Abstract Precise control of quantum systems is a cornerstone for realizing high-quality quantum technology such as quantum computing and quantum communication. The performance of control of systems often deteriorates due to systematic errors. In one-qubit control, the pulse length error (PLE) is a typical systematic error, which is often caused by deviation of the strength of the control field. A composite quantum gate (CQG) is a method for suppressing effects of such systematic errors at the cost of a long operation time. A longer operation time implies stronger decoherence, and thus a shorter CQG is preferable from the viewpoint of noise immunity. However, it has not been clear how short CQG can be implemented. This problem can be regarded as an optimization problem under constraints: optimizing the operation time while requiring the error robustness. In this paper, we find a lower bound on operation time of all CQGs with first-order robustness against the PLE, in which effects of the error are eliminated up to its first order. The derivation of this bound is based on a geometric property of robustness against the PLE. This can be used for search after high-performance CQGs.
Abstract Precise control of quantum systems is a cornerstone for realizing high-quality quantum technology such as quantum computing and quantum communication. The performance of control of systems often deteriorates due to systematic errors. In one-qubit control, the pulse length error (PLE) is a typical systematic error, which is often caused by deviation of the strength of the control field. A composite quantum gate (CQG) is a method for suppressing effects of such systematic errors at the cost of a long operation time. A longer operation time implies stronger decoherence, and thus a shorter CQG is preferable from the viewpoint of noise immunity. However, it has not been clear how short CQG can be implemented. This problem can be regarded as an optimization problem under constraints: optimizing the operation time while requiring the error robustness. In this paper, we find a lower bound on operation time of all CQGs with first-order robustness against the PLE, in which effects of the error are eliminated up to its first order. The derivation of this bound is based on a geometric property of robustness against the PLE. This can be used for search after high-performance CQGs.
Systematic errors hinder precise quantum control. Pulse length errors (PLEs) and off-resonance errors (OREs) are typical systematic errors that are encountered during one-qubit control. A composite pulse (CP) can help compensate for the effects of systematic errors during quantum operation. Several CPs that are robust against either PLE or ORE have been identified. However, few attempts have been made to construct CPs that are robust against both errors (bi-robust). We develop a novel bi-robust CP for one-qubit operations by modifying a PLE robust CP, which exhibits a shorter operation time than that of previously developed bi-robust CPs.
Abstract Precise control of quantum systems is one of the most important milestones for achieving practical quantum technologies, such as computation, sensing, and communication. Several factors deteriorate the control precision and thus their suppression is strongly demanded. One of the dominant factors is systematic errors, which are caused by discord between an expected parameter in control and its actual value. Error-robust control sequences, known as composite pulses, have been invented in the field of nuclear magnetic resonance (NMR). These sequences mainly focus on the suppression of errors in one-qubit control. The one-qubit control, which is the most fundamental in a wide range of quantum technologies, often suffers from detuning error. As there are many possible control sequences robust against the detuning error, it will practically be important to find ‘optimal’ robust controls with respect to several cost functions such as time required for operation, and pulse-area during the operation, which corresponds to the energy necessary for control. In this paper, we utilize the Pontryagin’s maximum principle (PMP), a tool for solving optimization problems under inequality constraints, to solve the time and pulse-area optimization problems. We analytically obtain pulse-area optimal controls robust against the detuning error. Moreover, we found that short-CORPSE, which is the shortest known composite pulse so far, is a probable candidate of the time optimal solution according to the PMP. We evaluate the performance of the pulse-area optimal robust control and the short-CORPSE, comparing with that of the direct operation.
Accurate quantum control is a key technology for realizing quantum information processing, such as quantum communication and quantum computation. In reality, a quantum state under control suffers from undesirable effects caused by systematic errors. A composite pulse (CP) is used to eliminate the effects of systematic errors during control. One-qubit control, which is the most fundamental in quantum control, is typically affected by two errors: pulse length error and off-resonance error (ORE). In this paper, we focus on ORE-robust CPs and systematically construct symmetric ones comprising three elementary operations in order to understand their properties. We find an infinitely large number of ORE-robust CPs, including the well-known CORPSE family, and evaluate their performance according to gate infidelity and operation time, both of which are important for the realization of accurate quantum control.
The precision of quantum operations is affected by unavoidable systematic errors. A composite pulse (CP), which has been well investigated in nuclear magnetic resonance (NMR), is a technique that suppresses the influence of systematic errors by replacing a single operation with a sequence of operations. In one-qubit operations, there are two typical systematic errors, Pulse Length Error (PLE) and Off Resonance Error (ORE). Recently, it was found that PLE robust CPs have a clear geometric property. In this study, we show that ORE robust CPs also have a simple geometric property, which is associated with trajectories on the Bloch sphere of the corresponding operations. We discuss the geometric property of ORE robust CPs using two examples.
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.
Due to its fast and robust characteristics, nonadiabatic geometric quantum computation with various optimized techniques has received much attention. However, these strategies either require precise pulse control or can only mitigate partial systematic errors, hindering their experimental development. Here, we propose a scheme for optimized composite nonadiabatic geometric quantum gates (OCNGQGs), which can further enhance the gate performance of the composite nonadiabatic geometric scheme. Specifically, by optimizing the path parameter, our scheme effectively resists systematic errors in both directions, i.e., Rabi frequency and detuning errors, while preserving the flexibility of pulse shapes. Numerical simulations demonstrate that our scheme offers superior gate robustness against these two types of errors compared to conventional schemes. Additionally, we propose to implement our scheme on superconducting transmon qubits, where the numerical results show the robustness of universal gates remaining evident within current technology. Therefore, our proposal provides a promising approach to achieve robust quantum gates for future scalable quantum computation.