arXiv:quant-ph/0209065

Minimum energy needed to perform a quantum logical gate

Julio R. Gea-Banacloche

Published Sep 9, 2002• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.quant-ph/0209065

Related papers

Energy requirements for quantum computation

Julio R. Gea-Banacloche

A lower bound on the amount of energy needed to carry out an elementary logical operation on a qubit system, with a given accuracy and in a given time, has been recently postulated. This paper is an attempt to formalize this bound and explore the conditions under which it may be expected to hold. For a specific, important case (namely, when the control system is a quantized electromagnetic field) it is shown how one can extend this result to a generally stronger constraint on the minimum energy density required, per pulse.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEMay 9, 20032 citations

Minimum Energy Requirements for Quantum Computation

Julio R. Gea-Banacloche

A lower bound on the amount of energy needed to carry out an elementary logical operation on a quantum computer, with a given accuracy and in a given time, is derived. The bound arises from the requirement that the controls used to manipulate the qubits, which ultimately are themselves quan-tum mechanical systems, must nonetheless be classical to a sufficiently good approximation; it is expected to hold under a wide variety of conditions, and independently of the nature of the physical systems used to encode the qubits. This could have important consequences for very large-scale quantum computations.

Physical Review LettersNov 4, 200274 citations

Lower bounds on the complexity of simulating quantum gates

Andrew M. Childs, Henry L. Haselgrove, Michael A. Nielsen

We give a simple proof of a formula for the minimal time required to simulate a two-qubit unitary operation using a fixed two-qubit Hamiltonian together with fast local unitaries. We also note that a related lower bound holds for arbitrary n-qubit gates.

arXiv:quant-ph/0307190Physical Review ANov 18, 200336 citations

Investigating the lower bound of minimum gate times using optimal control

Xiong-Peng Zhang, Bin Shao, Jian Zou

Motivated by a bound derived in a recent work [C. Arenz, B. Russell, D. Burgarth and H. Rabitz, New J. Phys. 19 (2017) 103015], we apply optimal control theory to the dynamics of qubit systems, with the goal of investigating the lower bound of minimum gate times. In practice, we not only need to reach the desired unitary gates but we need to do so in a reasonable time (below the typical decoherence time). Therefore, we employ the recently introduced lower bound to estimate the minimum gate time and resort to numerical gate optimization in order to study the tightness of the obtained bound and our findings verify the relationship between the internal Hamiltonian and the minimum evolution time remarkably well. Finally, we discuss both challenges and ways forward for obtaining the same efficacy under realistic conditions.

Modern Physics Letters BSep 7, 20180 citations

From quantum speed limits to energy-efficient quantum gates

Maxwell Aifer, Sebastian Deffner

Abstract While recent breakthroughs in quantum computing promise the nascence of the quantum information age, quantum states remain delicate to control. Moreover, the required energy budget for large scale quantum applications has only sparely been considered. Addressing either of these issues necessitates a careful study of the most energetically efficient implementation of elementary quantum operations. In the present analysis, we show that this optimal control problem can be solved within the powerful framework of quantum speed limits. To this end, we derive state-independent lower bounds on the energetic cost, from which we find the universally optimal implementation of unitary quantum gates, for both single and N -qubit operations.

arXiv:2202.01839New Journal of PhysicsApr 19, 202243 citations

Fundamental Energy Requirement of Reversible Quantum Operations

Giulio Chiribella, Yuxiang Yang, Renato Renner

Landauer’s principle asserts that any computation has an unavoidable energy cost that grows proportionally to its degree of logical irreversibility. But even a logically reversible operation, when run on a physical processor that operates on different energy levels, requires energy. Here we quantify this energy requirement, providing upper and lower bounds that coincide up to a constant factor. We derive these bounds from a general quantum resource-theoretic argument, which implies that the initial resource requirement for implementing a unitary operation within an error ε grows like 1/√ε times the amount of resource generated by the operation. Applying these results to quantum circuits, we find that their energy requirement can, by an appropriate design, be made independent of their time complexity.

Apr 1, 202129 citations