Masamitsu Bando

Concatenated Composite Pulses Compensating Simultaneous Systematic Errors

In NMR experiments and quantum computation, many pulse (quantum gate) sequences called the composite pulses, were developed to suppress one of two dominant errors; a pulse length error and an off-resonance error. We describe, in this paper, a general prescription to design a single-qubit concatenated composite pulse (CCCP) that is robust against two types of errors simultaneously. To this end, we introduce a new property, which is satisfied by some composite pulses and is sufficient to obtain a CCCP. Then we introduce a general method to design CCCPs with shorter execution time and less number of pulses.

Geometric aspects of composite pulses.

Unitary operations acting on a quantum system must be robust against systematic errors in control parameters for reliable quantum computing. Composite pulse technique in nuclear magnetic resonance realizes such a robust operation by employing a sequence of possibly poor-quality pulses. In this study, we demonstrate that two kinds of composite pulses—one compensates for a pulse length error in a one-qubit system and the other compensates for a J-coupling error in a two-qubit system—have a vanishing dynamical phase and thereby can be seen as geometric quantum gates, which implement unitary gates by the holonomy associated with dynamics of cyclic vectors defined in the text.

Designing robust unitary gates: Application to concatenated composite pulses

We propose a simple formalism to design unitary gates robust against given systematic errors. This formalism generalizes our previous observation [Y. Kondo and M. Bando, J. Phys. Soc. Jpn. 80, 054002 (2011)] that vanishing dynamical phase in some composite gates is essential to suppress pulse-length errors. By employing our formalism, we derive a composite unitary gate which can be seen as a concatenation of two known composite unitary operations. The obtained unitary gate has high fidelity over a wider range of error strengths compared to existing composite gates.

Minimal and robust composite two-qubit gates with Ising-type interaction

We construct a minimal robust controlled-NOT gate with an Ising-type interaction by which elementary two-qubit gates are implemented. It is robust against inaccuracy of the coupling strength and the obtained quantum circuits are constructed with the minimal number (N = 3) of elementary two-qubit gates and several one-qubit gates. It is noteworthy that all the robust circuits can be mapped to one-qubit circuits robust against a pulse length error. We also prove that a minimal robust SWAP gate cannot be constructed with N = 3 but requires N = 6 elementary two-qubit gates.

Geometric Quantum Gates, Composite Pulses, and Trotter–Suzuki Formulas

We show that all geometric quantum gates (GQGs in short), which are quantum gates only with geometric phases, are robust against control field strength errors. As examples of this observation, we show (1) how robust composite rf-pulses in NMR are geometrically constructed and (2) a composite rf-pulse based on Trotter–Suzuki Formulas is a GQG.

Implementation of holonomic quantum gates by an isospectral deformation of an Ising dimer chain

2particles; the qubit is a dimer. We find that the holonomic gates obtained are discrete but dense in the unitary group. Therefore an approximate gate for a desired one can be constructed with arbitrary accuracy. PACS numbers: 03.67.Lx, 03.65.Vf

Construction of arbitrary robust one-qubit operations using planar geometry

We show how to construct an arbitrary robust one-qubit unitary operation with a control Hamiltonian of

Applications of Concatenated Composite Pulses to NMR

{A}_{x}(t){\ensuremath{\sigma}}_{x}+{A}_{y}(t){\ensuremath{\sigma}}_{y}

COMPOSITE QUANTUM GATES FOR PRECISE QUANTUM CONTROL

, where

Planar Geometric Construction of Arbitrary Robust One-Qubit Operations

{\ensuremath{\sigma}}_{i}