dramatically reduce the gate depth of generic circuits. To that end, although various approaches have been proposed, practical realization may be hindered by stringent control requirements, or by poor compatibility with existing schemes for one- or two-qubit operations. Here researchers employ a scalable architecture comprising two types of qubits to realize switchable coupling. This allows for a simple control strategy to realize native three-qubit gates, which may become a key element in $e.g.$ quantum chemistry simulations.

arXiv:2004.08639•Physical Review Applied•Dec 4, 2020•25 citations

Universal Parity Quantum Computing

Michael Fellner, Anette Messinger, Kilian Ender +1 more

We propose a universal gate set for quantum computing with all-to-all connectivity and intrinsic robustness to bit-flip errors based on parity encoding. We show that logical controlled phase gate and R_{z} rotations can be implemented in parity encoding with single-qubit operations. Together with logical R_{x} rotations, implemented via nearest-neighbor controlled-NOT gates and an R_{x} rotation, these form a universal gate set. As the controlled phase gate requires only single-qubit rotations, the proposed scheme has advantages for several cornerstone quantum algorithms, e.g., the quantum Fourier transform. We present a method to switch between different encoding variants via partial on-the-fly encoding and decoding.

arXiv:2205.09505•Physical Review Letters•Oct 27, 2022•27 citations

Quantum State Analysis and Optimal Logic Synthesis for Linear Nearest Neighbor Architecture

Hai Cheng Xu, Zhijin Guan, Xueyun Cheng +1 more

Real quantum computing technologies have different restrictions and constraints which need to be considered during circuit synthesis. In certain technologies, only physically adjacent qubits can interact. It is common to use a pair of SWAP gates to bring the control and target qubits of any quantum gate to adjacent lines and maintain correct circuit functionality. This paper introduces a new method to synthesize linear nearest neighbor quantum circuit on the base of the analysis of quantum state in circuit. For all 3-qubit quantum circuit, experimental results shows that our algorithm can reduce the quantum cost by approximately 30% on average compared with one recent proposed method.

DEStech Transactions on Engineering and Technology Research•Mar 14, 2017•0 citations

Natural two-qubit gate for quantum computation using the XY interaction

Norbert Schuch, Jens Siewert

The two-qubit interaction Hamiltonian of a given physical implementation determines whether or not a two-qubit gate such as the controlled-NOT (CNOT) gate can be realized easily. It can be shown that, e.g., with the $\mathrm{XY}$ interaction more than one two-qubit operation is required in order to realize the CNOT operation. Here we propose a two-qubit gate for the $\mathrm{XY}$ interaction which combines the CNOT and SWAP operations. By using this gate quantum circuits can be implemented efficiently, even if only nearest-neighbor coupling between the qubits is available.

arXiv:quant-ph/0209035•Physical Review A•Mar 10, 2003•237 citations
We introduce a scheme for realizing universal quantum computing in a linear nearest neighbor architecture with fixed couplings. We first show how to realize a controlled-NOT gate operation between two adjacent qubits without having to isolate the two qubits from qubits adjacent to them. The gate operation is implemented by applying two consecutive pulses of equal duration, but varying amplitudes, on the target qubit. Since only a single control parameter is required in implementing our scheme, it is very efficient. We next show how our scheme can be used to realize single qubit rotations and two-qubit controlled-unitary operations. As most proposals for solid state implementations of a quantum computer use a one-dimensional line of qubits, the schemes presented here will be extremely useful.
We design a nearest-neighbor architectural layout that uses fixed positive and negative couplings between qubits, to overcome the effects of relative phases due to qubit precessions, both during idle times and gate operations. The scheme uses decoherence-free subspaces, and we show how to realize gate operations on these encoded qubits. The main advantage of our scheme is that most gate operations are realized by only varying a single control parameter, which greatly reduces the circuit complexity. Moreover, the scheme is robust against phase errors occurring as a result of finite rise and fall times due to non-ideal pulses.
We introduce a scheme for realizing arbitrary controlled-unitary operations in a two-qubit system. If the $2\ifmmode\times\else\texttimes\fi{}2$ unitary matrix is special unitary (has unit determinant), the controlled-unitary gate operation can be realized in a single pulse operation. The pulse in our scheme will constitute varying one of the parameters of the system between an arbitrarily maximum and a ``calculated'' minimum value. This parameter will constitute the variable parameter of the system while the other parameters, which include the coupling between the two qubits, will be treated as fixed parameters. The values of the parameters are what we solve for using our approach in order to realize an arbitrary controlled-unitary operation. We further show that the computational complexity of the operation is no greater than that required for a controlled-NOT (CNOT) gate. Since conventional schemes realize a controlled-unitary operation by breaking it into a sequence of single-qubit and CNOT gate operations, our method is an improvement because we not only require less time duration, but also fewer control lines to implement the same operation. To demonstrate improvement over other schemes, we show, as examples, how two controlled-unitary operations, one being the controlled-Hadamard gate, can be realized in a single pulse operation using our scheme. Furthermore, our method can be applied to a wide range of coupling schemes and can be used to realize gate operations between two qubits coupled via Ising, Heisenberg, and anisotropic interactions.
Minimizing gate depth is important for extending the computational power of a noisy quantum processor, and native multiqubit gates could dramatically reduce the gate depth of generic circuits. To that end, although various approaches have been proposed, practical realization may be hindered by stringent control requirements, or by poor compatibility with existing schemes for one- or two-qubit operations. Here researchers employ a scalable architecture comprising two types of qubits to realize switchable coupling. This allows for a simple control strategy to realize native three-qubit gates, which may become a key element in e.g.e.g.e.g. quantum chemistry simulations.
We propose a universal gate set for quantum computing with all-to-all connectivity and intrinsic robustness to bit-flip errors based on parity encoding. We show that logical controlled phase gate and R_{z} rotations can be implemented in parity encoding with single-qubit operations. Together with logical R_{x} rotations, implemented via nearest-neighbor controlled-NOT gates and an R_{x} rotation, these form a universal gate set. As the controlled phase gate requires only single-qubit rotations, the proposed scheme has advantages for several cornerstone quantum algorithms, e.g., the quantum Fourier transform. We present a method to switch between different encoding variants via partial on-the-fly encoding and decoding.
Real quantum computing technologies have different restrictions and constraints which need to be considered during circuit synthesis. In certain technologies, only physically adjacent qubits can interact. It is common to use a pair of SWAP gates to bring the control and target qubits of any quantum gate to adjacent lines and maintain correct circuit functionality. This paper introduces a new method to synthesize linear nearest neighbor quantum circuit on the base of the analysis of quantum state in circuit. For all 3-qubit quantum circuit, experimental results shows that our algorithm can reduce the quantum cost by approximately 30% on average compared with one recent proposed method.
The two-qubit interaction Hamiltonian of a given physical implementation determines whether or not a two-qubit gate such as the controlled-NOT (CNOT) gate can be realized easily. It can be shown that, e.g., with the XY\mathrm{XY}XY interaction more than one two-qubit operation is required in order to realize the CNOT operation. Here we propose a two-qubit gate for the XY\mathrm{XY}XY interaction which combines the CNOT and SWAP operations. By using this gate quantum circuits can be implemented efficiently, even if only nearest-neighbor coupling between the qubits is available.