Physical Optimization of Quantum Error Correction Circuits

Abstract

Quantum error correcting codes have been developed to protect a quantum computer from decoherence due to a noisy environment. In this paper, we present two methods for optimizing the physical implementation of such error correction schemes. First, we discuss an optimal quantum circuit implementation of the smallest error-correcting code (the three bit code). Quantum circuits are physically implemented by serial pulses, i.e. by switching on and off external parameters in the Hamiltonian one after another. In contrast to this, we introduce a new parallel switching method that allows faster gate operation by switching all external parameters simultaneously. These two methods are applied to electron spins in coupled quantum dots subject to a Heisenberg coupling H=J(t) S_1*S_2 which can generate the universal quantum gate `square-root-of-swap'. Using parallel pulses, the encoding for three-bit quantum error correction in a Heisenberg system can be accelerated by a factor of about two. We point out that parallel switching has potential applications for arbitrary quantum computer architectures.

13 pages, 6 figures

Cited by in corpus (52)

• Quantum state engineering with Josephson-junction devices
• Circuit Quantum Electrodynamics
• Semiconductor Spin Qubits
• A geometric theory of non-local two-qubit operations
• Hilbert space structure of a solid state quantum computer: two-electron states of a double quantum dot artificial molecule
• Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations
• Quantum computing with spin cluster qubits
• Natural two-qubit gate for quantum computation using the XY interaction
• Control of Spin Dynamics of Excitons in Nanodots for Quantum Operations
• Scalable quantum computing with Josephson charge qubits
• Fast spin-orbit qubit in an indium antimonide nanowire
• Spintronics and Quantum Dots for Quantum Computing and Quantum Communication
• Spin interactions and switching in vertically tunnel-coupled quantum dots
• Thermal entanglement of spins in a nonuniform magnetic field
• High-fidelity quantum gates in Si/SiGe double quantum dots
• Quantum brachistochrone curves as geodesics: obtaining accurate control protocols for time-optimal quantum gates
• Efficient C-Phase gate for single-spin qubits in quantum dots
• Silicon quantum computation based on magnetic dipolar coupling
• Five Two-Qubit Gates Are Necessary for Implementing Toffoli Gate
• Spin-Orbit Coupling and Time-Reversal Symmetry in Quantum Gates
• Exact two-qubit universal quantum circuit
• Interplay between Zeeman Coupling and Swap Action in Spin-based Quantum Computer Models: Error Correction in Inhomogeneous Magnetic Fields
• Cluster States From Heisenberg Interaction
• Efficient quantum circuits for one-way quantum computing
• Two-electron quantum dots as scalable qubits
• Controllable exchange coupling between two singlet-triplet qubits
• Optimal multiqubit operations for Josephson charge qubits
• Theoretical study of nuclear spin polarization and depolarization in self-assembled quantum dots
• Analysis of quantum coherence in bismuth-doped silicon: a system of strongly coupled spin qubits
• Effect of an inhomogeneous external magnetic field on a quantum dot quantum computer
• Generation of quantum logic operations from physical Hamiltonians
• Efficient purification protocols using iSWAP gates in solid-state qubits
• Controlling qubit arrays with anisotropic XXZ Heisenberg interaction by acting on a single qubit
• Coupled superconducting spin qubits with spin-orbit interaction
• Universal quantum computing with correlated spin-charge states
• Entanglement purification without controlled-NOT gates by using the natural dynamics of spin chains
• Implementing Shor's algorithm on Josephson Charge Qubits
• An algorithm for solving unconstrained unitary quantum brachistochrone problems
• Combined Error Correction Techniques for Quantum Computing Architectures
• Encoded Universality in Physical Implementations of a Quantum Computer
• Controlled-NOT logic with nonresonant Josephson phase qubits
• Entanglement in a three spin system controlled by electric and magnetic field
• A general formulation of time-optimal quantum control and optimality of singular protocols
• Four-level systems and a universal quantum gate
• A spinless spin qubit
• Inferring superposition and entanglement from measurements in a single basis
• Dynamical topological quantum computation using spin pulse control in the Heisenberg model
• Two and four-level systems in magnetic fields restricted in time
• Performance Assessment of Resonantly Driven Silicon Two-Qubit Quantum Gate
• Spreading entanglement through pairwise exchange interactions
• A second quantized approach to the Rabi problem
• Unleashing Optimizations in Dynamic Circuits through Branch Expansion