Abstract
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.
Highlights
Continuous-variable quantum information processing using bosonic modes [1,2,3,4,5,6,7,8] offers an attractive alternative to two-level qubits
We have presented a new class of “binomial” quantum error-correction codes for a bosonic mode
By constructing an explicit recovery process, we demonstrated that the binomial codes are protected to given order in the time step against continuous dissipative evolution under loss, gain, and dephasing errors
Summary
Continuous-variable quantum information processing using bosonic modes [1,2,3,4,5,6,7,8] offers an attractive alternative to two-level qubits. II, we introduce quantum error correction against discrete photon loss, photon gain, and dephasing errors through simple bosonic single-mode codes Ð4Þ wwanhodircdjhsEin↓srieal1⁄4astueðdpj3eritpo−ostphiteiffi3offi jnd9eioÞpf=ht2ah.seiTnoghriegjiEonnn↑alilyw1⁄4woðradpysffi3tffiaojn0dide−thteejc6etirÞtr=ho2er dephasing error is the logical word btoasims aPkeWp1⁄4rojPecσtijvWe measurements σihWσj, and if into the answer is negative and no photon loss errors were detected, the original state is recovered by making a unitary operation performing a state transfer jEnσi ↔ jWσi Such complex operations applied to a cavity-ancilla qubit system are technically feasible [41,42,43,44]. After the detection of an error, the original state is recovered by a unitary operation performing a state transfer between the subspaces of the error and logical code words
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
