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/0505122 · Physical Review A

Quantum computation via translation-invariant operations on a chain of qubits

Robert Raussendorf

Published Nov 1, 2005• 55 citations
arXivHTMLPDF

Abstract

A scheme of universal quantum computation is described that does not require local control. All the required operations, an Ising-type interaction and spatially uniform simultaneous one-qubit gates, are translation invariant.
DOI
10.1103/physreva.72.052301

Related papers

Reversible universal quantum computation within translation-invariant systems

K. G. H. Vollbrecht, J. I. Cirac

We show how to perform reversible universal quantum computation on a translationally invariant pure state, using only global operations based on next-neighbor interactions. We do not need to break the translational symmetry of the state at any time during the computation. Since the proposed scheme fulfills the locality condition of a quantum cellular automata, we present a reversible quantum cellular automaton capable of universal quantum computation.

arXiv:quant-ph/0502143•Physical Review A•Jan 18, 2006•32 citations

Quantum Computation with Untunable Couplings

Xingxiang Zhou, Zheng-Wei Zhou, Guang‐Can Guo +1 more

Most quantum computer realizations require the ability to apply local fields and tune the couplings between qubits, in order to realize single bit and two bit gates which are necessary for universal quantum computation. We present a scheme to remove the necessity of switching the couplings between qubits for two bit gates, which are more costly in many cases. Our strategy is to compute with encoded qubits in and out of carefully designed interaction free subspaces analogous to decoherence free subspaces. We give two examples to show how universal quantum computation is realized in our scheme with local manipulations to physical qubits only, for both diagonal and off diagonal interactions.

arXiv:quant-ph/0209142•Physical Review Letters•Oct 21, 2002•76 citations

Globally controlled universal quantum computation with arbitrary subsystem dimension

Gerardo A. Paz-Silva, Gavin K. Brennen, Jason Twamley

We present a scheme to perform universal quantum computation using global control with an arbitrary subsystem dimension (not necessarily finite). The scheme is developed over a one spatial dimension $N$-element array, using only mirror-symmetric logical encoding, global pulses for single subsystem operations, uniform Ising-type interaction, and an all zero initial pure state. A mechanism using ancillary degrees of freedom for subsystem specific measurement is also presented.

arXiv:0811.4245•Physical Review A•Nov 12, 2009•5 citations

Scalable quantum computation via local control of only two qubits

Daniel Klaus Burgarth, Koji Maruyama, Michael Murphy +4 more

We apply quantum control techniques to a long spin chain by acting only on two qubits at one of its ends, thereby implementing universal quantum computation by a combination of quantum gates on these qubits and indirect swap operations across the chain. It is shown that the control sequences can be computed and implemented efficiently. We discuss the application of these ideas to physical systems such as superconducting qubits in which full control of long chains is challenging.

arXiv:0905.3373•Physical Review A•Apr 22, 2010•103 citations

Schemes for parallel quantum computation without local control of qubits

Simon C. Benjamin

Typical quantum computing schemes require transformations (gates) to be targeted at specific elements (qubits). In many physical systems, direct targeting is difficult to achieve; an alternative is to encode local gates into globally applied transformations. Here we demonstrate the minimum physical requirements for such an approach: a one-dimensional array composed of two alternating ``types'' of two-state system. Each system need be sensitive only to the net state of its nearest neighbors, i.e. the number in state $``\ensuremath{\uparrow}''$ minus the number in $``\ensuremath{\downarrow}.''$ Additionally, we show that all such arrays can perform quite general parallel operations. A broad range of physical systems and interactions is suitable: we highlight two examples.

arXiv:quant-ph/9909007•Physical Review A•Jan 18, 2000•83 citations

Minimal ancilla-controlled quantum computation

Timothy J Proctor, Erika Andersson, Viv M. Kendon

We characterise a model of universal quantum computation where the register (computational) qubits are controlled by ancillary qubits, using only a single fixed interaction between register and ancillary qubits. No additional access is required to the computational register and the dynamics of both the register and ancilla are unitary. This scheme is inspired by the measurement-based ancilla-driven quantum computation of Anders et al. [PRA 82, 020301(R), 2010], but does not require measurements of the ancillas, and in this respect is similar to the original gate based model of quantum computation. We consider what possible forms this ancilla-register interaction can take, with a proof that the interaction is necessarily locally equivalent to SWAP combined with an entangling controlled gate. We further show which Hamiltonians can create such interactions and discuss two examples; the two-qubit XY Hamiltonian and a particular case of the XXZ Hamiltonian. We then give an example of a simple, finite and fault tolerant gate set for universal quantum computation in this model.

•Jul 23, 2013•0 citations
Most quantum computer realizations require the ability to apply local fields and tune the couplings between qubits, in order to realize single bit and two bit gates which are necessary for universal quantum computation. We present a scheme to remove the necessity of switching the couplings between qubits for two bit gates, which are more costly in many cases. Our strategy is to compute with encoded qubits in and out of carefully designed interaction free subspaces analogous to decoherence free subspaces. We give two examples to show how universal quantum computation is realized in our scheme with local manipulations to physical qubits only, for both diagonal and off diagonal interactions.
We present a scheme to perform universal quantum computation using global control with an arbitrary subsystem dimension (not necessarily finite). The scheme is developed over a one spatial dimension NNN-element array, using only mirror-symmetric logical encoding, global pulses for single subsystem operations, uniform Ising-type interaction, and an all zero initial pure state. A mechanism using ancillary degrees of freedom for subsystem specific measurement is also presented.
Typical quantum computing schemes require transformations (gates) to be targeted at specific elements (qubits). In many physical systems, direct targeting is difficult to achieve; an alternative is to encode local gates into globally applied transformations. Here we demonstrate the minimum physical requirements for such an approach: a one-dimensional array composed of two alternating ``types'' of two-state system. Each system need be sensitive only to the net state of its nearest neighbors, i.e. the number in state $``\ensuremath{\uparrow}''$ minus the number in $``\ensuremath{\downarrow}.''$ Additionally, we show that all such arrays can perform quite general parallel operations. A broad range of physical systems and interactions is suitable: we highlight two examples.
We characterise a model of universal quantum computation where the register (computational) qubits are controlled by ancillary qubits, using only a single fixed interaction between register and ancillary qubits. No additional access is required to the computational register and the dynamics of both the register and ancilla are unitary. This scheme is inspired by the measurement-based ancilla-driven quantum computation of Anders et al. [PRA 82, 020301(R), 2010], but does not require measurements of the ancillas, and in this respect is similar to the original gate based model of quantum computation. We consider what possible forms this ancilla-register interaction can take, with a proof that the interaction is necessarily locally equivalent to SWAP combined with an entangling controlled gate. We further show which Hamiltonians can create such interactions and discuss two examples; the two-qubit XY Hamiltonian and a particular case of the XXZ Hamiltonian. We then give an example of a simple, finite and fault tolerant gate set for universal quantum computation in this model.