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

arXiv:2211.00777

An improvement on the versatility of secure multi-party quantum computation protocol: exploitation of triorthogonal quantum error-correcting codes

Petr A. Mishchenko, Keita Xagawa

Published Nov 1, 2022• 0 citations
arXivHTMLPDF

Abstract

Secure multi-party quantum computation (MPQC) protocol is a versatile tool that enables error-free distributed quantum computation to a group of $n$ mutually distrustful quantum nodes even when some of the quantum nodes do not follow the instructions of the protocol honestly. However, in case of the MPQC protocols built on top of the quantum error correction technique, the versatility is significantly affected by the fact that one has to choose a particular quantum error-correcting code (QECC), which immediately applies a constraint on the number of quantum nodes $n$. Therefore, in this talk, we suggest a modified MPQC protocol based on triorthogonal QECCs which applies significantly less constraint on the number of quantum nodes $n$ if compared to the previously suggested MPQC protocol based on triply-even QECCs. Especially, the variety of available options in the region of a small number of quantum nodes $n$ becomes important in the noisy intermediate-scale quantum (NISQ) era.

DOI
10.48550/arxiv.2211.00777

Related papers

Secure multiparty quantum computation protocol for quantum circuits: The exploitation of triply even quantum error-correcting codes

Petr A. Mishchenko, Keita Xagawa

Secure multiparty quantum computation (MPQC) protocol is a cryptographic primitive allowing error-free distributed quantum computation to a group of $n$ mutually distrustful quantum nodes even when some quantum nodes disobey the instructions of the protocol. Here we suggest a modified MPQC protocol that adopts unconventional quantum error-correcting codes and as a consequence reduces the number of qubits required for the protocol execution. In particular, the replacement of the self-dual Calderbank-Shor-Steane quantum error-correcting codes with triply even ones permits us to avoid the previously indispensable but resource-intensive procedure of the ``magic-state'' verification. Besides, since every extra qubit reduces the credibility of physical devices, our suggestion makes the MPQC protocol more accessible for the near-future technology by reducing the number of necessary qubits per quantum node from ${n}^{2}+\mathrm{\ensuremath{\Theta}}(r)n$, where $r$ is the security parameter, to ${n}^{2}+3n$.

arXiv:2206.04871•Physical Review A•Aug 28, 2024•1 citation

On secret sharing-based classical and quantum multi-party computation

J.G. Hölting

Secure multi-party computation (MPC) is a cryptographic primitive that lets a num- ber N of mutually distrustful parties compute a function f (x1, . . . , xN ) on their private inputs xi such that at the end of the MPC protocol, each honest party obtains the func- tion’s correct output and no adversary controlling a certain subset of parties learns any- thing about the honest parties’ inputs beyond what can be inferred from the function’s output value. In 2002, [Smi01] and [CGS02] introduced the notion of multi-party quan- tum computation (MPQC) in which arbitrary quantum circuits can be evaluated in a distributed manner, secure against a quantum adversary. Few protocols for MPQC are known. We present a fundamental study of the building blocks of MPC and MPQC in the information-theoretic setting with a focus on protocols built on top of (quantum) se- cret sharing schemes. In particular, we point out structural similarities and differences and compile an extensive list of theoretical feasibility results for the maximum number of corrupted parties within classical and quantum secret sharing and MPC protocols.

•Jan 1, 2020•0 citations

Secure multiparty quantum computation with (only) a strict honest majority

Michael Ben-Or, Claude Crépeau, Daniel Gottesman +2 more

Secret sharing and multiparty computation (also called “secure function evaluation”) are fundamental primitives in modern cryptography, allowing a group of mutually distrustful players to perform correct, distributed computations under the sole assumption that some number of them will follow the protocol honestly. This paper investigates how much trust is necessary – that is, how many players must remain honest – in order for distributed quantum computations to be possible. We present a verifiable quantum secret sharing (VQSS) protocol, and a general secure multiparty quantum computation (MPQC) protocol, which can tolerate any ⌊ n−1 2 ⌋ cheaters among n players. Previous protocols for these tasks tolerated ⌊ n−1 n−1 4 ⌋ and ⌊ 6 ⌋ cheaters, respectively. The threshold we achieve is tight — even in the classical case, “fair ” multiparty computation is not possible if any set of n/2 players can cheat. Our protocols rely on approximate quantum errorcorrecting codes, which can tolerate a larger fraction of errors than traditional, exact codes. We introduce new families of authentication schemes and approximate codes tailored to the needs of our protocols, as well as new state purification techniques along the lines of those used in fault-tolerant quantum circuits.

•Jan 1, 2008•83 citations

Secure Multiparty Quantum Computation with (Only) a Strict Honest Majority

Michael Ben-Or, Claude Crépeau, Daniel Gottesman +2 more

Secret sharing and multiparty computation (also called "secure function evaluation") are fundamental primitives in modern cryptography, allowing a group of mutually distrustful players to perform correct, distributed computations under the sole assumption that some number of them will follow the protocol honestly. This paper investigates how much trust is necessary -- that is, how many players must remain honest -- in order for distributed quantum computations to be possible. We present a verifiable quantum secret sharing (VQSS) protocol, and a general secure multiparty quantum computation (MPQC) protocol, which can tolerate any \left[ {\frac{{n - 1}} {2}} \right] cheaters among n players. Previous protocols for these tasks tolerated \left[ {\frac{{n - 1}} {4}} \right] and \left[ {\frac{{n - 1}} {6}} \right] cheaters, respectively. The threshold we achieve is tight -- even in the classical case, "fair" multiparty computation is not possible if any set of n/2 players can cheat. Our protocols rely on approximate quantum errorcorrecting codes, which can tolerate a larger fraction of errors than traditional, exact codes. We introduce new families of authentication schemes and approximate codes tailored to the needs of our protocols, as well as new state purification techniques along the lines of those used in faulttolerant quantum circuits.

arXiv:0801.1544•Annual Symposium on Foundations of Computer Science•Jan 1, 2006•89 citations

Delegating Multi-Party Quantum Computations vs. Dishonest Majority in Two Quantum Rounds

Theodoros Kapourniotis, Elham Kashefi, Luka Music +1 more

Multi-Party Quantum Computation (MPQC) has attracted a lot of attention as a potential killer-app for quantum networks through it's ability to preserve privacy and integrity of the highly valuable computations they would enable. Contributing to the latest challenges in this field, we present a composable protocol achieving blindness and verifiability even in the case of a single honest client. The security of our protocol is reduced, in an information-theoretically secure way, to that of a classical composable Secure Multi-Party Computation (SMPC) used to coordinate the various parties. Our scheme thus provides a statistically secure upgrade of such classical scheme to a quantum one with the same level of security. In addition, (i) the clients can delegate their computation to a powerful fully fault-tolerant server and only need to perform single qubit operations to unlock the full potential of multi-party quantum computation; (ii) the amount of quantum communication with the server is reduced to sending quantum states at the beginning of the computation and receiving the output states at the end, which is optimal and removes the need for interactive quantum communication; and (iii) it has a low constant multiplicative qubit overhead compared to the single-client delegated protocol it is built upon. The main technical ingredient of our paper is the bootstraping of the MPQC construction by Double Blind Quantum Computation, a new composable resource for blind multiparty quantum computation, that demonstrates the surprising fact that the full protocol does not require verifiability of all components to achieve security.

arXiv:2102.12949•Feb 25, 2021•3 citations

Secure multiparty quantum computation with few qubits

Victoria Lipińska, Jérémy Ribeiro, Stephanie Wehner

We consider the task of secure multiparty distributed quantum computation on a quantum network. We propose a protocol based on quantum error correction which reduces the number of necessary qubits. That is, each of the $n$ nodes in our protocol requires an operational workspace of ${n}^{2}+4n$ qubits, as opposed to the previously shown $\mathrm{\ensuremath{\Omega}}\left(({n}^{3}+{n}^{2}{s}^{2})logn\right)$ qubits, where $s$ is a security parameter. Additionally, we reduce the communication complexity by a factor of $O({n}^{3}log(n))$ qubits per node compared to existing protocols. To achieve universal computation, we develop a distributed procedure for verifying magic states, which allows us to apply distributed gate teleportation and which may be of independent interest. We showcase our protocol in a small example for a seven-node network.

arXiv:2004.10486•Physical Review A•Aug 7, 2020•16 citations
Secure multi-party quantum computation (MPQC) protocol is a versatile tool that enables error-free distributed quantum computation to a group of nnn mutually distrustful quantum nodes even when some of the quantum nodes do not follow the instructions of the protocol honestly. However, in case of the MPQC protocols built on top of the quantum error correction technique, the versatility is significantly affected by the fact that one has to choose a particular quantum error-correcting code (QECC), which immediately applies a constraint on the number of quantum nodes nnn. Therefore, in this talk, we suggest a modified MPQC protocol based on triorthogonal QECCs which applies significantly less constraint on the number of quantum nodes nnn if compared to the previously suggested MPQC protocol based on triply-even QECCs. Especially, the variety of available options in the region of a small number of quantum nodes nnn becomes important in the noisy intermediate-scale quantum (NISQ) era.
Secure multiparty quantum computation (MPQC) protocol is a cryptographic primitive allowing error-free distributed quantum computation to a group of nnn mutually distrustful quantum nodes even when some quantum nodes disobey the instructions of the protocol. Here we suggest a modified MPQC protocol that adopts unconventional quantum error-correcting codes and as a consequence reduces the number of qubits required for the protocol execution. In particular, the replacement of the self-dual Calderbank-Shor-Steane quantum error-correcting codes with triply even ones permits us to avoid the previously indispensable but resource-intensive procedure of the ``magic-state'' verification. Besides, since every extra qubit reduces the credibility of physical devices, our suggestion makes the MPQC protocol more accessible for the near-future technology by reducing the number of necessary qubits per quantum node from ${n}^{2}+\mathrm{\ensuremath{\Theta}}(r)n$, where rrr is the security parameter, to n2+3n{n}^{2}+3nn2+3n.
Secure multi-party computation (MPC) is a cryptographic primitive that lets a num- ber N of mutually distrustful parties compute a function f (x1, . . . , xN ) on their private inputs xi such that at the end of the MPC protocol, each honest party obtains the func- tion’s correct output and no adversary controlling a certain subset of parties learns any- thing about the honest parties’ inputs beyond what can be inferred from the function’s output value. In 2002, [Smi01] and [CGS02] introduced the notion of multi-party quan- tum computation (MPQC) in which arbitrary quantum circuits can be evaluated in a distributed manner, secure against a quantum adversary. Few protocols for MPQC are known. We present a fundamental study of the building blocks of MPC and MPQC in the information-theoretic setting with a focus on protocols built on top of (quantum) se- cret sharing schemes. In particular, we point out structural similarities and differences and compile an extensive list of theoretical feasibility results for the maximum number of corrupted parties within classical and quantum secret sharing and MPC protocols.
Secret sharing and multiparty computation (also called “secure function evaluation”) are fundamental primitives in modern cryptography, allowing a group of mutually distrustful players to perform correct, distributed computations under the sole assumption that some number of them will follow the protocol honestly. This paper investigates how much trust is necessary – that is, how many players must remain honest – in order for distributed quantum computations to be possible. We present a verifiable quantum secret sharing (VQSS) protocol, and a general secure multiparty quantum computation (MPQC) protocol, which can tolerate any ⌊ n−1 2 ⌋ cheaters among n players. Previous protocols for these tasks tolerated ⌊ n−1 n−1 4 ⌋ and ⌊ 6 ⌋ cheaters, respectively. The threshold we achieve is tight — even in the classical case, “fair ” multiparty computation is not possible if any set of n/2 players can cheat. Our protocols rely on approximate quantum errorcorrecting codes, which can tolerate a larger fraction of errors than traditional, exact codes. We introduce new families of authentication schemes and approximate codes tailored to the needs of our protocols, as well as new state purification techniques along the lines of those used in fault-tolerant quantum circuits.
Secret sharing and multiparty computation (also called "secure function evaluation") are fundamental primitives in modern cryptography, allowing a group of mutually distrustful players to perform correct, distributed computations under the sole assumption that some number of them will follow the protocol honestly. This paper investigates how much trust is necessary -- that is, how many players must remain honest -- in order for distributed quantum computations to be possible. We present a verifiable quantum secret sharing (VQSS) protocol, and a general secure multiparty quantum computation (MPQC) protocol, which can tolerate any \left[ {\frac{{n - 1}} {2}} \right] cheaters among n players. Previous protocols for these tasks tolerated \left[ {\frac{{n - 1}} {4}} \right] and \left[ {\frac{{n - 1}} {6}} \right] cheaters, respectively. The threshold we achieve is tight -- even in the classical case, "fair" multiparty computation is not possible if any set of n/2 players can cheat. Our protocols rely on approximate quantum errorcorrecting codes, which can tolerate a larger fraction of errors than traditional, exact codes. We introduce new families of authentication schemes and approximate codes tailored to the needs of our protocols, as well as new state purification techniques along the lines of those used in faulttolerant quantum circuits.
Multi-Party Quantum Computation (MPQC) has attracted a lot of attention as a potential killer-app for quantum networks through it's ability to preserve privacy and integrity of the highly valuable computations they would enable. Contributing to the latest challenges in this field, we present a composable protocol achieving blindness and verifiability even in the case of a single honest client. The security of our protocol is reduced, in an information-theoretically secure way, to that of a classical composable Secure Multi-Party Computation (SMPC) used to coordinate the various parties. Our scheme thus provides a statistically secure upgrade of such classical scheme to a quantum one with the same level of security. In addition, (i) the clients can delegate their computation to a powerful fully fault-tolerant server and only need to perform single qubit operations to unlock the full potential of multi-party quantum computation; (ii) the amount of quantum communication with the server is reduced to sending quantum states at the beginning of the computation and receiving the output states at the end, which is optimal and removes the need for interactive quantum communication; and (iii) it has a low constant multiplicative qubit overhead compared to the single-client delegated protocol it is built upon. The main technical ingredient of our paper is the bootstraping of the MPQC construction by Double Blind Quantum Computation, a new composable resource for blind multiparty quantum computation, that demonstrates the surprising fact that the full protocol does not require verifiability of all components to achieve security.
We consider the task of secure multiparty distributed quantum computation on a quantum network. We propose a protocol based on quantum error correction which reduces the number of necessary qubits. That is, each of the nnn nodes in our protocol requires an operational workspace of n2+4n{n}^{2}+4nn2+4n qubits, as opposed to the previously shown $\mathrm{\ensuremath{\Omega}}\left(({n}^{3}+{n}^{2}{s}^{2})logn\right)$ qubits, where sss is a security parameter. Additionally, we reduce the communication complexity by a factor of O(n3log(n))O({n}^{3}log(n))O(n3log(n)) qubits per node compared to existing protocols. To achieve universal computation, we develop a distributed procedure for verifying magic states, which allows us to apply distributed gate teleportation and which may be of independent interest. We showcase our protocol in a small example for a seven-node network.