Ancilla-driven blind quantum computation for clients with different quantum capabilities

2025-04-30 0 0 525.3KB 14 页 10玖币
侵权投诉
Dai et al.
RESEARCH
Ancilla-driven blind quantum computation for
clients with different quantum capabilities
Qunfeng Dai1, Junyu Quan2, Xiaoping Lou3and Qin Li1*
*Correspondence: liqin@xtu.edu.cn
1School of Computer Science,
Xiangtan University, Xiangtan,
China
Full list of author information is
available at the end of the article
Abstract
Blind quantum computation (BQC) allows a client with limited quantum power
to delegate his quantum computational task to a powerful server and still keep
his input, output, and algorithm private. There are mainly two kinds of models
about BQC, namely circuit-based and measurement-based models. In addition, a
hybrid model called ancilla-driven universal blind quantum computing (ADBQC)
was proposed by combining the properties of both circuit-based and
measurement-based models, where all unitary operations on the register qubits
can be realized with the aid of single ancillae coupled to the register qubits.
However, in the ADBQC model, the quantum capability of the client is strictly
limited to preparing single qubits. If a client can only perform single-qubit
measurements or a few simple quantum gates, he may also want to delegate his
computation to a remote server via ADBQC. This paper solves the problem and
extends the existing model by proposing two types of ADBQC protocols for
clients with different quantum capabilities, such as performing single-qubit
measurements or single-qubit gates. Furthermore, in the proposed two ADBQC
protocols, clients can detect whether servers are honest or not with a high
probability by using corresponding verifiable techniques.
Keywords: Blind quantum computation; Verifiable blind quantum computation;
Ancilla-driven quantum computation; Quantum entanglement
1 Introduction
The implementation of quantum computing is generally based on circuit-based
model [13] and measurement-based model [412]. In the circuit-based model, quan-
tum computing is realized by directly acting single-qubit or multi-qubit gates on
the qubits in quantum registers. In contrast, the measurement-based model is im-
plemented by performing adaptive single-qubit measurements on a highly entangled
resource state. Since the two models can simulate each other, they are computation-
ally equivalent. Each model has its own advantages and disadvantages and which
one is chosen mainly depends on the physical system and the quantum devices of
the user.
In 2010, a mixture of the two models, called ancilla-driven quantum computation
(ADQC), was proposed by Anders et al. [13], where qubits are stored in quantum
registers like the circuit-based model, whereas the operations on the register are
performed by measuring an ancilla attached to the register in different bases simi-
lar to the measurement-based model. The main feature of ADQC is that the ancilla
qubit is coupled to various qubits of register through a fixed two-qubit entangle-
ment operator (HH)CZ, and only the ancilla qubit is initialized and measured.
arXiv:2210.09878v1 [quant-ph] 18 Oct 2022
Dai et al. Page 2 of 14
Due to the entanglement effect of the register and ancilla, arbitrary quantum opera-
tions on qubits of the register can be realized by performing suitable measurements
on the ancilla. ADQC has excellent advantages in some physical systems where
register qubits with long decoherence time are difficult to operate, while relatively
short-lived ancilla qubits are easier to control and can be prepared and measured
quickly, such as neutral atoms in optical lattices [14], cavity QED superconducting
qubits [15], and aluminum ions in optics [16,17]. Besides, ADQC can simulate any
positive operator valued measurement (POVM) on register qubits by accessing a
fully controlled ancilla which is attached to the register sequentially. Therefore, it
is also useful for experimental systems where their measurements would destroy
physical qubits, such as photonic systems.
Although quantum computation has been extensively studied, the physical real-
ization of it is still very challenging. Even if quantum computers become available,
they are likely to be owned by only a handful of centers around the world much like
today’s supercomputer rental system. Clients who want to utilize these quantum
resources can only delegate their computational tasks to the organizations that own
quantum computers. The burdens of clients are greatly reduced in such a delegated
quantum computing model, but their privacy is seriously threatened. Fortunately,
some quantum cryptographic techniques, such as quantum key distribution [18,19],
quantum identity authentication [20,21], and quantum secret sharing [22], can be
utilized to protect the privacy of clients.
Blind quantum computation (BQC) as a combination of quantum computation
and quantum cryptography is a kind of delegated quantum computing that can
protect private data of clients. It allows a client who only has some simple quantum
devices to delegate quantum computing tasks to a powerful quantum server, while
keeping the data of the client including input, output, and algorithm hidden from the
server. The first BQC protocol was proposed by Childs based on the circuit model
[23], where the client Alice must possess quantum memory, prepare |0i, and have the
ability to perform SW AP gates. Broadbent, Fitzsimons, and Kashefi proposed the
first universal BQC protocol (known as the BFK protocol) [24], in which the client
only needs to prepare single-qubit states and does not require quantum memory
and the ability to perform complex quantum gates. Then Morimae et al. proposed
another BQC model [8] in which the client only makes measurements, as in some
experimental settings such as quantum optical systems, the measurement of a qubit
is much easier than generating a single-qubit state. Since then, a series of BQC
protocols were proposed based on these two protocols [2535] and a few proof-of-
principle experiments were demonstrated in photonic systems [36,37]. Recently, Li
et al. proposed a new model of BQC where a client only needs to perform several
single-qubit gates [38] and it provides a new research path for BQC.
An ancilla-driven blind quantum computing (ADBQC) protocol was proposed by
applying the BQC technology to the ADQC model [39], which realized the ADQC
in the way of delegated quantum computing for the first time. After that, another
ADQC protocol without performing measurements was proposed to further enrich
the field of ADQC [40]. In ADBQC, it is implemented in a very monolithic way,
and clients should generate various single qubits. In fact, it is unrealistic that all
users have the same quantum ablitity. As mentioned above, BQC mainly deals with
Dai et al. Page 3 of 14
three types of clients. Therefore, it is also necessary to design ADBQC protocols
suitable for various clients with different quantum capability, such as performing
single-qubit measurements or gates. This paper extends the existing ADBQC model
by proposing two ADBQC protocols for another two kinds of clients who only have
the ability to perform single-qubit measurements or gates. Moreover, the proposed
ADBQC protocols can be verifiable, as clients can easily verify whether the server
deviates from the calculation by introducing the trap qubit technology.
The rest of this paper is organized as follows. Section 2 describes the preliminaries,
including basic notations and structure of the circuit gadgets needed to realize
ADBQC. In section 3, we briefly review a typical ADBQC protocol for the users
who prepare single-qubit states [39]. Section 4 presents two ADBQC protocols for
another two types of users and analyzes the security and the verifiability of them.
The last section gives a conclusion of this paper.
2 Preliminaries
In this section, we give a brief introduction to ADBQC. A more detailed description
is available in [13,39,41]. There are two types of qubits in ADBQC: register qubit
and ancilla qubit. The role of ancilla qubit is to indirectly control the evolution of the
register qubit by performing operations such as single-qubit gates and single-qubit
measurements on the ancilla qubit after establishing the entanglement between the
ancilla and register qubits. We first review the notations and unitary matrices used
in a typical ADBQC protocol [39], then present the structure of circuit gadgets
which can be used to simulate HRZ(θ) and CZ gates. By combining these gadgets,
ADQC can be realized blindly in the form of delegated computation. In addition,
we refer to the client as Alice and the server as Bob for simplicity.
2.1 Review of ADBQC in Ref. [41]
Let the notation {|±i} denote Xbasis measurement and {|0i,|1i} denote Zbasis
measurement. Measurement outcome is represented by Si∈ {0,1}associated with
±and the subscript iof smeans the i-th measurement. Set the state |+α,ϕi=
cos(α
2)|0i+esin(α
2)|1i, the state |−α,ϕi= cos(α
2)|0i − esin(α
2)|1i, the rotation
operator about the xaxe RX(θ) = eiθX
2, and the rotation operator about the z
axe RZ(θ) = eiθZ
2. And the Pauli matrices are defined as
X="0 1
1 0 #, Y ="0i
i0#, Z ="1 0
01#(1)
ADBQC is performed with the help of different single ancillae, on which single-
qubits measurements and 2-qubit entangle operators e
EAR determined by the AD-
BQC scheme chosen by Bob and the computation progress are carried out, where
e
EAR = (HH)CZ or CZ(HH). An ancilla |+γ iis coupled to register
qubits with e
EAR and then is measured in certain basis {|±θ,φi}. The back-ation
of this measurement on the register qubit can be described by a Kraus operator
K±=Aθ,φ|e
EAR|+γ iA[42], and P±=tr(K±†
RK±
R) are the probabilities of ob-
taining measurement outcomes + or .
Arbitrary single-qubit gates together with the CN OT gate form the universal
set of gates for quantum computation. Two ways are used in ADBQC to carry
摘要:

Daietal.RESEARCHAncilla-drivenblindquantumcomputationforclientswithdi erentquantumcapabilitiesQunfengDai1,JunyuQuan2,XiaopingLou3andQinLi1**Correspondence:liqin@xtu.edu.cn1SchoolofComputerScience,XiangtanUniversity,Xiangtan,ChinaFulllistofauthorinformationisavailableattheendofthearticleAbstractBlind...

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