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

arXiv:quant-ph/9705026 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Hamiltonians for quantum computing

Vladimir Privman, Dima V. Mozyrsky, Steven P. Hotaling

Published Jul 1, 1997• 0 citations
arXivHTMLPDF

Abstract

We argue that the analog nature of quantum computing makes the usual design approach of constructing complicated logical operations from many simple gates inappropriate. Instead, we propose to design multi-spin quantum gates in which the input and output two-state systems (spins) are not necessarily identical. We outline the design criteria for such devices and then review recent results for single-unit Hamiltonians that accomplish the NOT and XOR functions.

DOI
10.1117/12.277664

Related papers

Hamiltonians for Quantum Computing

Vladimir Privman A, Dmitry Mozyrsky, Steven P. Hotaling

We argue that the analog nature of quantum computing makes the usual design approach of constructing complicated logical operations from many simple gates inappropriate. Instead, we propose to design multi-spin quantum gates in which the input and output two-state systems (spins) are not necessarily identical. We outline the design criteria for such devices and then review recent results for single-unit Hamiltonians that accomplish the NOT and XOR functions.

•Jan 1, 1997•1 citation

Design of Gates for Quantum Computation: The Three-Spin XOR Gate in Terms of Two-Spin Interactions

Dima Mozyrsky, Vladimir Privman A, Steven P. Hotaling

We propose to design multispin quantum gates in which the input and output two-state systems (spins) are not necessarily identical. We describe the motivations for such studies and then derive an explicit general two-spin interaction Hamiltonian which accomplishes the quantum XOR gate function for a system of three spins: two input and one output.

arXiv:quant-ph/9610008•International Journal of Modern Physics B•Feb 20, 1998•6 citations

Quantum Hamiltonian Computing protocols for molecular electronics Boolean logic gates

Omid Faizy Namarvar, Olivier Giraud, Bertrand Georgeot +1 more

Abstract Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different designs, where the logical outputs are encoded either at fixed energy and spatial positioning of the quantum states, or at different energies. We use these results to construct quantum Boolean adders involving a minimal number of quantum states with the two designs. We also establish a matrix algebra giving an analogy between classical Boolean logic gates and quantum ones, and assess the possibilities of both designs for more complex gates.

arXiv:1812.00395•Quantum Science and Technology•May 23, 2019•10 citations

Digital-Analog Quantum Computing with Qudits

Alatz Alvarez-Ahedo, Mikel Garcia de Andoin, Mikel Sanz

Digital-analog quantum computing with two-level systems is a computational paradigm that combines an analog Hamiltonian with single-qubit gates to achieve universality. We extend this framework to $d$-level systems by conjugating an analog Hamiltonian block with single-qudit gates drawn from the Weyl-Heisenberg basis, which provides a natural set of operations for qudit architectures. More specifically, we propose a protocol to simulate arbitrary two-body Hamiltonians with at most $O(d^4 n^2)$ analog blocks. The power of this approach is illustrated by the simulation of many-body qudit spin Hamiltonians including magnetic quadrupolar terms.

quant-pharXiv:2512.17697•Dec 22, 2025

Quantum computation and spin physics (invited)

David Peter Divincenzo

A brief review is given of the physical implementation of quantum computation within spin systems or other two-state quantum systems. The importance of the controlled-NOT or quantum XOR gate as the fundamental primitive operation of quantum logic is emphasized. Recent developments in the use of quantum entanglement to build error-robust quantum states, and the simplest protocol for quantum error correction, are discussed.

arXiv:cond-mat/9612125•Journal of Applied Physics•Apr 15, 1997•25 citations

Minimal resource to design spin-based quantum transistors

Alan C. Santos

Designing quantum analogous of classical computers components is the heart of quantum information processors. In this sense, for quantum devices, quantum transistors are believed to be as necessary as the classical ones for classical devices. In this paper we design the smallest spin-based quantum transistor. In fact, while previous schemes explore entangled quantum state for simulating the performance of quantum transistors gate (open and close it), in this paper we show that such task can be achieved by a controllable external magnetic field in a three-spin quantum system. Thus, we could reduce the number of physical spins required to design the quantum transistor, since the gate in our transistor is composed by a single-spin, instead two-spin systems. To analyze the performance of our quantum transistor, we consider its robustness against two decohering environments.

arXiv:1804.07320•Apr 19, 2018•1 citation
We argue that the analog nature of quantum computing makes the usual design approach of constructing complicated logical operations from many simple gates inappropriate. Instead, we propose to design multi-spin quantum gates in which the input and output two-state systems (spins) are not necessarily identical. We outline the design criteria for such devices and then review recent results for single-unit Hamiltonians that accomplish the NOT and XOR functions.
Abstract Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different designs, where the logical outputs are encoded either at fixed energy and spatial positioning of the quantum states, or at different energies. We use these results to construct quantum Boolean adders involving a minimal number of quantum states with the two designs. We also establish a matrix algebra giving an analogy between classical Boolean logic gates and quantum ones, and assess the possibilities of both designs for more complex gates.
Digital-analog quantum computing with two-level systems is a computational paradigm that combines an analog Hamiltonian with single-qubit gates to achieve universality. We extend this framework to ddd-level systems by conjugating an analog Hamiltonian block with single-qudit gates drawn from the Weyl-Heisenberg basis, which provides a natural set of operations for qudit architectures. More specifically, we propose a protocol to simulate arbitrary two-body Hamiltonians with at most O(d4n2)O(d^4 n^2)O(d4n2) analog blocks. The power of this approach is illustrated by the simulation of many-body qudit spin Hamiltonians including magnetic quadrupolar terms.
Designing quantum analogous of classical computers components is the heart of quantum information processors. In this sense, for quantum devices, quantum transistors are believed to be as necessary as the classical ones for classical devices. In this paper we design the smallest spin-based quantum transistor. In fact, while previous schemes explore entangled quantum state for simulating the performance of quantum transistors gate (open and close it), in this paper we show that such task can be achieved by a controllable external magnetic field in a three-spin quantum system. Thus, we could reduce the number of physical spins required to design the quantum transistor, since the gate in our transistor is composed by a single-spin, instead two-spin systems. To analyze the performance of our quantum transistor, we consider its robustness against two decohering environments.