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arXiv:quant-ph/0302198 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum computers and decoherence: exorcising the demon from the machine

Daniel A. Lidar, Lian-Ao Wu

Published May 9, 2003• 4 citations
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Abstract

Decoherence is the main obstacle to the realization of quantum computers. Until recently it was thought that quantum error correcting codes are the only complete solution to the decoherence problem. Here we present an alternative that is based on a combination of a decoherence-free subspace encoding and the application of strong and fast pulses: ``encoded recoupling and decoupling'' (ERD). This alternative has the advantage of lower encoding overhead (as few as two physical qubits per logical qubit suffice), and direct application to a number of promising proposals for the experimental realization of quantum computers.

DOI
10.1117/12.488754

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Decoherence is the main obstacle to the realization of quantum computers. Until recently it was thought that quantum error correcting codes are the only complete solution to the decoherence problem. Here we present an alternative that is based on a combination of a decoherence-free subspace encoding and the application of strong and fast pulses: ``encoded recoupling and decoupling'' (ERD). This alternative has the advantage of lower encoding overhead (as few as two physical qubits per logical qubit suffice), and direct application to a number of promising proposals for the experimental realization of quantum computers.
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing or eliminating errors, but not one, alone, will serve as a panacea. One must therefore take advantage of the strength of each of these techniques so that we may extend the coherence times of the quantum systems and create more reliable computing devices. To this end we give a general strategy for using dynamical decoupling operations on encoded subspaces. These encodings may be of any form; of particular importance are decoherence-free subspaces and quantum error correction codes. We then give means for empirically determining an appropriate set of dynamical decoupling operations for a given experiment. Using these techniques, we then propose a comprehensive encoding solution to many of the problems of quantum computing proposals which use exchange-type interactions. This uses a decoherence-free subspace and an efficient set of dynamical decoupling operations. It also addresses the problem of controllability in solid-state quantum dot devices.
A recently developed theory for eliminating decoherence and design constraints in quantum computers, ``encoded recoupling and decoupling,'' is shown to be fully compatible with a promising proposal for an architecture enabling scalable ion-trap quantum computation [D. Kielpinski et al., Nature (London) 417, 709 (2002)]. Logical qubits are encoded into pairs of ions. Logic gates are implemented using the S\o{}rensen-M\o{}lmer (SM) scheme applied to pairs of ions at a time. The encoding offers continuous protection against collective dephasing. Decoupling pulses, that are also implemented using the SM scheme directly to the encoded qubits, are capable of further reducing various other sources of qubit decoherence, such as due to differential dephasing and due to decohered vibrational modes. The feasibility of using the relatively slow SM pulses in a decoupling scheme quenching the latter source of decoherence follows from the observed 1/f1/f1/f spectrum of the vibrational bath.
Proposals for scalable quantum computing devices suffer not only from decoherence due to the interaction with their environment, but also from severe engineering constraints. Here we introduce a practical solution to these major concerns, addressing solid-state proposals in particular. Decoherence is first reduced by encoding a logical qubit into two qubits, then completely eliminated by an efficient set of decoupling pulse sequences. The same encoding removes the need for single-qubit operations, which pose a difficult design constraint. We further show how the dominant decoherence processes can be identified empirically, in order to optimize the decoupling pulses.
A quantum computer is an information processing systems that utilizes invertible logic elements to perform reversible logic operations. It can also perform irreversible logic operations. Thus, in principle, it can compute the information transformation rule of any physical system for which the rules are known. A quantum computer can be designed to perform parallel computation on a massive scale, and therefore can have fast execution time. The basic structure of a quantum computer includes 1) a quantum register, or a configuration of quantum-mechanical energy states to store quantum bits (qubits) of information, 2) a quantum processor designed to induce quantum mechanical interactions between any arbitrary pair of qubits to perform a specified logic operations. 3) a quantum bus or network for transferring qubits from the registers to the processor and vice versa, and 4) a physical mechanisms for non-destructive measurements on the qubits. Quantum mechanical systems with the potential for realizing quantum computers include ion-trap quantum computers, cavity quantum electrodynamics quantum computers, photon-trap quantum computers, nuclear magnetic resonance quantum computers, and superconducting quantum computers. Decoherence [1 ,2] possesses the greatest challenge to the practical realization of quantum computers, because it causes the collapse of the quantum superposition states that contain the vital results of qubit manipulations. Decoherence processes are measurement-induced, noise-induced, and environment-induced [3] . Schemes to correct or circumvent the detrimental effects of decoherence in quantum processors fall into active error-correction schemes, and passive error-correction schemes [4]. Active error-correction schemes are designed to detect and correct for errors during computation. Algorithmic fault-tolerant computing [5, 6] is the most promising active-error correction scheme. In fault-tolerant computing, ancillary qubits are encoded into data blocks of the quantum registers. They are then used to detect errors. Once detected appropriate error-correction algorithms are then employed to rectify the errors. The implementation of fault-tolerant quantum computing has been hampered by the lack of practical universal set of quantum gates that can process an encoded data without propagating or introducing additional errors. Passive-error correction schemes [7] attempt to finding Hilbert subspaces that are intrinsically free of decoherence effects [8]. The key to quantum computing in such a decoherence-free subspace is the identification of mechanisms that can effect quantum mechanical interactions between the decoherence-free states without taking the system out of the decoherence-free environment. The challenge is to identify and employ physical processes that can achieve these goals.
A method for quantum computation in the presence of spontaneous emission is proposed. The method combines strong and fast (dynamical decoupling) pulses and a quantum error correcting code that encodes n logical qubits into only n+1n+1n+1 physical qubits. Universal, fault-tolerant, quantum computation is shown to be possible in this scheme using Hamiltonians relevant to a range of promising proposals for the physical implementation of quantum computers.