34 research outputs found
Channel-Optimized Quantum Error Correction
We develop a theory for finding quantum error correction (QEC) procedures
which are optimized for given noise channels. Our theory accounts for
uncertainties in the noise channel, against which our QEC procedures are
robust. We demonstrate via numerical examples that our optimized QEC procedures
always achieve a higher channel fidelity than the standard error correction
method, which is agnostic about the specifics of the channel. This demonstrates
the importance of channel characterization before QEC procedures are applied.
Our main novel finding is that in the setting of a known noise channel the
recovery ancillas are redundant for optimized quantum error correction. We show
this using a general rank minimization heuristic and supporting numerical
calculations. Therefore, one can further improve the fidelity by utilizing all
the available ancillas in the encoding block.Comment: 12 pages, 9 figure
Optimal control of two qubits via a single cavity drive in circuit quantum electrodynamics
Optimization of the fidelity of control operations is of critical importance
in the pursuit of fault-tolerant quantum computation. We apply optimal control
techniques to demonstrate that a single drive via the cavity in circuit quantum
electrodynamics can implement a high-fidelity two-qubit all-microwave gate that
directly entangles the qubits via the mutual qubit-cavity couplings. This is
performed by driving at one of the qubits' frequencies which generates a
conditional two-qubit gate, but will also generate other spurious interactions.
These optimal control techniques are used to find pulse shapes that can perform
this two-qubit gate with high fidelity, robust against errors in the system
parameters. The simulations were all performed using experimentally relevant
parameters and constraints.Comment: Final published versio
Robust Quantum Error Correction via Convex Optimization
We present a semidefinite program optimization approach to quantum error
correction that yields codes and recovery procedures that are robust against
significant variations in the noise channel. Our approach allows us to optimize
the encoding, recovery, or both, and is amenable to approximations that
significantly improve computational cost while retaining fidelity. We
illustrate our theory numerically for optimized 5-qubit codes, using the
standard [5,1,3] code as a benchmark. Our optimized encoding and recovery
yields fidelities that are uniformly higher by 1-2 orders of magnitude against
random unitary weight-2 errors compared to the [5,1,3] code with standard
recovery. We observe similar improvement for a 4-qubit decoherence-free
subspace code.Comment: 4 pages, including 3 figures. v2: new example