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/0503151 · New Journal of Physics

A relational quantum computer using only two-qubit total spin measurement and an initial supply of highly mixed single-qubit states

Terry Rudolph, S. Virmani

Published Oct 27, 2005• 19 citations
arXivHTMLPDF

Abstract

We prove that universal quantum computation is possible using only (i) the physically natural measurement on two qubits which distinguishes the singlet from the triplet subspace and (ii) qubits prepared in almost any three different (potentially highly mixed) states. In some sense this measurement is a 'more universal' dynamical element than a universal two-qubit unitary gate, since the latter must be supplemented by measurement. Because of the rotational invariance of the measurement used, our scheme is robust to collective decoherence in a manner very different to previous proposals—in effect it is only ever sensitive to the relational properties of the qubits.

DOI
10.1088/1367-2630/7/1/228

Related papers

Relational quantum computing using only maximally mixed initial qubit states

Terry Rudolph, S. Virmani

We disprove the conjecture of [1], namely that it would require smarter authors to find a way of making the two-qubit singlet/triplet measurement quantum computationally universal given an ensemble of initial single qubit states with less than three linearly independent Bloch vectors. We show, in fact, that an initial ensemble of maximally mixed single qubits suffices.

•Jul 7, 2021•1 citation

The two-qubit singlet/triplet measurement is universal for quantum computing given only maximally-mixed initial states

Terry Rudolph, S. Virmani

Abstract In order to delineate which minimalistic physical primitives can enable the full power of universal quantum computing, it has been fruitful to consider various measurement based architectures which reduce or eliminate the use of coherent unitary evolution, and also involve operations that are physically natural. In this context previous works had shown that the triplet-singlet measurement of two qubit angular momentum (or equivalently two qubit exchange symmetry) yields the power of quantum computation given access to a few additional different single qubit states or gates. However, Freedman, Hastings and Shokrian-Zini1 recently proposed a remarkable conjecture, called the ‘STP=BQP’ conjecture, which states that the two-qubit singlet/triplet measurement is quantum computationally universal given only an initial ensemble of maximally mixed single qubits. In this work we prove this conjecture. This provides a method for quantum computing that is fully rotationally symmetric (i.e. reference frame independent), using primitives that are physically very-accessible, naturally resilient to certain forms of error, and provably the simplest possible.

arXiv:2107.03239•Nature Communications•Nov 28, 2023•3 citations

Symmetry Protected Quantum Computation

Michael Hartley Freedman, Matthew B. Hastings, Modjtaba Shokrian Zini

We consider a model of quantum computation using qubits where it is possible to measure whether a given pair are in a singlet (total spin 0 ) or triplet (total spin 1 ) state. The physical motivation is that we can do these measurements in a way that is protected against revealing other information so long as all terms in the Hamiltonian are SU(2) -invariant. We conjecture that this model is equivalent to BQP. Towards this goal, we show: (1) this model is capable of universal quantum computation with polylogarithmic overhead if it is supplemented by single qubit X and Z gates. (2) Without any additional gates, it is at least as powerful as the weak model of "permutational quantum computation" of Jordan [14, 18]. (3) With postselection, the model is equivalent to PostBQP.

arXiv:2105.04649•Quantum•Sep 28, 2021•9 citations

Universal quantum computation using exchange interactions and measurements of single- and two-spin observables

Lian-Ao Wu, Daniel A. Lidar

We show how to construct a universal set of quantum logic gates using control over exchange interactions and single- and two-spin measurements only. Single-spin unitary operations are teleported between neighboring spins instead of being executed directly, thus potentially eliminating a major difficulty in the construction of several of the most promising proposals for solid-state quantum computation, such as spin-coupled quantum dots, donor-atom nuclear spins in silicon, and electrons on helium. Contrary to previous proposals dealing with this difficulty, our scheme requires no encoding redundancy. We also discuss an application to superconducting phase qubits.

arXiv:quant-ph/0208118•Physical Review A•May 28, 2003•13 citations

Universal Quantum Computation with Spin- 1 / 2 Pairs and Heisenberg Exchange

Jeremy Levy

An efficient and intuitive framework for universal quantum computation is presented that uses pairs of spin-1/2 particles to form logical qubits and a single physical interaction, Heisenberg exchange, to produce all gate operations. Only two Heisenberg gate operations are required to produce a controlled pi-phase shift, compared to nineteen for exchange-only proposals employing three spins. Evolved from well-studied decoherence-free subspaces, this architecture inherits immunity from collective decoherence mechanisms. The simplicity and adaptability of this approach should make it attractive for spin-based quantum computing architectures.

arXiv:quant-ph/0101057•Physical Review Letters•Sep 17, 2002•407 citations

Decoherence-free universal quantum computation with symmetric qubit clusters

Christian Boudreault, Hichem Eleuch, Michael Hilke +1 more

One of the most challenging problems for the realization of a scalable quantum computer is to design a physical device that keeps the error rate for each quantum processing operation low. These errors can originate from the accuracy of quantum manipulation, such as the sweeping of a gate voltage in solid state qubits or the duration of a laser pulse in optical schemes. Errors also result from decoherence, which is often regarded as more crucial in the sense that it is inherent to the quantum system, being fundamentally a consequence of the coupling to the external environment. Grouping small collections of qubits into clusters with symmetries may serve to protect parts of the calculation from decoherence. In this work, we use 4-level cores with a straightforward generalization of discrete rotational symmetry, called $\omega$-rotation invariance, to encode pairs of coupled qubits and universal 2-qubit logical gates. We propose a scalable scheme for universal quantum computation where cores play the role of quantum-computational transistors, or \textit{quansistors} for short. Embedding in the environment, initialization and readout are achieved by tunnel-coupling the quansistor to leads. The external leads are explicitly considered and are assumed to be the main source of decoherence. We show that quansistors can be dynamically decoupled from the leads by tuning their internal parameters, giving them the versatility required to act as controllable quantum memory units. With this dynamical decoupling, logical operations within quansistors are also symmetry-protected from unbiased noise in their parameters. We identify technologies that could implement $\omega$-rotation invariance. Many of our results can be generalized to higher-level $\omega$-rotation-invariant systems, or adapted to clusters with other symmetries.

•Jun 1, 2021•0 citations
We prove that universal quantum computation is possible using only (i) the physically natural measurement on two qubits which distinguishes the singlet from the triplet subspace and (ii) qubits prepared in almost any three different (potentially highly mixed) states. In some sense this measurement is a 'more universal' dynamical element than a universal two-qubit unitary gate, since the latter must be supplemented by measurement. Because of the rotational invariance of the measurement used, our scheme is robust to collective decoherence in a manner very different to previous proposals—in effect it is only ever sensitive to the relational properties of the qubits.
Abstract In order to delineate which minimalistic physical primitives can enable the full power of universal quantum computing, it has been fruitful to consider various measurement based architectures which reduce or eliminate the use of coherent unitary evolution, and also involve operations that are physically natural. In this context previous works had shown that the triplet-singlet measurement of two qubit angular momentum (or equivalently two qubit exchange symmetry) yields the power of quantum computation given access to a few additional different single qubit states or gates. However, Freedman, Hastings and Shokrian-Zini1 recently proposed a remarkable conjecture, called the ‘STP=BQP’ conjecture, which states that the two-qubit singlet/triplet measurement is quantum computationally universal given only an initial ensemble of maximally mixed single qubits. In this work we prove this conjecture. This provides a method for quantum computing that is fully rotationally symmetric (i.e. reference frame independent), using primitives that are physically very-accessible, naturally resilient to certain forms of error, and provably the simplest possible.
We consider a model of quantum computation using qubits where it is possible to measure whether a given pair are in a singlet (total spin 0 ) or triplet (total spin 1 ) state. The physical motivation is that we can do these measurements in a way that is protected against revealing other information so long as all terms in the Hamiltonian are SU(2) -invariant. We conjecture that this model is equivalent to BQP. Towards this goal, we show: (1) this model is capable of universal quantum computation with polylogarithmic overhead if it is supplemented by single qubit X and Z gates. (2) Without any additional gates, it is at least as powerful as the weak model of "permutational quantum computation" of Jordan [14, 18]. (3) With postselection, the model is equivalent to PostBQP.
We show how to construct a universal set of quantum logic gates using control over exchange interactions and single- and two-spin measurements only. Single-spin unitary operations are teleported between neighboring spins instead of being executed directly, thus potentially eliminating a major difficulty in the construction of several of the most promising proposals for solid-state quantum computation, such as spin-coupled quantum dots, donor-atom nuclear spins in silicon, and electrons on helium. Contrary to previous proposals dealing with this difficulty, our scheme requires no encoding redundancy. We also discuss an application to superconducting phase qubits.
An efficient and intuitive framework for universal quantum computation is presented that uses pairs of spin-1/2 particles to form logical qubits and a single physical interaction, Heisenberg exchange, to produce all gate operations. Only two Heisenberg gate operations are required to produce a controlled pi-phase shift, compared to nineteen for exchange-only proposals employing three spins. Evolved from well-studied decoherence-free subspaces, this architecture inherits immunity from collective decoherence mechanisms. The simplicity and adaptability of this approach should make it attractive for spin-based quantum computing architectures.
One of the most challenging problems for the realization of a scalable quantum computer is to design a physical device that keeps the error rate for each quantum processing operation low. These errors can originate from the accuracy of quantum manipulation, such as the sweeping of a gate voltage in solid state qubits or the duration of a laser pulse in optical schemes. Errors also result from decoherence, which is often regarded as more crucial in the sense that it is inherent to the quantum system, being fundamentally a consequence of the coupling to the external environment. Grouping small collections of qubits into clusters with symmetries may serve to protect parts of the calculation from decoherence. In this work, we use 4-level cores with a straightforward generalization of discrete rotational symmetry, called ω\omegaω-rotation invariance, to encode pairs of coupled qubits and universal 2-qubit logical gates. We propose a scalable scheme for universal quantum computation where cores play the role of quantum-computational transistors, or \textit{quansistors} for short. Embedding in the environment, initialization and readout are achieved by tunnel-coupling the quansistor to leads. The external leads are explicitly considered and are assumed to be the main source of decoherence. We show that quansistors can be dynamically decoupled from the leads by tuning their internal parameters, giving them the versatility required to act as controllable quantum memory units. With this dynamical decoupling, logical operations within quansistors are also symmetry-protected from unbiased noise in their parameters. We identify technologies that could implement ω\omegaω-rotation invariance. Many of our results can be generalized to higher-level ω\omegaω-rotation-invariant systems, or adapted to clusters with other symmetries.