When a universal quantum computer is used by the public, it is assumed that it will be in the form of a quantum cloud server that exists in a few bases due to its cost. In this cloud server, privacy will be a crucial issue, and a blind quantum computation protocol will be necessary so that each user can use the server without the details of the calculations being revealed. It is also important to be able to verify that the server is performing calculations as instructed by the user, since quantum calculations cannot be verified by classical computation. In this paper, we put forward a protocol that achieves blindness using the quantum one-time pad for encryption and a T-like gate, and while verifying computation using trap qubits.
Blind quantum computation is a new quantum secure protocol, which enables Alice who does not have enough quantum technology to delegate her computation to Bob who has a fully-fledged quantum power without revealing her input, output and algorithm. So far, blind quantum computation has been considered only for the circuit model and the measurement-based model. Here we consider the possibility and the limitation of blind quantum computation in the ancilla-driven model, which is a hybrid of the circuit and the measurement-based models.
Blind quantum computing enables a client, who does not have enough quantum technologies, to delegate her quantum computing to a remote quantum server in such a way that her privacy is protected against the server. Some blind quantum computing protocols can be made verifiable, which means that the client can check the correctness of server's quantum computing. Can any blind protocol always be made verifiable? In this paper, we answer to the open problem affirmatively. We propose a plug-in that makes any universal blind quantum computing protocol automatically verifiable. The idea is that the cl…
Because quantum computers are expensive, it is envisaged that individuals who want to utilize them would do so by delegating their calculations to someone who has a quantum computer. When quantum computer users delegate computations to quantum servers, they wish to keep information about their calculations hidden from the servers. The protocol of delegating a calculation while hiding information about the calculation from the server is called {\sl blind quantum computation protocol}. Prior research on single-server's blind quantum computation protocol required users to have quantum capabilitie…
It is called blind quantum computation(BQC) that a client who has limited quantum technologies can delegate her quantum computing to a server who has fully-advanced quantum computers. But the privacy of the client's quantum inputs, algorithms and outputs is still a challenge. To realize a secure BQC, we mainly study how to hide quantum fourier transform (QFT) performed on Bell states. In this paper, three cases are considered as follows. For the first case, we design primary BQC protocols of QFT performed on qubits 12 of belonging to $\{|ϕ^\pm\rangle_{12},$ $|ψ^\pm\rangle_{12}\}$ with relevant…
In blind quantum computation (BQC), a client delegates her quantum computation to a server with universal quantum computers who learns nothing about the client's private information. In measurement-based BQC model, entangled states are generally used to realize quantum computing. However, to generate a large-scale entangled state in experiment becomes a challenge issue. In circuit-based BQC model, single-qubit gates can be realized precisely, but entangled gates are probabilistically successful. This remains a challenge to realize entangled gates with a deterministic method in some systems. To…
Quantum computers, besides offering substantial computational speedups, are also expected to provide the possibility of preserving the privacy of a computation. Here we show the first such experimental demonstration of blind quantum computation where the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantum computation that enables a client to delegate a computation to a quantum server. We demonstrate various blind delegated computations, including one- and two-qubit gates and the Deutsch and Grover algorithms. Remar…
In this paper, we give a quantum circuit that calculates symmetrized functions. Our algorithm applies the original Grover's algorithm or a variant thereof such as AFGA (adaptive fixed point Grover's algorithm). Our algorithm uses AFGA in conjunction with two new techniques we call "targeting two hypotheses" and "blind targeting". Suppose AFGA drives the starting state $|s\rangle$ to the target state $|t\rangle$. When targeting two hypotheses, $|t\rangle$ is a superposition $a_0|0\rangle + a_1|1\rangle$ of two orthonormal states or hypotheses $|0\rangle$ and $|1\rangle$. When targeting blindly,…
On the Computational Complexity of Blind Quantum Machine Learning
Delft University of Technology（代尔夫特理工大学）；QuTech；Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学卡弗里纳米科学研究所）；Leiden Institute of Physics (LION), Leiden University（莱顿大学物理研究所）
Blind quantum computation (BQC) is a model in which a computation is performed on a server by a client such that the server is kept blind about the input, the algorithm, and the output of the computation. Here we layout a general framework for BQC which, unlike the previous BQC models, does not constructed on specific computational model. A main ingredient of our construction is gate teleportation. We demonstrate that our framework can be straightforwardly implemented on circuit-based models as well as measurement-based models of quantum computation. We illustrate our construction by showing t…
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 regis…
After quantum computers come out, governments and rich companies will have the abilities to buy these useful quantum computers, meanwhile they are familiar with these technologies proficiently. If a client wants to perform quantum computing but she does not have quantum computers with relevant quantum technologies. She can seek help from the server and pay his salary, but she does not want to leak anything to the server. Blind quantum computing (BQC) give a good method for the client to realized her quantum computing. In this article, we propose a new BQC protocol of quantum fourier transform …
Simulation of Two-Qubit Grover Algorithm in MBQC with Universal Blind Quantum Computation
Electronics and Telecommunications Research Institute (ETRI)（电子电信研究所）；Cryptography Engineering Laboratory, Electronics and Telecommunications Research Institute (ETRI)（电子电信研究所密码工程实验室）
Quantum computing has considerable advantages in solving some problems over its classical counterpart. Currently various physical systems are developed to construct quantum computers but it is still challenging and the first use of quantum computers may adopt the cloud style. Blind quantum computing (BQC) provides a solution for clients with limited quantum capabilities to delegate their quantum computation to remote quantum servers while keeping input, output, and even algorithm private. In this paper, we propose three multi-party verifiable blind quantum computing (VBQC) protocols with ident…
In the universal blind quantum computation problem, a client wants to make use of a single quantum server to evaluate $C|0\rangle$ where $C$ is an arbitrary quantum circuit while keeping $C$ secret. The client's goal is to use as few resources as possible. This problem, with a representative protocol by Broadbent, Fitzsimons and Kashefi [FOCS09, arXiv:0807.4154], has become fundamental to the study of quantum cryptography, not only because of its own importance, but also because it provides a testbed for new techniques that can be later applied to related problems (for example, quantum computa…
This paper proposes a model of tripartite blind quantum computation (TBQC), in which three independent participants hold different resources and accomplish a computational task through cooperation. The three participants are called C,S,T separately, where C needs to compute on his private data, and T has the required quantum algorithm, and S provides sufficient quantum computational resources. Then two concrete TBQC protocols are constructed. The first protocol is designed based on Broadbent-Fitzsimons-Kashefi protocol, and it cannot prevent from collusive attack of two participants. Then base…
The development of new superconducting circuits and the improvement of existing ones rely on the accurate modeling of spectral properties which are key to achieving the needed advances in qubit performance. Systematic circuit analysis at the lumped-element level, starting from a circuit network and culminating in a Hamiltonian appropriately describing the quantum properties of the circuit, is a well-established procedure, yet cumbersome to carry out manually for larger circuits. We present work utilizing symbolic computer algebra and numerical diagonalization routines versatile enough to tackl…
A significant problem for current quantum computers is noise. While there are many distinct noise channels, the depolarizing noise model often appropriately describes average noise for large circuits involving many qubits and gates. We present a method to mitigate the depolarizing noise by first estimating its rate with a noise-estimation circuit and then correcting the output of the target circuit using the estimated rate. The method is experimentally validated on the simulation of the Heisenberg model. We find that our approach in combination with readout-error correction, randomized compili…
The mapping of quantum circuits to qubits represented by ion states in a storage ring quantum computer is examined. Serial, parallel and hybrid architectures for mapping such qubits onto a storage ring quantum computer are presented. Parallelism is an important part of the SRQC architecture in terms of multiple ions, windows and lasers. A "predecessor problem" that arises in such architectures is identified and a solution is proposed. Representative numerical sizing and timing calculations are presented. The entire methodology is very general and extends to several implementation options. Open…
Blind quantum computing [A. Broadbent, J. Fitzsimons, and E. Kashefi, Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science 517 (2009)] is a secure cloud quantum computing protocol which enables a client (who does not have enough quantum technology at her disposal) to delegate her quantum computation to a server (who has a universal quantum computer) without leaking any relevant information to the server. In [T. Morimae and K. Fujii, Phys. Rev. A {\bf87}, 050301(R) (2013)], a new blind quantum computing protocol, so called the measuring-Alice protocol, was proposed. …
In this work, we propose a generalization of the current most widely used quantum computing hardware metric known as the quantum volume. The quantum volume specifies a family of random test circuits defined such that the logical circuit depth is equal to the total number of qubits used in the computation. However, such square circuit shapes do not directly relate to many specific applications for which one may wish to use a quantum computer. Based on surveying available resource estimates for known quantum algorithms, we generalize the quantum volume to a handful of representative circuit shap…
We provide and experimentally demonstrate an accreditation protocol that upper-bounds the variation distance between noisy and noiseless probability distributions of the outputs of arbitrary quantum computations. We accredit the outputs of twenty-four quantum circuits executed on programmable superconducting hardware, ranging from depth nine circuits on ten qubits to depth twenty-one circuits on four qubits. Our protocol requires implementing the "target" quantum circuit along with a number of random Clifford circuits and subsequently post-processing the outputs of these Clifford circuits. Imp…
For quantum computer circuits, it is proposed that they have, besides the presently used compact graphs, an expanded system of subgraphs, in line with the quantum mechanics superposition axiom. The representation of each process by these suggested graphs is equivalent to the algebraic notation of the process.
Generative modeling is a flavor of machine learning with applications ranging from computer vision to chemical design. It is expected to be one of the techniques most suited to take advantage of the additional resources provided by near-term quantum computers. We implement a data-driven quantum circuit training algorithm on the canonical Bars-and-Stripes data set using a quantum-classical hybrid machine. The training proceeds by running parameterized circuits on a trapped ion quantum computer, and feeding the results to a classical optimizer. We apply two separate strategies, Particle Swarm an…
First solid state quantum computer was built using transmons (cooper pair boxes). The operation of the computer is limited because of using a number of the rigit cooper boxes working with fixed frequency at temperatures of superconducting material. Here, we propose a novel architecture of quantum computer based on a flexible wire circuit of many coupled quantum nodes containing controlled atomic (molecular) ensembles. We demonstrate wide opportunities of the proposed computer. Firstly, we reveal a perfect storage of external photon qubits to multi-mode quantum memory node and demonstrate a rev…
We derive a deterministic protocol to implement a general single-qubit POVM on near-term circuit-based quantum computers. The protocol has a modular structure, such that an $n$-element POVM is implemented as a sequence of $(n-1)$ circuit modules. Each module performs a $2$-element POVM. Two variations of the protocol are suggested, one optimal in terms of number of ancilla qubits, the other optimal in terms of number of qubit gate operations and quantum circuit depth. We use the protocol to implement $2$- and $3$-element POVMs on two publicly available quantum computing devices. The results we…
Blind quantum computation is a secure delegated quantum computing protocol where Alice who does not have sufficient quantum technology at her disposal delegates her computation to Bob who has a fully-fledged quantum computer in such a way that Bob cannot learn anything about Alice's input, output, and algorithm. Protocols of blind quantum computation have been proposed for several qubit measurement-based computation models, such as the graph state model, the Affleck-Kennedy-Lieb-Tasaki model, and the Raussendorf-Harrington-Goyal topological model. Here, we consider blind quantum computation fo…
The well-known Deutsch Algorithm (DA) and Deutsch-Jozsha Algorithm (DJA) both are used as an evidence to the power of quantum computers over classical computation mediums. In these theoretical experiments, it has been shown that a quantum computer can find the answer with certainty within a few steps although classical electronic systems must evaluate more iterations than quantum computer. In this paper, it is shown that a classical computation system formed by using ordinary electronic parts may perform the same task with equal performance than quantum computers. DA and DJA quantum circuits a…
With the rapid progress made by industry and academia, quantum computers with dozens of qubits or even larger size are being realized. However, the fidelity of existing quantum computers often sharply decreases as the circuit depth increases. Thus, an ideal quantum circuit simulator on classical computers, especially on high-performance computers, is needed for benchmarking and validation. We design a large-scale simulator of universal random quantum circuits, often called 'quantum supremacy circuits', and implement it on Sunway TaihuLight. The simulator can be used to accomplish the following…
We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size ($n\lesssim 50$), and measure it on several state-of-the-art transmon devices, finding values as high as 16. The quantum volume is linked to system error rates, and is empirically reduced by uncontrolled interactions within the system. It quantifies the largest random circuit of equal width and depth that the computer successfully implements. Quantum computing systems with high-fidelity operations, high connectivity, large calibrated gate sets, and c…
Blind quantum computation (BQC) allows that a client who has limited quantum abilities can delegate quantum computation to a server who has advanced quantum technologies but learns nothing about the client's private information. However, it still remains a challenge to directly encrypt quantum algorithms in circuits model. To solve the problem, we propose GTUBQC, the first gate teleportation-based universal BQC protocol. In this paper, we consider a scenario where a trusted center is responsible for preparing initial states, a client with the ability to perform X, Z does not require any quantu…
Most quantum gate errors can be characterized by two error models, namely the probabilistic error model and the Kraus error model. We proved that for a quantum circuit with either of those two models or a mix of both, the propagation error in terms of Frobenius norm is upper bounded by $2(1 - (1 - r)^m)$, where $0 \le r < 1$ is a constant independent of the qubit number and circuit depth, and $m$ is the number of gates in the circuit. Numerical experiments of synthetic quantum circuits and quantum Fourier transform circuits are performed on the simulator of the IBM Vigo quantum computer to ver…
Rapid advancement in the domain of quantum technologies has opened up researchers to the real possibility of experimenting with quantum circuits and simulating small-scale quantum programs. Nevertheless, the quality of currently available qubits and environmental noise poses a challenge in the smooth execution of the quantum circuits. Therefore, efficient design automation flows for mapping a given algorithm to the Noisy Intermediate Scale Quantum (NISQ) computer becomes of utmost importance. State-of-the-art quantum design automation tools are primarily focused on reducing logical depth, gate…
We define formally decohered quantum computers (using density matrices), and present a simulation of them by a probabalistic classical Turing Machine. We study the slowdown of the simulation for two cases: (1) sequential quantum computers, or quantum Turing machines(QTM), and (2) parallel quantum computers, or quantum circuits. This paper shows that the computational power of decohered quantum computers depends strongly on the amount of parallelism in the computation. The expected slowdown of the simulation of a QTM is polynomial in time and space of the quantum computation, for any non zero d…
Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation…
So far, superconducting quantum computers have certain constraints on qubit connectivity, such as nearest-neighbor couplings. To overcome this limitation, we propose a scalable architecture to simultaneously connect several pairs of distant qubits via a dispersively coupled quantum bus. The building-block of the bus is composed of orthogonal coplanar waveguide resonators connected through ancillary flux qubits working in the ultrastrong coupling regime. This regime activates virtual processes that boost the effective qubit-qubit interaction, which results in quantum gates on the nanosecond tim…
The first realization of solid state quantum computer was demonstrated recently by using artificial atoms -- transmons in superconducting resonator. Here, we propose a novel architecture of flexible and scalable quantum computer based on a waveguide circuit coupling many quantum nodes of controlled atomic ensembles. For the first time, we found the optimal practically attainable parameters of the atoms and circuit for 100{%} efficiency of quantum memory for multi qubit photon fields and confirmed experimentally the predicted perfect storage. Then we revealed self modes for reversible transfer …
Blind quantum computation is a scheme that adds unconditional security to cloud quantum computation. In the protocol proposed by Broadbent, Fitzsimons, and Kashefi, the ability to prepare and transmit a single qubit is required for a user (client) who uses a quantum computer remotely. In case a weak coherent pulse is used as a pseudo single photon source, however, we must introduce decoy states, owing to the inherent risk of transmitting multiple photon. In this study, we demonstrate that by using a heralded single photon source and a probabilistic photon number resolving detector, we can gain…
The performance of quantum gates is often assessed using some form of randomized benchmarking. However, the existing methods become infeasible for more than approximately five qubits. Here we show how to use a simple and customizable class of circuits -- randomized mirror circuits -- to perform scalable, robust, and flexible randomized benchmarking of Clifford gates. We show that this technique approximately estimates the infidelity of an average many-qubit logic layer, and we use simulations of up to 225 qubits with physically realistic error rates in the range 0.1-1% to demonstrate its scala…
Recently, the dynamics simulation of light-harvesting complexes as an open quantum system, in the weak and strong coupling regimes, has received much attention. In this paper, we investigate a digital quantum simulation approach of the Fenna-Matthews-Olson (FMO) photosynthetic pigment-protein complex surrounded with a Markovian bath, i.e., memoryless, based on a nuclear magnetic resonance (NMR) quantum computer. For this purpose, we apply the decoupling(recoupling) method, which is turn off(on) the couplings and also Solovay-Kitaev techniques to decompose Hamiltonian and Lindbladians into effi…
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wavefunctions that are relevant in the behavior of the system under study. Hamiltonian symmetries are an important instrument, to classify relevant many-particle wavefunctions, and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions ba…
We investigate the possibility of "having someone carry out the work of executing a function for you, but without letting him learn anything about your input". Say Alice wants Bob to compute some known function f upon her input x, but wants to prevent Bob from learning anything about x. The situation arises for instance if client Alice has limited computational resources in comparison with mistrusted server Bob, or if x is an inherently mobile piece of data. Could there be a protocol whereby Bob is forced to compute f(x) "blindly", i.e. without observing x? We provide such a blind computation …
Dynamic simulation of materials is a promising application for near-term quantum computers. Current algorithms for Hamiltonian simulation, however, produce circuits that grow in depth with increasing simulation time, limiting feasible simulations to short-time dynamics. Here, we present a method for generating circuits that are constant in depth with increasing simulation time for a subset of one-dimensional materials Hamiltonians, thereby enabling simulations out to arbitrarily long times. Furthermore, by removing the effective limit on the number of feasibly simulatable time-steps, the const…
We give a cheat sensitive protocol for blind universal quantum computation that is efficient in terms of computational and communication resources: it allows one party to perform an arbitrary computation on a second party's quantum computer without revealing either which computation is performed, or its input and output. The first party's computational capabilities can be extremely limited: she must only be able to create and measure single-qubit superposition states. The second party is not required to use measurement-based quantum computation. The protocol requires the (optimal) exchange of …
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivity, and coherence times, a quantum circuit optimization is essential to make the best use of near-term quantum devices. We introduce a new circuit optimizer called AQCEL, which aims to remove redundant controlled operations from controlled gates, depending on initial states of the circuit. Especially, the AQCEL can remove unnecessary qubit controls from multi-controlled gates in polynomial computational resources, even when all the relevant qubits are entangled, by identifying zero…
Verifiable blind quantum computing is a secure delegated quantum computing where a client with a limited quantum technology delegates her quantum computing to a server who has a universal quantum computer. The client's privacy is protected (blindness) and the correctness of the computation is verifiable by the client in spite of her limited quantum technology (verifiability). There are mainly two types of protocols for verifiable blind quantum computing: the protocol where the client has only to generate single-qubit states, and the protocol where the client needs only the ability of single-qu…
We propose a very large family of benchmarks for probing the performance of quantum computers. We call them volumetric benchmarks (VBs) because they generalize IBM's benchmark for measuring quantum volume \cite{Cross18}. The quantum volume benchmark defines a family of square circuits whose depth $d$ and width $w$ are the same. A volumetric benchmark defines a family of rectangular quantum circuits, for which $d$ and $w$ are uncoupled to allow the study of time/space performance trade-offs. Each VB defines a mapping from circuit shapes -- $(w,d)$ pairs -- to test suites $\mathcal{C}(w,d)$. A t…
This paper addresses the problem of finding the depth overhead that will be incurred when running quantum circuits on near-term quantum computers. Specifically, it is envisaged that near-term quantum computers will have low qubit connectivity: each qubit will only be able to interact with a subset of the other qubits, a reality typically represented by a qubit interaction graph in which a vertex represents a qubit and an edge represents a possible direct 2-qubit interaction (gate). Thus the depth overhead is unavoidably incurred by introducing swap gates into the quantum circuit to enable gene…
