New class of quantum error-correcting codes for a bosonic mode

By M. Michael, M. Silveri, R. T. Brierley, Victor V. Albert, J. Salmilehto, Liang Jiang, Steven M. Girvin. 2016

455 citations recorded by the source corpus.

We construct a new class of quantum error-correcting codes for a bosonic mode which are advantageous for applications in quantum memories, communication, and scalable computation. These 'binomial quantum codes' are formed from a finite superposition of Fock states weighted with binomial coefficients. The binomial codes can exactly correct errors that are polynomial up to a specific degree in bosonic creation and annihilation operators, including amplitude damping and displacement noise as well as boson addition and dephasing errors. For realistic continuous-time dissipative evolution, the codes can perform approximate quantum error correction to any given order in the timestep between error detection measurements. We present an explicit approximate quantum error recovery operation based on projective measurements and unitary operations. The binomial codes are tailored for detecting boson loss and gain errors by means of measurements of the generalized number parity. We discuss optimization of the binomial codes and demonstrate that by relaxing the parity structure, codes with even lower unrecoverable error rates can be achieved. The binomial codes are related to existing two-mode bosonic codes but offer the advantage of requiring only a single bosonic mode to correct amplitude damping as well as the ability to correct other errors. Our codes are similar in spirit to 'cat codes' based on superpositions of the coherent states, but offer several advantages such as smaller mean number, exact rather than approximate orthonormality of the code words, and an explicit unitary operation for repumping energy into the bosonic mode. The binomial quantum codes are realizable with current superconducting circuit technology and they should prove useful in other quantum technologies, including bosonic quantum memories, photonic quantum communication, and optical-to-microwave up- and down-conversion.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/f799e8be2ba13ee62ce756f43b2feb5437d75b78

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Citations in the corpus

Quantum information processing and quantum optics with circuit quantum electrodynamics (2020, background): “Such brute-force approaches are viable up to around 1,000 qubits — a loose estimate — limited primarily by packaging, signal routing and the size of dilution refrig-a”
Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer (2020, background): “Examples of bosonic codes include GKP [20], dual-rail [3, 54], cat [55, 56], hypercat [57, 58], binomial [59], and general rotation-symmetric codes [60].”
Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code (2019, background): “[7] M.”
Quantum Simulators: Architectures and Opportunities (2019, background): “Quantum elements include linear resonant elements operating as cavities or photon (bosonic) reservoirs [80], and nonlinear elements operating as artificial multi-level atoms (qudits), twolevel atoms, spins, or qubits [79, 81].”
Fast universal control of an oscillator with weak dispersive coupling to a qubit (2021, methodology): “The binomial kitten code is the smallest binomial code for which the loss of a single photon is correctable [2, 5, 6, 13, 22], with logical states given by |+Z〉 = (|0〉+ |4〉) / √ 2 and |−Z〉 = |2〉.”
Performance and structure of single-mode bosonic codes (2017, methodology): “This form of error correction unfortunately does not correct products of dephasing and photon loss or gain errors, which are in principle errors against which the code can correct [23].”