Lattice models or structures are geometrical objects with mathematical forms, that are used to represent physical systems. They have been used widely in diverse fields, namely, in condensed matter physics, to study degrees of freedom of molecules in chemistry and in studying polymer dynamics and protein structures to name a few. In this article we discuss an encoding methodology of lattice structures in computational basis states of qubits (as used in quantum computing algorithms). We demonstrate a specific use case of lattice models in protein structure prediction. We do not propose any quantum algorithm to solve the protein structure prediction problem, instead, we propose a generic encoding methodology of lattice structures.
It is proposed to map the quantum information qubit not to individual spin 1/2 states, but to the collective spin states being eigenfunctions of the Hamiltonian including spin-spin interactions, which may be not small. Such an approach allows to introduce more stable calculation basis for quantum computer based on the solid state NMR systems.
We consider the problem of encoding classical information into unknown qudit states belonging to any basis, of a maximal set of mutually unbiased bases, by one party and then decoding by another party who has perfect knowledge of the basis. Working with qudits of prime dimensions, we point out a no-go theorem that forbids shift operations on arbitrary unknown states. We then provide the necessary conditions for reliable encoding/decoding.
In this paper, we study the unconditional security of the so-called measurement device independent quantum key distribution (MDIQKD) with the basis-dependent flaw in the context of phase encoding schemes. We propose two schemes for the phase encoding, the first one employs a phase locking technique with the use of non-phase-randomized coherent pulses, and the second one uses conversion of standard BB84 phase encoding pulses into polarization modes. We prove the unconditional security of these schemes and we also simulate the key generation rate based on simple device models that accommodate im…
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization landscapes. We tackle these challenges by introducing a new variational quantum algorithm that benefits from two innovations: multi-basis graph encodings and nonlinear activation functions. Our technique results in increased optimization performance, a factor of two increase in effective quantum resources, and a quadratic reduction in measurement complexity. Wh…
Multiple quantum coherences are typically characterised by their coherence number and the number of spins that make up the state, though only the coherence number is normally measured. We present a simple set of measurements that extend our knowledge of the multiple quantum state by recording the coherences in both the $x$ basis and the usual $z$ basis. The coherences in the two bases are related by a similarity transformation. We characterize the growth of the multiple quantum coherences via measurements in the two bases, and show that the rate varies with the coefficient of the driving term …
Quantum key distribution (QKD) promises provably secure communications. In order to improve the secret key rate, combining a biased basis choice with the decoy-state method is proposed. Concomitantly, there is a basis-independent detection efficiency condition, which usually cannot be satisfied in a practical system, such as the time-phase encoding. Fortunately, this flaw has been recently removed theoretically and experimentally using the fact that the expected yields of single-photon states prepared in two bases stay the same for a given measurement basis. However, the security proofs do not…
Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal quantum computation with a fixed set of operations but arbitrary encoding. By storing a qubit in the parity of two or four qumodes, all computing processes can be implemented by basis state preparations, continuous-variable exponential-swap operations, and swap-tests. Our formalism inherits the advantages that the quantum information is decoupled from collec…
We introduce and analyse the problem of encoding classical information into different resources of a quantum state. More precisely, we consider a general class of communication scenarios characterised by encoding operations that commute with a unique resource destroying map and leave free states invariant. Our motivating example is given by encoding information into coherences of a quantum system with respect to a fixed basis (with unitaries diagonal in that basis as encodings and the decoherence channel as a resource destroying map), but the generality of the framework allows us to explore ap…
We propose efficient-phase-encoding protocols for continuous-variable quantum key distribution using coherent states and postselection. By these phase encodings, the probability of basis mismatch is reduced and total efficiency is increased. We also propose mixed-state protocols by omitting a part of classical communication steps in the efficient-phase-encoding protocols. The omission implies a reduction of information to an eavesdropper and possibly enhances the security of the protocols. We investigate the security of the protocols against individual beam splitting attack.
Efficient methods for loading given classical data into quantum circuits are essential for various quantum algorithms. In this paper, we propose an algorithm called Approximate Amplitude Encoding that can effectively load all the components of a given real-valued data vector into the amplitude of quantum state, while the previous proposal can only load the absolute values of those components. The key of our algorithm is to variationally train a shallow parameterized quantum circuit, using the results of two types of measurement; the standard computational-basis measurement plus the measurement…
Due to the limitations of present-day quantum hardware, it is especially critical to design algorithms that make the best possible use of available resources. When simulating quantum many-body systems on a quantum computer, straightforward encodings that transform many-body Hamiltonians into qubit Hamiltonians use $N$ of the available basis states of an $N$-qubit system, whereas $2^N$ are in theory available. We explore an efficient encoding that uses the entire set of basis states, where terms in the Hamiltonian are mapped to qubit operators with a Hamiltonian that acts on the basis states in…
Quantum computers can outperform classical computers in certain tasks. However, there are still many challenges to the current quantum computers such as decoherence and fault tolerance, and other drawbacks such as portability and accessibility. In this study, we circumvent these issues by realizing an analog quantum emulation device (AQED) where each qubit state is represented by a unique analog signal. It is possible to do this because previously it was shown that Hermitian operations on a Hilbert space are not unique to quantum systems and can also be applied to a basis of complex signals th…
Measurement-device-independent quantum key distribution (MDIQKD) is a revolutionary protocol since it is physically immune to all attacks on the detection side. However, the protocol still keeps the strict assumptions on the source side that the four BB84-states must be perfectly prepared to ensure security. Some protocols release part of the assumptions in the encoding system to keep the practical security, but the performance would be dramatically reduced. In this work, we present a MDIQKD protocol that requires less knowledge of encoding system to combat the troublesome modulation errors an…
In our recent work, we have examined various fermion to qubit mappings in the context of quantum simulation including the original Bravyi-Kitaev Superfast encoding (OSE) as well as a generalized version (GSE). We return to OSE and compare it against the Jordan-Wigner (JW) transform for quantum chemistry considering the number of qubits required, the Pauli weight of terms in the transformed Hamiltonians, and the $L_1$ norm of the Hamiltonian. We considered a test set of molecular systems known as the Atomization Energy 6 (AE6) as well as Hydrogen lattices. Our results showed that the resource e…
Emerging quantum algorithms that process data require that classical input data be represented as a quantum state. These data-processing algorithms often follow the gate model of quantum computing--which requires qubits to be initialized to a basis state, typically $\lvert 0 \rangle$--and thus often employ state generation circuits to transform the initialized basis state to a data-representation state. There are many ways to encode classical data in a qubit, and the oft-applied approach of basis encoding does not allow optimization to the extent that other variants do. In this work, we thus c…
Calibration of the polarization basis between the transmitter and receiver is an important task in quantum key distribution (QKD). An effective polarization-basis tracking scheme will decrease the quantum bit error rate (QBER) and improve the efficiency of a polarization encoding QKD system. In this paper, we proposed a polarization-basis tracking scheme using only unveiled sifted key bits while performing error correction by legitimate users, rather than introducing additional reference light or interrupting the transmission of quantum signals. A polarization-encoding fiber BB84 QKD prototype…
It is suggested to map the qubits into solid state NMR spin system collective states instead of the states of the individual spin. Such an approach introduces the stable computational basis without any additional actions and allows to obtain the universal set of quantum gates, which operation time is determined only by a RF pulse duration.
We describe methods for simulating general second-quantized Hamiltonians using the compact encoding, in which qubit states encode only the occupied modes in physical occupation number basis states. These methods apply to second-quantized Hamiltonians composed of a constant number of interactions, i.e., linear combinations of ladder operator monomials of fixed form. Compact encoding leads to qubit requirements that are optimal up to logarithmic factors. We show how to use sparse Hamiltonian simulation methods for second-quantized Hamiltonians in compact encoding, give explicit implementations f…
In quantum communications, quantum states are employed for the transmission of information between remote parties. This usually requires sharing knowledge of the measurement bases through a classical public channel in the sifting phase of the protocol. Here, we demonstrate a quantum communication scheme where the information on the bases is shared "non-classically", by encoding this information in the same photons used for carrying the data. This enhanced capability is achieved by exploiting the localization of the photonic wave function, observed when the photons are prepared and measured in …
Compact quantum data representations are essential to the emerging field of quantum algorithms for data analysis. We introduce two new data encoding schemes, QCrank and QBArt, which have a high degree of quantum parallelism through uniformly controlled rotation gates. QCrank encodes a sequence of real-valued data as rotations of the data qubits, allowing for high storage density. QBArt directly embeds a binary representation of the data in the computational basis, requiring fewer quantum measurements and lending itself to well-understood arithmetic operations on binary data. We present several…
We present a formalism for encoding the logical basis of a qubit into subspaces of multiple physical levels. The need for this multilevel encoding arises naturally in situations where the speed of quantum operations exceeds the limits imposed by the addressability of individual energy levels of the qubit physical system. A basic feature of the multilevel encoding formalism is the logical equivalence of different physical states and correspondingly, of different physical transformations. This logical equivalence is a source of a significant flexibility in designing logical operations, while the…
Today's most widely used method of encoding quantum information in optical qubits is the dual-rail basis, often carried out through the polarisation of a single photon. On the other hand, many stationary carriers of quantum information - such as atoms - couple to light via the single-rail encoding in which the qubit is encoded in the number of photons. As such, interconversion between the two encodings is paramount in order to achieve cohesive quantum networks. In this paper, we demonstrate this by generating an entangled resource between the two encodings and using it to teleport a dual-rail …
Measurement-based quantum computing is one of the most promising quantum computing models. Although various universal resource states have been proposed so far, it was open whether only two Pauli bases are enough for both of universal measurement-based quantum computing and its verification. In this paper, we construct a universal hypergraph state that only requires $X$ and $Z$-basis measurements for universal measurement-based quantum computing. We also show that universal measurement-based quantum computing on our hypergraph state can be verified in polynomial time using only $X$ and $Z$-bas…
In the first part of this paper we analyze possible quantum computational capacities due to quantum queries associated with equi-partitions of pure orthogonal states. Special emphasis is given to the parity of product states and to functional parity. The second part is dedicated to a critical review of the relational encoding of multipartite states across (space-like separated) space-time regions; a property often referred to as "quantum nonlocality."
One of the main challenges for the manipulation and storage of multipartite entanglement is its fragility under noise. We present a simple recipe for the systematic enhancement of the resistance of multipartite entanglement against any local noise with a privileged direction in the Bloch sphere. For the case of exact local dephasing along any given basis, and for all noise strengths, our prescription grants full robustness: Even states with exponentially decaying entanglement are mapped to states whose entanglement is constant. In contrast to previous techniques resorting to complex logical-qu…
We present a description of encoding/decoding for a concatenated quantum code that enables both protection against quantum computational errors and the occurrence of one quantum erasure. For this, it is presented how encoding and decoding for quantum graph codes are done, which will provide the protection against the occurrence of computational errors (external code). As internal code is used encoding and decoding via scheme of GHZ states for protection against the occurrence of one quantum erasure.
A Matched Spectral Benchmark of Quantum Inspired Feature Maps
Department of Computer Science, University of Lagos（拉各斯大学计算机科学系）；Department of Physics, University of Lagos（拉各斯大学物理系）；Department of Chemical Engineering, University of Notre Dame（圣母大学化学工程系）
All known qudit-based prepare-and-measure quantum key distribution (PM-QKD) schemes are more error resilient than their qubit-based counterparts. Their high error resiliency comes partly from the careful encoding of multiple bits of signals used to generate the raw key in each transmitted qudit so that the same eavesdropping attempt causes a higher bit error rate (BER) in the raw key. Here I show that highly error-tolerant PM-QKD schemes can be constructed simply by encoding one bit of classical information in each transmitted qudit in the form $(|i\rangle\pm|j\rangle)/\sqrt{2}$, where $|i\ran…
Representation-split Carleman lattice Boltzmann with near-unit step success probability on quantum computers
Chalmers University of Technology（查尔姆斯理工大学）；Fondazione Istituto Italiano di TecnologiaCenter for Life Nano-Neuroscience at La Sapienza（意大利技术研究院基金会拉萨皮恩扎生命纳米神经科学中心）
Simulating electronic structure on a quantum computer requires encoding of fermionic systems onto qubits. Common encoding methods transform a fermionic system of $N$ spin-orbitals into an $N$-qubit system, but many of the fermionic configurations do not respect the required conditions and symmetries of the system so the qubit Hilbert space in this case may have unphysical states and thus can not be fully utilized. We propose a generalized qubit-efficient encoding (QEE) scheme that requires the qubit number to be only logarithmic in the number of configurations that satisfy the required conditi…
