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AIP conference proceedings

Encoding qubits in a rotor

Amir Kalev, Philippe Raynal, Jun Suzuki, Berthold‐Georg Englert, Timothy C. Ralph, Ping Koy Lam

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We present a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the system. We also show, using quantum error‐correcting codes, how to protect the qubits against small errors in angular position and momentum which may affect the rotor. Finally, we propose a possible realization of qubits encoded in orbital angular momentum of a single photon.

DOI
10.1063/1.3630149

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We present a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the system. We also show, using quantum error‐correcting codes, how to protect the qubits against small errors in angular position and momentum which may affect the rotor. Finally, we propose a possible realization of qubits encoded in orbital angular momentum of a single photon.
We propose a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the system. We also show, using quantum error-correcting codes, how to protect the qubits against small errors in angular position and momentum which may affect the rotor. We then discuss the feasibility of this scheme and suggest several candidates for its implementation. The proposed scheme is immediately generalizable to qudits of any finite dimension.
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by distributing quantum information over six qubits which is the minimal number for the present task (see reference [1]). The encoding and error recovery operations for such a code are presented. It is noted that the present code is also a three-qubit quantum hidded information code over each qubit. In addition, an encoding scheme for hiding nnn-qubit quantum information over each qubit is proposed.
Abstract The stable operation of quantum computers will rely on error correction, in which single quantum bits of information are stored redundantly in the Hilbert space of a larger system. Such encoded qubits are commonly based on arrays of many physical qubits, but can also be realized using a single higher-dimensional quantum system, such as a harmonic oscillator1–3. In such a system, a powerful encoding has been devised based on periodically spaced superpositions of position eigenstates4–6. Various proposals have been made for realizing approximations to such states, but these have thus far remained out of reach7–11. Here we demonstrate such an encoded qubit using a superposition of displaced squeezed states of the harmonic motion of a single trapped 40Ca+ ion, controlling and measuring the mechanical oscillator through coupling to an ancillary internal-state qubit12. We prepare and reconstruct logical states with an average squared fidelity of 87.3 ± 0.7 per cent. Also, we demonstrate a universal logical single-qubit gate set, which we analyse using process tomography. For Pauli gates we reach process fidelities of about 97 per cent, whereas for continuous rotations we use gate teleportation and achieve fidelities of approximately 89 per cent. This control method opens a route for exploring continuous variable error correction as well as hybrid quantum information schemes using both discrete and continuous variables13. The code states also have direct applications in quantum sensing, allowing simultaneous measurement of small displacements in both position and momentum14, 15.
I present a new approach for designing quantum error-correcting codes guaranteeing a physically natural implementation of Clifford operations. Inspired by the scheme put forward by Gottesman, Kitaev, and Preskill for encoding a qubit in an oscillator in which Clifford operations may be performed via Gaussian unitaries, this approach yields new schemes for encoding a qubit in a large spin in which single-qubit Clifford operations may be performed via spatial rotations. I construct all possible examples of such codes, provide universal-gate-set implementations using quadratic angular-momentum Hamiltonians, and derive criteria for when these codes exactly correct physically relevant errors.
In , Gottesman, Kitaev, and Preskill described a method to encode a qubit in the continuous Hilbert space of an oscillator's position and momentum variables. This encoding provides a natural error-correction scheme that can correct errors due to small shifts of the position or momentum wave functions (i.e., use of the displacement operator). We present bounds on the size of correctable shift errors when both qubit and ancilla states may contain errors. We then use these bounds to constrain the quality of input qubit and ancilla states.
The orbital angular momentum carried by single photons represents a promising resource in the quantum information field. In this paper we report a series of optical schemes adopted for the manipulation of quantum states encoded in the orbital angular momentum exploiting the q-plate device. We further demonstrate the capability of generating hybrid entangled states as well as quantum states in dimension higher than two. Indeed we present the manipulation of ququart states encoded in the polarization and orbital angular momentum, which have been adopted for new quantum cryptographic protocols