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Ancillary Qubits

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Yasuhiro Takahashi – One of the best experts on this subject based on the ideXlab platform.

  • Power of uninitialized Qubits in shallow quantum circuits
    Theoretical Computer Science, 2021
    Co-Authors: Yasuhiro Takahashi, Seiichiro Tani
    Abstract:

    Abstract We study uninitialized Qubits, whose initial state is arbitrary and unknown, in relation to the computational power of shallow quantum circuits. To do this, we consider uniform families of shallow quantum circuits with n input Qubits, O ( log ⁡ n ) initialized Ancillary Qubits, and n O ( 1 ) uninitialized Ancillary Qubits, where the input Qubits only act as control Qubits. We show that such a circuit with depth O ( ( log ⁡ n ) 2 ) can compute any symmetric Boolean function on n bits that is computable by a uniform family of polynomial-size classical circuits. Since it is unlikely that this can be done with only O ( log ⁡ n ) initialized Ancillary Qubits, our result provides evidence that the presence of uninitialized Ancillary Qubits increases the computational power of shallow quantum circuits with only O ( log ⁡ n ) initialized Ancillary Qubits. On the other hand, to understand the limitations of uninitialized Qubits, we focus on sub-logarithmic-depth quantum circuits and show the impossibility of computing the parity function on n bits.

  • STACS – Power of Uninitialized Qubits in Shallow Quantum Circuits
    , 2018
    Co-Authors: Yasuhiro Takahashi, Seiichiro Tani
    Abstract:

    We study the computational power of shallow quantum circuits with O(log n) initialized and n^{O(1)} uninitialized Ancillary Qubits, where n is the input length and the initial state of the uninitialized Ancillary Qubits is arbitrary. First, we show that such a circuit can compute any symmetric function on n bits that is classically computable in polynomial time. Then, we regard such a circuit as an oracle and show that a polynomial-time classical algorithm with the oracle can estimate the elements of any unitary matrix corresponding to a constant-depth quantum circuit on n Qubits. Since it seems unlikely that these tasks can be done with only O(log n) initialized Ancillary Qubits, our results give evidences that adding uninitialized Ancillary Qubits increases the computational power of shallow quantum circuits with only O(log n) initialized Ancillary Qubits. Lastly, to understand the limitations of uninitialized Ancillary Qubits, we focus on near-logarithmic-depth quantum circuits with them and show the impossibility of computing the parity function on n bits.

  • Shallow Quantum Circuits with Uninitialized Ancillary Qubits.
    arXiv: Quantum Physics, 2016
    Co-Authors: Yasuhiro Takahashi, Seiichiro Tani
    Abstract:

    We study the computational power of shallow quantum circuits with $n$ input Qubits, one output qubit, and two types of Ancillary Qubits: $O(\log n)$ initialized and $n^{O(1)}$ uninitialized Qubits. The initial state of the uninitialized Ancillary Qubits is arbitrary, but we have to return their state into the initial one at the end of the computation. First, we show that such circuits can compute various symmetric functions on $n$ bits, such as threshold functions. Then, we consider a polynomial-time probabilistic classical algorithm with an oracle that can perform such a circuit. We show that it can estimate the elements of any unitary matrix that can be implemented by a constant-depth quantum circuit on $n$ Qubits. Since it is not known whether these tasks can be done with only $O(\log n)$ initialized Ancillary Qubits, our results show the possibility that augmenting uninitialized Ancillary Qubits increases the computational power of shallow quantum circuits with only $O(\log n)$ initialized Ancillary Qubits. On the other hand, we give the cases where augmenting uninitialized Ancillary Qubits does not. More concretely, we consider near-logarithmic-depth quantum circuits with only $O(\log n)$ initialized Ancillary Qubits such that they include unbounded fan-out gates on a small number of Qubits and unbounded Toffoli gates. We show that they cannot compute the parity function on $n$ bits, even when they are augmented by $n^{O(1)}$ uninitialized Ancillary Qubits.

Prasanta K. Panigrahi – One of the best experts on this subject based on the ideXlab platform.

  • Demonstration of the no-hiding theorem on the 5-Qubit IBM quantum computer in a category-theoretic framework
    Quantum Information Processing, 2019
    Co-Authors: Amolak Ratan Kalra, Navya Gupta, Bikash K. Behera, Shiroman Prakash, Prasanta K. Panigrahi
    Abstract:

    The quantum no-hiding theorem, first proposed by Braunstein and Pati (Phys Rev Lett 98:080502, 2007 ), was verified experimentally by Samal et al. (Phys Rev Lett 186:080401, 2011 ) using NMR quantum processor. Till then, this fundamental test has not been explored in any other experimental architectures. Here, we demonstrate the above no-hiding theorem using the IBM 5Q quantum processor. Categorical algebra developed by Coecke and Duncan (New J Phys 13:043016, 2011 ) has been used for better visualization of the no-hiding theorem by analyzing the quantum circuit using the ZX calculus. The experimental results confirm the recovery of missing information by the application of local unitary operations on the Ancillary Qubits.

  • Demonstration of the No-Hiding Theorem on the 5 Qubit IBM Quantum Computer in a Category Theoretic Framework
    Quantum Information Processing, 2019
    Co-Authors: Amolak Ratan Kalra, Navya Gupta, Bikash K. Behera, Shiroman Prakash, Prasanta K. Panigrahi
    Abstract:

    Quantum no-Hiding theorem, first proposed by Braunstein and Pati [Phys. Rev. Lett. 98, 080502 (2007)], was verified experimentally by Samal et al. [Phys. Rev. Lett. 186, 080401 (2011)] using NMR quantum processor. Till then, this fundamental test has not been explored in any of the experimental architecture. Here, we demonstrate the above no-hiding theorem using the IBM 5Q quantum processor. Categorical algebra developed by Coecke and Duncan [New J. Phys. 13, 043016 (2011)] has been used for better visualization of the no-hiding theorem by analyzing the quantum circuit using the ZX calculus. The experimental results confirm the recovery of missing information by the application of local unitary operations on the Ancillary Qubits.

Seiichiro Tani – One of the best experts on this subject based on the ideXlab platform.

  • Power of uninitialized Qubits in shallow quantum circuits
    Theoretical Computer Science, 2021
    Co-Authors: Yasuhiro Takahashi, Seiichiro Tani
    Abstract:

    Abstract We study uninitialized Qubits, whose initial state is arbitrary and unknown, in relation to the computational power of shallow quantum circuits. To do this, we consider uniform families of shallow quantum circuits with n input Qubits, O ( log ⁡ n ) initialized Ancillary Qubits, and n O ( 1 ) uninitialized Ancillary Qubits, where the input Qubits only act as control Qubits. We show that such a circuit with depth O ( ( log ⁡ n ) 2 ) can compute any symmetric Boolean function on n bits that is computable by a uniform family of polynomial-size classical circuits. Since it is unlikely that this can be done with only O ( log ⁡ n ) initialized Ancillary Qubits, our result provides evidence that the presence of uninitialized Ancillary Qubits increases the computational power of shallow quantum circuits with only O ( log ⁡ n ) initialized Ancillary Qubits. On the other hand, to understand the limitations of uninitialized Qubits, we focus on sub-logarithmic-depth quantum circuits and show the impossibility of computing the parity function on n bits.

  • STACS – Power of Uninitialized Qubits in Shallow Quantum Circuits
    , 2018
    Co-Authors: Yasuhiro Takahashi, Seiichiro Tani
    Abstract:

    We study the computational power of shallow quantum circuits with O(log n) initialized and n^{O(1)} uninitialized Ancillary Qubits, where n is the input length and the initial state of the uninitialized Ancillary Qubits is arbitrary. First, we show that such a circuit can compute any symmetric function on n bits that is classically computable in polynomial time. Then, we regard such a circuit as an oracle and show that a polynomial-time classical algorithm with the oracle can estimate the elements of any unitary matrix corresponding to a constant-depth quantum circuit on n Qubits. Since it seems unlikely that these tasks can be done with only O(log n) initialized Ancillary Qubits, our results give evidences that adding uninitialized Ancillary Qubits increases the computational power of shallow quantum circuits with only O(log n) initialized Ancillary Qubits. Lastly, to understand the limitations of uninitialized Ancillary Qubits, we focus on near-logarithmic-depth quantum circuits with them and show the impossibility of computing the parity function on n bits.

  • Shallow Quantum Circuits with Uninitialized Ancillary Qubits.
    arXiv: Quantum Physics, 2016
    Co-Authors: Yasuhiro Takahashi, Seiichiro Tani
    Abstract:

    We study the computational power of shallow quantum circuits with $n$ input Qubits, one output qubit, and two types of Ancillary Qubits: $O(\log n)$ initialized and $n^{O(1)}$ uninitialized Qubits. The initial state of the uninitialized Ancillary Qubits is arbitrary, but we have to return their state into the initial one at the end of the computation. First, we show that such circuits can compute various symmetric functions on $n$ bits, such as threshold functions. Then, we consider a polynomial-time probabilistic classical algorithm with an oracle that can perform such a circuit. We show that it can estimate the elements of any unitary matrix that can be implemented by a constant-depth quantum circuit on $n$ Qubits. Since it is not known whether these tasks can be done with only $O(\log n)$ initialized Ancillary Qubits, our results show the possibility that augmenting uninitialized Ancillary Qubits increases the computational power of shallow quantum circuits with only $O(\log n)$ initialized Ancillary Qubits. On the other hand, we give the cases where augmenting uninitialized Ancillary Qubits does not. More concretely, we consider near-logarithmic-depth quantum circuits with only $O(\log n)$ initialized Ancillary Qubits such that they include unbounded fan-out gates on a small number of Qubits and unbounded Toffoli gates. We show that they cannot compute the parity function on $n$ bits, even when they are augmented by $n^{O(1)}$ uninitialized Ancillary Qubits.

Amolak Ratan Kalra – One of the best experts on this subject based on the ideXlab platform.

  • Demonstration of the no-hiding theorem on the 5-Qubit IBM quantum computer in a category-theoretic framework
    Quantum Information Processing, 2019
    Co-Authors: Amolak Ratan Kalra, Navya Gupta, Bikash K. Behera, Shiroman Prakash, Prasanta K. Panigrahi
    Abstract:

    The quantum no-hiding theorem, first proposed by Braunstein and Pati (Phys Rev Lett 98:080502, 2007 ), was verified experimentally by Samal et al. (Phys Rev Lett 186:080401, 2011 ) using NMR quantum processor. Till then, this fundamental test has not been explored in any other experimental architectures. Here, we demonstrate the above no-hiding theorem using the IBM 5Q quantum processor. Categorical algebra developed by Coecke and Duncan (New J Phys 13:043016, 2011 ) has been used for better visualization of the no-hiding theorem by analyzing the quantum circuit using the ZX calculus. The experimental results confirm the recovery of missing information by the application of local unitary operations on the Ancillary Qubits.

  • Demonstration of the No-Hiding Theorem on the 5 Qubit IBM Quantum Computer in a Category Theoretic Framework
    Quantum Information Processing, 2019
    Co-Authors: Amolak Ratan Kalra, Navya Gupta, Bikash K. Behera, Shiroman Prakash, Prasanta K. Panigrahi
    Abstract:

    Quantum no-Hiding theorem, first proposed by Braunstein and Pati [Phys. Rev. Lett. 98, 080502 (2007)], was verified experimentally by Samal et al. [Phys. Rev. Lett. 186, 080401 (2011)] using NMR quantum processor. Till then, this fundamental test has not been explored in any of the experimental architecture. Here, we demonstrate the above no-hiding theorem using the IBM 5Q quantum processor. Categorical algebra developed by Coecke and Duncan [New J. Phys. 13, 043016 (2011)] has been used for better visualization of the no-hiding theorem by analyzing the quantum circuit using the ZX calculus. The experimental results confirm the recovery of missing information by the application of local unitary operations on the Ancillary Qubits.

Gui-lu Long – One of the best experts on this subject based on the ideXlab platform.

  • Quantum simulation of quantum channels in nuclear magnetic resonance
    Physical Review A, 2017
    Co-Authors: Tao Xin, Enrique Solano, Shijie Wei, J. S. Pedernales, Gui-lu Long
    Abstract:

    We propose and experimentally demonstrate an efficient framework for the quantum simulation of quantum channels in NMR. Our approach relies on the suitable decomposition of non-unitary operators in a linear combination of $d$ unitary ones, which can be then experimentally implemented with the assistance of a number of Ancillary Qubits that grows logarithmically in $d$. As a proof-of-principle demonstration, we realize the quantum simulation of three quantum channels for a single-qubit: phase damping (PD), amplitude damping (AD), and depolarizing (DEP) channels. For these paradigmatic cases, we measure key features, such as the fidelity of the initial state and the associated von Neuman entropy for a qubit evolving through these channels. Our experiments are carried out using nuclear spins in a liquid sample and NMR control techniques.

  • Experimental simulation of quantum tunneling in small systems
    Scientific reports, 2013
    Co-Authors: Guanru Feng, Liang Hao, Fei Hao Zhang, Gui-lu Long
    Abstract:

    It is well known that quantum computers are superior to classical computers in efficiently simulating quantum systems. Here we report the first experimental simulation of quantum tunneling through potential barriers, a widespread phenomenon of a unique quantum nature, via NMR techniques. Our experiment is based on a digital particle simusimulation algorithm and requires very few spin-1/2 nuclei without the need of Ancillary Qubits. The occurrence of quantum tunneling through a barrier, together with the oscillation of the state in potential wells, are clearly observed through the experimental results. This experiment has clearly demonstrated the possibility to observe and study profound physical phenomena within even the reach of small quantum computers.