50 research outputs found
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.Comment: 37+9 pages, 13 figures. v3: minor changes, new references. v2:
extended the reduction between composable and local security to include
entangled inputs, substantially rewritten the introduction to the Abstract
Cryptography (AC) framewor
qBitcoin: A Peer-to-Peer Quantum Cash System
A decentralized online quantum cash system, called qBitcoin, is given. We
design the system which has great benefits of quantization in the following
sense. Firstly, quantum teleportation technology is used for coin transaction,
which prevents from the owner of the coin keeping the original coin data even
after sending the coin to another. This was a main problem in a classical
circuit and a blockchain was introduced to solve this issue. In qBitcoin, the
double-spending problem never happens and its security is guaranteed
theoretically by virtue of quantum information theory. Making a block is time
consuming and the system of qBitcoin is based on a quantum chain, instead of
blocks. Therefore a payment can be completed much faster than Bitcoin. Moreover
we employ quantum digital signature so that it naturally inherits properties of
peer-to-peer (P2P) cash system as originally proposed in Bitcoin.Comment: 11 pages, 2 figure
Dynamical studies of macroscopic superposition states: Phase engineering of controlled entangled number states of Bose-Einstein condensate in multiple wells
We provide a scheme for the generation of entangled number states of
Bose-Einstein condensates in multiple wells with cyclic pairwise connectivity.
The condensate ground state in a multiple well trap can self-evolve, when phase
engineered with specific initial phase differences between the neighboring
wells, to a macroscopic superposition state with controllable entanglement --
to multiple well generalization of double well NOON states. We demonstrate
through numerical simulations the creation of entangled states in three and
four wells and then explore the creation of "larger" entangled states where
there are either a larger number of particles in each well or a larger number
of wells. The type of entanglement produced as the particle numbers, or
interaction strength, increases changes in a novel and initially unexpected
manner.Comment: 13 pages, 14 figure
A simple protocol for fault tolerant verification of quantum computation
With experimental quantum computing technologies now in their infancy, the search for efficient means of testing the correctness of these quantum computations is becoming more pressing. An approach to the verification of quantum computation within the framework of interactive proofs has been fruitful for addressing this problem. Specifically, an untrusted agent (prover) alleging to perform quantum computations can have his claims verified by another agent (verifier) who only has access to classical computation and a small quantum device for preparing or measuring single qubits. However, when this quantum device is prone to errors, verification becomes challenging and often existing protocols address this by adding extra assumptions, such as requiring the noise in the device to be uncorrelated with the noise on the prover's devices. In this paper, we present a simple protocol for verifying quantum computations, in the presence of noisy devices, with no extra assumptions. This protocol is based on post hoc techniques for verification, which allow for the prover to know the desired quantum computation and its input. We also perform a simulation of the protocol, for a one-qubit computation, and find the error thresholds when using the qubit repetition code as well as the Steane code
Correlations of observables in chaotic states of macroscopic quantum systems
We study correlations of observables in energy eigenstates of chaotic systems
of a large size . We show that the bipartite entanglement of two subsystems
is quite strong, whereas macroscopic entanglement of the total system is
absent. It is also found that correlations, either quantum or classical, among
less than points are quite small. These results imply that chaotic states
are stable. Invariance of these properties under local operations is also
shown.Comment: 5 pages, 2 figure
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.Comment: 46 pages, 10 figures. Additional protocol added which allows
arbitrary circuits to be verified with polynomial securit
Necessity of Superposition of Macroscopically Distinct States for Quantum Computational Speedup
For quantum computation, we investigate the conjecture that the superposition
of macroscopically distinct states is necessary for a large quantum speedup.
Although this conjecture was supported for a circuit-based quantum computer
performing Shor's factoring algorithm [A. Ukena and A. Shimizu, Phys. Rev. A69
(2004) 022301], it needs to be generalized for it to be applicable to a large
class of algorithms and/or other models such as measurement-based quantum
computers. To treat such general cases, we first generalize the indices for the
superposition of macroscopically distinct states. We then generalize the
conjecture, using the generalized indices, in such a way that it is
unambiguously applicable to general models if a quantum algorithm achieves
exponential speedup. On the basis of this generalized conjecture, we further
extend the conjecture to Grover's quantum search algorithm, whose speedup is
large but quadratic. It is shown that this extended conjecture is also correct.
Since Grover's algorithm is a representative algorithm for unstructured
problems, the present result further supports the conjecture.Comment: 18 pages, 5 figures. Fixed typos throughout the manuscript. This
version has been publishe
Measurement-based quantum computation in a 2D phase of matter
Recently it has been shown that the non-local correlations needed for
measurement based quantum computation (MBQC) can be revealed in the ground
state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model involving nearest
neighbor spin-3/2 interactions on a honeycomb lattice. This state is not
singular but resides in the disordered phase of ground states of a large family
of Hamiltonians characterized by short-range-correlated valence bond solid
states. By applying local filtering and adaptive single particle measurements
we show that most states in the disordered phase can be reduced to a graph of
correlated qubits that is a scalable resource for MBQC. At the transition
between the disordered and Neel ordered phases we find a transition from
universal to non-universal states as witnessed by the scaling of percolation in
the reduced graph state.Comment: 8 pages, 6 figures, comments welcome. v2: published versio
Verification of Quantum Computation and the Price of Trust
International audienc
Improved hardness results for the guided local Hamiltonian problem
Estimating the ground state energy of a local Hamiltonian is a central problem in quantum chemistry. In order to further investigate its complexity and the potential of quantum algorithms for quantum chemistry, Gharibian and Le Gall (STOC 2022) recently introduced the guided local Hamiltonian problem (GLH), which is a variant of the local Hamiltonian problem where an approximation of a ground state (which is called a guiding state) is given as an additional input. Gharibian and Le Gall showed quantum advantage (more precisely, BQP-completeness) for GLH with 6-local Hamiltonians when the guiding state has fidelity (inverse-polynomially) close to 1/2 with a ground state. In this paper, we optimally improve both the locality and the fidelity parameter: we show that the BQP-completeness persists even with 2-local Hamiltonians, and even when the guiding state has fidelity (inverse-polynomially) close to 1 with a ground state. Moreover, we show that the BQP-completeness also holds for 2-local physically motivated Hamiltonians on a 2D square lattice or a 2D triangular lattice. Beyond the hardness of estimating the ground state energy, we also show BQP-hardness persists when considering estimating energies of excited states of these Hamiltonians instead. Those make further steps towards establishing practical quantum advantage in quantum chemistry