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

International Journal of Quantum Information

QUANTUM PRECISION LIMITS FOR ANY IMPLEMENTATION OF SINGLE QUBIT GATES UNDER CONSERVATION LAWS

Tokishiro Karasawa, Masanao Ozawa, Julio R. Gea-Banacloche, Kae Nemoto

Published Jul 1, 2008• 0 citations
Publisher

Abstract

A quantum gate is implemented by control interactions between qubits and their ancilla system. It has been shown that the control interactions have possibilities to induce the dynamical decoherence on the qubits if an additive conservation law is assumed in the interactions and the ancilla system is finite. This decoherece put the precision limit on the gate, which cannot be removed from the qubit by optimizing the interaction and the initialization of the ancilla system. In this paper, we give the outline of investigating the precision limit which is formulated by the lower bound of the gate infidelity, one minus the squared fidelity, for an arbitrary self-adjoint gate on a single qubit. We show rigorous lower bounds in terms of the variance of the conserved quantity and a simple geometrical relation between the conservation law to be assumed and the gates to be implemented. We also comment on another approach to provide the precision limit for an arbitrary single qubit gate under a conservation law.

DOI
10.1142/s0219749908003980

Related papers

Gate fidelity of arbitrary single-qubit gates constrained by conservation laws

Tokishiro Karasawa, Julio R. Gea-Banacloche, Masanao Ozawa

Recent investigations show that conservation laws limit the accuracy of gate operations in quantum computing. The inevitable error under the angular momentum conservation law has been evaluated so far for the CNOT, Hadamard and NOT gates for spin-1/2 qubits, while the SWAP gate has no constraint. Here, we extend the above results to general single-qubit gates. We obtain an upper bound of the gate fidelity of arbitrary single-qubit gates implemented under arbitrary conservation laws, determined by the geometry of the conservation law and the gate operation on the Bloch sphere as well as the size of the ancilla.

arXiv:0809.3095•Journal of Physics A Mathematical and Theoretical•May 14, 2009•26 citations

Conservation-law-induced quantum limits for physical realizations of the quantum NOT gate

Tokishiro Karasawa, Masanao Ozawa

In recent investigations, it has been found that conservation laws generally lead to precision limits on quantum computing. Lower bounds of the error probability have been obtained for various logic operations from the commutation relation between the noise operator and the conserved quantity or from the recently developed universal uncertainty principle for the noise-disturbance trade-off in general measurements. However, the problem of obtaining the precision limit to realizing the quantum NOT gate has eluded a solution from these approaches. Here, we develop a method for this problem based on analyzing the trace distance between the output state from the realization under consideration and the one from the ideal gate. Using the mathematical apparatus of orthogonal polynomials, we obtain a general lower bound on the error probability for the realization of the quantum NOT gate in terms of the number of qubits in the control system under conservation of the total angular momentum of the computational qubit plus the control system along the direction used to encode the computational basis. The lower bound turns out to be more stringent than one might expect from previous results. Our method is expected to lead to more accurate estimates for physical realizations of various types of quantum computations under conservation laws and to contribute to related problems such as the accuracy of programmable quantum processors.

arXiv:0705.1880•Physical Review A•Mar 19, 2007•20 citations

UNCERTAINTY PRINCIPLE FOR QUANTUM INSTRUMENTS AND COMPUTING

Masanao Ozawa

The notion of quantum instruments is formalized as statistical equivalence classes of all the possible quantum measurements and mathematically characterized as normalized completely positive map valued measures under naturally acceptable axioms. Recently, universally valid uncertainty relations have been established to set a precision limit for any instruments given a disturbance constraint in a form more general than the one originally proposed by Heisenberg. One of them leads to a quantitative generalization of the Wigner–Araki–Yanase theorem on the precision limit of measurements under conservation laws. Applying this, a rigorous lower bound is obtained for the gate error probability of physical implementations of Hadamard gates on a standard qubit of a spin 1/2 system by interactions with control fields or ancilla systems obeying the angular momentum conservation law.

arXiv:quant-ph/0310071•International Journal of Quantum Information•Dec 1, 2003•42 citations

Conservative Quantum Computing

Masanao Ozawa

The Wigner-Araki-Yanase theorem shows that conservation laws limit the accuracy of measurement. Here, we generalize the argument to show that conservation laws limit the accuracy of quantum logic operations. A rigorous lower bound is obtained of the error probability of any physical realization of the controlled-NOT gate under the constraint that the computational basis is represented by a component of spin, and that physical implementations obey the angular momentum conservation law. The lower bound is shown to be inversely proportional to the number of ancilla qubits or the strength of the external control field.

arXiv:quant-ph/0112179•Physical Review Letters•Jul 16, 2002•78 citations

Wigner-Araki-Yanase theorem and the realizability of quantum computing (Mathematical Study of Quantum Dynamical Systems and Its Application to Quantum Computer)

Masanao Ozawa

The Wigner-Araki-Yanase theorem shows that conservation laws limit the accuracy of measurement.Here, we generalize the argument to show that conservation laws limit the accuracy of quantum logic operations.A rigorous lower bound is obtained of the error probability of any physical realization of the controlled-NOT gate under the constraint that the computational basis is represented by a component of spin and that physical implementations obey the angular momentum conservation law.The lower bound is shown to be inversely proportional to the number of ancilla qubits or the strength of the external control field.

数理解析研究所講究録•Jan 1, 2004•0 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
A quantum gate is implemented by control interactions between qubits and their ancilla system. It has been shown that the control interactions have possibilities to induce the dynamical decoherence on the qubits if an additive conservation law is assumed in the interactions and the ancilla system is finite. This decoherece put the precision limit on the gate, which cannot be removed from the qubit by optimizing the interaction and the initialization of the ancilla system. In this paper, we give the outline of investigating the precision limit which is formulated by the lower bound of the gate infidelity, one minus the squared fidelity, for an arbitrary self-adjoint gate on a single qubit. We show rigorous lower bounds in terms of the variance of the conserved quantity and a simple geometrical relation between the conservation law to be assumed and the gates to be implemented. We also comment on another approach to provide the precision limit for an arbitrary single qubit gate under a conservation law.
Recent investigations show that conservation laws limit the accuracy of gate operations in quantum computing. The inevitable error under the angular momentum conservation law has been evaluated so far for the CNOT, Hadamard and NOT gates for spin-1/2 qubits, while the SWAP gate has no constraint. Here, we extend the above results to general single-qubit gates. We obtain an upper bound of the gate fidelity of arbitrary single-qubit gates implemented under arbitrary conservation laws, determined by the geometry of the conservation law and the gate operation on the Bloch sphere as well as the size of the ancilla.
In recent investigations, it has been found that conservation laws generally lead to precision limits on quantum computing. Lower bounds of the error probability have been obtained for various logic operations from the commutation relation between the noise operator and the conserved quantity or from the recently developed universal uncertainty principle for the noise-disturbance trade-off in general measurements. However, the problem of obtaining the precision limit to realizing the quantum NOT gate has eluded a solution from these approaches. Here, we develop a method for this problem based on analyzing the trace distance between the output state from the realization under consideration and the one from the ideal gate. Using the mathematical apparatus of orthogonal polynomials, we obtain a general lower bound on the error probability for the realization of the quantum NOT gate in terms of the number of qubits in the control system under conservation of the total angular momentum of the computational qubit plus the control system along the direction used to encode the computational basis. The lower bound turns out to be more stringent than one might expect from previous results. Our method is expected to lead to more accurate estimates for physical realizations of various types of quantum computations under conservation laws and to contribute to related problems such as the accuracy of programmable quantum processors.
The notion of quantum instruments is formalized as statistical equivalence classes of all the possible quantum measurements and mathematically characterized as normalized completely positive map valued measures under naturally acceptable axioms. Recently, universally valid uncertainty relations have been established to set a precision limit for any instruments given a disturbance constraint in a form more general than the one originally proposed by Heisenberg. One of them leads to a quantitative generalization of the Wigner–Araki–Yanase theorem on the precision limit of measurements under conservation laws. Applying this, a rigorous lower bound is obtained for the gate error probability of physical implementations of Hadamard gates on a standard qubit of a spin 1/2 system by interactions with control fields or ancilla systems obeying the angular momentum conservation law.
The Wigner-Araki-Yanase theorem shows that conservation laws limit the accuracy of measurement. Here, we generalize the argument to show that conservation laws limit the accuracy of quantum logic operations. A rigorous lower bound is obtained of the error probability of any physical realization of the controlled-NOT gate under the constraint that the computational basis is represented by a component of spin, and that physical implementations obey the angular momentum conservation law. The lower bound is shown to be inversely proportional to the number of ancilla qubits or the strength of the external control field.
The Wigner-Araki-Yanase theorem shows that conservation laws limit the accuracy of measurement.Here, we generalize the argument to show that conservation laws limit the accuracy of quantum logic operations.A rigorous lower bound is obtained of the error probability of any physical realization of the controlled-NOT gate under the constraint that the computational basis is represented by a component of spin and that physical implementations obey the angular momentum conservation law.The lower bound is shown to be inversely proportional to the number of ancilla qubits or the strength of the external control field.
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.