Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

Energy needed to send a bit

Rolf W. Landauer

Published Jan 8, 1998• 15 citations
Publisher

Abstract

Earlier work demonstrated that quantum–mechanical machinery can be used to transmit classical bits without a minimal unavoidable energy cost per bit. It is shown that a very minor variation of the earlier proposal also works for qubits. In addition, some casual remarks about error control in quantum parallelism are provided.
DOI
10.1098/rspa.1998.0161

Related papers

Minimal Energy Requirements in Communication

Rolf W. Landauer

The literature describing the energy needs for a communications channel has been dominated by analyses of linear electromagnetic transmission, often without awareness that this is a special case. This case leads to the conclusion that an amount of energy equal to kTln 2, where kT is the thermal noise per unit bandwidth, is needed to transmit a bit, and more if quantized channels are used with photon energies hnu > kT. Alternative communication methods are proposed to show that there is no unavoidable minimal energy requirement per transmitted bit. These methods are invoked as part of an analysis of ultimate limits and not as practical procedures.

Science•Jun 28, 1996•191 citations

How many bits are needed to transmit a qubit reliably?

P. K. Aravind

Physics Letters A•May 1, 1998•2 citations

Quantum fingerprinting without a shared phase reference

Michał Lipka, Marcin Jarzyna, Michał Jachura +1 more

One of the standard communication complexity problems is deciding whether bit strings held by two separate parties Alice (A) and Bob (B) are equal or different. In the simultaneous message passing model, A and B send certain information to a Referee, who makes the decision. The overall goal is to minimize the amount of communication involved while not exceeding desired error probability. This is achieved by sending only fingerprints of the original n-bit strings. In the best classical protocols, these scale as O(√n) if A and B have no access to shared randomness [1]. The recently proposed [2] and demonstrated quantum fingerprinting [3], exploiting phase-modulated weak coherent pulses, provides O(log2n) scaling in the number of used qubits, but needs phase stability between A and B. Here we introduce and analyse a quantum fingerprinting protocol based on two-photon interference which does require a shared phase reference and works in scenarios when the global phase of transmitted signals becomes completely random. Interestingly, the performance of this protocol, quantified in terms of the Chernoff information [4], is enhanced through the use of non-classical single-photon states, even in the regime of high transmission loss.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2017•0 citations

Far Fewer Qubits Required for “Quantum Memory” Quantum Computers

Erika K. Carlson

Incorporating storage units for quantum information into quantum computers may allow researchers to build such devices with several orders of magnitude fewer qubits in their processors.

Physics•Sep 28, 2021•0 citations

Constant Overhead Quantum Fault-Tolerance with Quantum Expander Codes

Omar Fawzi, Antoine Grospellier, Anthony Leverrier

The threshold theorem is a seminal result in the field of quantum computing asserting that arbitrarily long quantum computations can be performed on a faulty quantum computer provided that the noise level is below some constant threshold. This remarkable result comes at the price of increasing the number of qubits (quantum bits) by a large factor that scales polylogarithmically with the size of the quantum computation we wish to realize. Minimizing the space overhead for fault-tolerant quantum computation is a pressing challenge that is crucial to benefit from the computational potential of quantum devices. In this paper, we study the asymptotic scaling of the space overhead needed for fault-tolerant quantum computation. We show that the polylogarithmic factor in the standard threshold theorem is in fact not needed and that there is a fault-tolerant construction that uses a number of qubits that is only a constant factor more than the number of qubits of the ideal computation. This result was conjectured by Gottesman who suggested to replace the concatenated codes from the standard threshold theorem by quantum error-correcting codes with a constant encoding rate. The main challenge was then to find an appropriate family of quantum codes together with an efficient classical decoding algorithm working even with a noisy syndrome. The efficiency constraint is crucial here: bear in mind that qubits are inherently noisy and that faults keep accumulating during the decoding process. The role of the decoder is therefore to keep the number of errors under control during the whole computation. On a technical level, our main contribution is the analysis of the SMALL-SET-FLIP decoding algorithm applied to the family of quantum expander codes . We show that it can be parallelized to run in constant time while correcting sufficiently many errors on both the qubits and the syndrome to keep the error under control. These tools can be seen as a quantum generalization of the BIT-FLIP algorithm applied to the (classical) expander codes of Sipser and Spielman.

arXiv:1808.03821•Annual Symposium on Foundations of Computer Science•Oct 1, 2018•110 citations

Error Rate Reduced for Scalable Quantum Technology

Mark Buchanan

A scalable system for controlling quantum bits demonstrates a very low error rate, which is essential for making practical devices.

Physics•Jul 24, 2023•0 citations
The literature describing the energy needs for a communications channel has been dominated by analyses of linear electromagnetic transmission, often without awareness that this is a special case. This case leads to the conclusion that an amount of energy equal to kTln 2, where kT is the thermal noise per unit bandwidth, is needed to transmit a bit, and more if quantized channels are used with photon energies hnu > kT. Alternative communication methods are proposed to show that there is no unavoidable minimal energy requirement per transmitted bit. These methods are invoked as part of an analysis of ultimate limits and not as practical procedures.
One of the standard communication complexity problems is deciding whether bit strings held by two separate parties Alice (A) and Bob (B) are equal or different. In the simultaneous message passing model, A and B send certain information to a Referee, who makes the decision. The overall goal is to minimize the amount of communication involved while not exceeding desired error probability. This is achieved by sending only fingerprints of the original n-bit strings. In the best classical protocols, these scale as O(√n) if A and B have no access to shared randomness [1]. The recently proposed [2] and demonstrated quantum fingerprinting [3], exploiting phase-modulated weak coherent pulses, provides O(log2n) scaling in the number of used qubits, but needs phase stability between A and B. Here we introduce and analyse a quantum fingerprinting protocol based on two-photon interference which does require a shared phase reference and works in scenarios when the global phase of transmitted signals becomes completely random. Interestingly, the performance of this protocol, quantified in terms of the Chernoff information [4], is enhanced through the use of non-classical single-photon states, even in the regime of high transmission loss.
The threshold theorem is a seminal result in the field of quantum computing asserting that arbitrarily long quantum computations can be performed on a faulty quantum computer provided that the noise level is below some constant threshold. This remarkable result comes at the price of increasing the number of qubits (quantum bits) by a large factor that scales polylogarithmically with the size of the quantum computation we wish to realize. Minimizing the space overhead for fault-tolerant quantum computation is a pressing challenge that is crucial to benefit from the computational potential of quantum devices. In this paper, we study the asymptotic scaling of the space overhead needed for fault-tolerant quantum computation. We show that the polylogarithmic factor in the standard threshold theorem is in fact not needed and that there is a fault-tolerant construction that uses a number of qubits that is only a constant factor more than the number of qubits of the ideal computation. This result was conjectured by Gottesman who suggested to replace the concatenated codes from the standard threshold theorem by quantum error-correcting codes with a constant encoding rate. The main challenge was then to find an appropriate family of quantum codes together with an efficient classical decoding algorithm working even with a noisy syndrome. The efficiency constraint is crucial here: bear in mind that qubits are inherently noisy and that faults keep accumulating during the decoding process. The role of the decoder is therefore to keep the number of errors under control during the whole computation. On a technical level, our main contribution is the analysis of the SMALL-SET-FLIP decoding algorithm applied to the family of quantum expander codes . We show that it can be parallelized to run in constant time while correcting sufficiently many errors on both the qubits and the syndrome to keep the error under control. These tools can be seen as a quantum generalization of the BIT-FLIP algorithm applied to the (classical) expander codes of Sipser and Spielman.