arXiv subjects

Joseph F. Fitzsimons

Publications and source records attributed to Joseph F. Fitzsimons.

34 records · Page 2Linked to original sources

arXiv2015

Quantum assisted Gaussian process regression

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] can be applied to Gaussian process regression (GPR), leading to an exponential reduction in computation time in some instances. We show that even in some cases not ideally suited to the quantum linear systems algorithm, a polynomial increase in efficiency still occurs.

quant-ph↗

arXiv2015

Device-Independent Verifiable Blind Quantum Computation

As progress on experimental quantum processors continues to advance, the problem of verifying the correct operation of such devices is becoming a pressing concern. The recent discovery of protocols for verifying computation performed by entangled but non-communicating quantum processors holds the promise of certifying the correctness of arbitrary quantum computations in a fully device-independent manner. Unfortunately, all known schemes have prohibitive overhead, with resources scaling as extremely high degree polynomials in the number of gates constituting the computation. Here we present a novel approach based on a combination of verified blind quantum computation and Bell state self-testing. This approach has dramatically reduced overhead, with resources scaling as only $O(m^4\ln m)$ in the number of gates.

quant-ph↗

arXiv2015

Fast graph operations in quantum computation

The connection between certain entangled states and graphs has been heavily studied in the context of measurement-based quantum computation as a tool for understanding entanglement. Here we show that this correspondence can be harnessed in the reverse direction to yield a graph data structure which allows for more efficient manipulation and comparison of graphs than any possible classical structure. We introduce efficient algorithms for many transformation and comparison operations on graphs represented as graph states, and prove that no classical data structure can have similar performance for the full set of operations studied.

quant-ph↗

arXiv2015

Unconditionally verifiable blind computation

Blind Quantum Computing (BQC) allows a client to have a server carry out a quantum computation for them such that the client's input, output and computation remain private. A desirable property for any BQC protocol is verification, whereby the client can verify with high probability whether the server has followed the instructions of the protocol, or if there has been some deviation resulting in a corrupted output state. A verifiable BQC protocol can be viewed as an interactive proof system leading to consequences for complexity theory. The authors, together with Broadbent, previously proposed a universal and unconditionally secure BQC scheme where the client only needs to be able to prepare single qubits in separable states randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. In this paper we extend that protocol with new functionality allowing blind computational basis measurements, which we use to construct a new verifiable BQC protocol based on a new class of resource states. We rigorously prove that the probability of failing to detect an incorrect output is exponentially small in a security parameter, while resource overhead remains polynomial in this parameter. The new resource state allows entangling gates to be performed between arbitrary pairs of logical qubits with only constant overhead. This is a significant improvement on the original scheme, which required that all computations to be performed must first be put into a nearest neighbour form, incurring linear overhead in the number of qubits. Such an improvement has important consequences for efficiency and fault-tolerance thresholds.

quant-ph↗

arXiv2015

A quantum approach to homomorphic encryption

Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum homomorphic encryption scheme that enables a broad class of quantum computation on encrypted data. A particular instance of our encoding hides up to a constant fraction of the information encrypted. This fraction can be made arbitrarily close to unity with overhead scaling only polynomially in the message length. This highlights the potential of our protocol to hide a non-trivial amount of information, and is suggestive of a large class of encodings that might yield better security.

quant-ph↗

arXiv2014

Overcoming efficiency constraints on blind quantum computation

Blind quantum computation allows a user to delegate a computation to an untrusted server while keeping the computation hidden. A number of recent works have sought to establish bounds on the communication requirements necessary to implement blind computation, and a bound based on the no-programming theorem of Nielsen and Chuang has emerged as a natural limiting factor. Here we show that this constraints only hold in limited scenarios and show how to overcome it using a method based on iterated gate-teleportations. We present our results as a family of protocols, with varying degrees of computational-ability requirements on the client. Certain protocols in this family exponentially outperform previously known schemes in terms of total communication. The approach presented here can be adapted to other distributed computing protocols to reduce communication requirements.

quant-ph↗

arXiv2014

Composable security of delegated quantum computation

Delegating difficult computations to remote large computation facilities, with appropriate security guarantees, is a possible solution for the ever-growing needs of personal computing power. For delegated computation protocols to be usable in a larger context---or simply to securely run two protocols in parallel---the security definitions need to be composable. Here, we define composable security for delegated quantum computation. We distinguish between protocols which provide only blindness---the computation is hidden from the server---and those that are also verifiable---the client can check that it has received the correct result. We show that the composable security definition capturing both these notions can be reduced to a combination of several distinct "trace-distance-type" criteria---which are, individually, non-composable security definitions. Additionally, we study the security of some known delegated quantum computation protocols, including Broadbent, Fitzsimons and Kashefi's Universal Blind Quantum Computation protocol. Even though these protocols were originally proposed with insufficient security criteria, they turn out to still be secure given the stronger composable definitions.

quant-ph↗

arXiv2014

Freely Scalable Quantum Technologies using Cells of 5-to-50 Qubits with Very Lossy and Noisy Photonic Links

Exquisite quantum control has now been achieved in small ion traps, in nitrogen-vacancy centres and in superconducting qubit clusters. We can regard such a system as a universal cell with diverse technological uses from communication to large-scale computing, provided that the cell is able to network with others and overcome any noise in the interlinks. Here we show that loss-tolerant entanglement purification makes quantum computing feasible with the noisy and lossy links that are realistic today: With a modestly complex cell design, and using a surface code protocol with a network noise threshold of 13.3%, we find that interlinks which attempt entanglement at a rate of 2MHz but suffer 98% photon loss can result in kilohertz computer clock speeds (i.e. rate of high fidelity stabilizer measurements). Improved links would dramatically increase the clock speed. Our simulations employed local gates of a fidelity already achieved in ion trap devices.

quant-ph↗

arXiv2014

Limitations on information theoretically secure quantum homomorphic encryption

Homomorphic encryption is a form of encryption which allows computation to be carried out on the encrypted data without the need for decryption. The success of quantum approaches to related tasks in a delegated computation setting has raised the question of whether quantum mechanics may be used to achieve information theoretically secure fully homomorphic encryption. Here we show, via an information localisation argument, that deterministic fully homomorphic encryption necessarily incurs exponential overhead if perfect security is required.

quant-ph↗

arXiv2014

On the hardness of classically simulating the one clean qubit model

Deterministic quantum computation with one quantum bit (DQC1) is a model of quantum computing where the input restricted to containing a single qubit in a pure state and with all other qubits in a completely-mixed state, with only a single qubit measurement at the end of the computation [E. Knill and R. Laflamme, Phys. Rev. Lett. {\bf81}, 5672 (1998)]. While it is known that DQC1 can efficiently solve several problems for which no known classical efficient algorithms exist, the question of whether DQC1 is really more powerful than classical computation remains open. In this paper, we introduce a slightly modified version of DQC1, which we call DQC1$_k$, where $k$ output qubits are measured, and show that DQC1$_k$ cannot be classically efficiently simulated for any $k\geq3$ unless the polynomial hierarchy collapses at the third level.

quant-ph↗

arXiv2013

Experimental verification of quantum computations

Quantum computers are expected to offer substantial speedups over their classical counterparts and to solve problems that are intractable for classical computers. Beyond such practical significance, the concept of quantum computation opens up new fundamental questions, among them the issue whether or not quantum computations can be certified by entities that are inherently unable to compute the results themselves. Here we present the first experimental verification of quantum computations. We show, in theory and in experiment, how a verifier with minimal quantum resources can test a significantly more powerful quantum computer. The new verification protocol introduced in this work utilizes the framework of blind quantum computing and is independent of the experimental quantum-computation platform used. In our scheme, the verifier is only required to generate single qubits and transmit them to the quantum computer. We experimentally demonstrate this protocol using four photonic qubits and show how the verifier can test the computer's ability to perform measurement-based quantum computations.

quant-ph↗

arXiv2013

The Quantum Frontier

The success of the abstract model of computation, in terms of bits, logical operations, programming language constructs, and the like, makes it easy to forget that computation is a physical process. Our cherished notions of computation and information are grounded in classical mechanics, but the physics underlying our world is quantum. In the early 80s researchers began to ask how computation would change if we adopted a quantum mechanical, instead of a classical mechanical, view of computation. Slowly, a new picture of computation arose, one that gave rise to a variety of faster algorithms, novel cryptographic mechanisms, and alternative methods of communication. Small quantum information processing devices have been built, and efforts are underway to build larger ones. Even apart from the existence of these devices, the quantum view on information processing has provided significant insight into the nature of computation and information, and a deeper understanding of the physics of our universe and its connections with computation. We start by describing aspects of quantum mechanics that are at the heart of a quantum view of information processing. We give our own idiosyncratic view of a number of these topics in the hopes of correcting common misconceptions and highlighting aspects that are often overlooked. A number of the phenomena described were initially viewed as oddities of quantum mechanics. It was quantum information processing, first quantum cryptography and then, more dramatically, quantum computing, that turned the tables and showed that these oddities could be put to practical effect. It is these application we describe next. We conclude with a section describing some of the many questions left for future work, especially the mysteries surrounding where the power of quantum information ultimately comes from.

quant-ph↗

arXiv2013

Optimal Blind Quantum Computation

Blind quantum computation allows a client with limited quantum capabilities to interact with a remote quantum computer to perform an arbitrary quantum computation, while keeping the description of that computation hidden from the remote quantum computer. While a number of protocols have been proposed in recent years, little is currently understood about the resources necessary to accomplish the task. Here we present general techniques for upper and lower bounding the quantum communication necessary to perform blind quantum computation, and use these techniques to establish a concrete bounds for common choices of the client's quantum capabilities. Our results show that the UBQC protocol of Broadbent, Fitzsimons and Kashefi [1], comes within a factor of 8/3 of optimal when the client is restricted to preparing single qubits. However, we describe a generalization of this protocol which requires exponentially less quantum communication when the client has a more sophisticated device.

quant-ph↗

arXiv2012

The information capacity of a single photon

Quantum states of light are the obvious choice for communicating quantum information. To date, encoding information into the polarisation states of single photons has been widely used as these states form an natural closed two state qubit. However, photons are able to encode much more -- in principle infinite -- information via the continuous spatio-temporal degrees of freedom. Here we consider the information capacity of an optical quantum channel, such as an optical fibre, where a spectrally encoded single photon is the means of communication. We use the Holevo bound to calculate an upper bound on the channel capacity, and relate this to the spectral encoding basis and the spectral properties of the channel. Further, we derive analytic bounds on the capacity of such channels, and in the case of a symmetric two-state encoding calculate the exact capacity of the corresponding channel.

quant-ph↗

arXiv2012

Quantum walks with encrypted data

In the setting of networked computation, data security can be a significant concern. Here we consider the problem of allowing a server to remotely manipulate client supplied data, in such a way that both the information obtained by the client about the server's operation and the information obtained by the server about the client's data are significantly limited. We present a protocol for achieving such functionality in two closely related models of restricted quantum computation -- the Boson sampling and quantum walk models. Due to the limited technological requirements of the Boson scattering model, small scale implementations of this technique are feasible with present-day technology.

quant-ph↗

arXiv2011

Experimental Demonstration of Blind Quantum Computing

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. Remarkably, the client only needs to be able to prepare and transmit individual photonic qubits. Our demonstration is crucial for future unconditionally secure quantum cloud computing and might become a key ingredient for real-life applications, especially when considering the challenges of making powerful quantum computers widely available.

quant-ph↗