We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably bounded amplitudes, the algorithm requires resources that are polynomial in the number of qubits. Such sequences of states occur naturally in the problem of encoding a classical probability distribution in a quantum register.
The efficient preparation of input distributions is an important problem in obtaining quantum advantage in a wide range of domains. We propose a novel quantum algorithm for the efficient preparation of arbitrary normal distributions in quantum registers. To the best of our knowledge, our work is the first to leverage the power of Mid-Circuit Measurement and Reuse (MCMR), in a way that is broadly applicable to a range of state-preparation problems. Specifically, our algorithm employs a repeat-until-success scheme, and only requires a constant-bounded number of repetitions in expectation. In the…
We present many ensembles of states that can be remotely prepared by using minimum classical bits from Alice to Bob and their previously shared entangled state and prove that we have found all the ensembles in two-dimensional case. Furthermore we show that any pure quantum state can be remotely and faithfully prepared by using finite classical bits from Alice to Bob and their previously shared nonmaximally entangled state though no faithful quantum teleportation protocols can be achieved by using a nonmaximally entangled state.
Recently, a series of articles by Combes et al. has shown that it was possible to greatly improve the measurement rate of a register of qubits for given detector resources by means of a clever feedback control scheme. However, this speed-up came at an exponential cost in terms of complexity and memory use. In this article, I propose a simple efficient algorithm --exponentially more frugal in memory and less complex to implement-- which is asymptotically as fast. I use extensively the implicit classicality of the situation to provide a slightly more straightforward interpretation of the results…
We present a protocol for encoding $N$ real numbers stored in $N$ memory registers into the amplitudes of the quantum superposition that describes the state of $\log_2N$ qubits. This task is one of the main steps in quantum machine learning algorithms applied to classical data. The protocol combines partial CNOT gate rotations with probabilistic projection onto the desired state. The number of additional ancilla qubits used during the implementation of the protocol, as well as the number of quantum gates, scale linearly with the number of qubits in the processing register and hence logarithmic…
Quantum computing promises to provide exponential speed-ups to certain classes of problems. In many such algorithms, a classical vector $\mathbf{b}$ is encoded in the amplitudes of a quantum state $\left |b \right >$. However, efficiently preparing $\left |b \right >$ is known to be a difficult problem because an arbitrary state of $Q$ qubits generally requires approximately $2^Q$ entangling gates, which results in significant decoherence on today's Noisy Intermediate Scale Quantum (NISQ) computers. We present a deterministic (nonvariational) algorithm that allows one to flexibly reduce the qu…
We propose a fault tolerant loading scheme to produce an array of fermions in an optical lattice of the high fidelity required for applications in quantum information processing and the modelling of strongly correlated systems. A cold reservoir of Fermions plays a dual role as a source of atoms to be loaded into the lattice via a Raman process and as a heat bath for sympathetic cooling of lattice atoms. Atoms are initially transferred into an excited motional state in each lattice site, and then decay to the motional ground state, creating particle-hole pairs in the reservoir. Atoms transferre…
Both classical and quantum computations operate with the registers of bits. At nanometer scale the quantum fluctuations at the position of a given bit, say, a quantum dot, not only lead to the decoherence of quantum state of this bit, but also affect the quantum states of the neighboring bits, and therefore affect the state of the whole register. That is why the requirement of reliable separate access to each bit poses the limit on miniaturization, i.e, constrains the memory capacity and the speed of computation. In the present paper we suggest an algorithmic way to tackle the problem of const…
Merely by existing, all physical systems register information. And by evolving dynamically in time, they transform and process that information. The laws of physics determine the amount of information that a physical system can register (number of bits) and the number of elementary logic operations that a system can perform (number of ops). The universe is a physical system. This paper quantifies the amount of information that the universe can register and the number of elementary operations that it can have performed over its history. The universe can have performed no more than $10^{120}$ op…
In a previous paper [quant-ph/0408045] we described a quantum algorithm to prepare an arbitrary state of a quantum register with arbitrary fidelity. Here we present an alternative algorithm which uses a small number of quantum oracles encoding the most significant bits of the absolute value of the complex amplitudes, and a small number of oracles encoding the most significant bits of the phases. The algorithm given here is considerably simpler than the one described in [quant-ph/0408045], on the assumption that a sufficient amount of knowledge about the distribution of the absolute values of t…
We describe and analyze a hybrid approach to scalable quantum computation based on an optically connected network of few-qubit quantum registers. We show that probabilistically connected five-qubit quantum registers suffice for deterministic, fault-tolerant quantum computation even when state preparation, measurement, and entanglement generation all have substantial errors. We discuss requirements for achieving fault-tolerant operation for two specific implementations of our approach.
We present a scheme in which any pure qubit $|ϕ=\cosθ|0+\sinθe^{i\varp hi}|1$ could be remotely prepared by using minimum classical bits and the previously shared non-maximally entangled states, on condition that the receiver holds the knowledge of $θ$. Several methods are available to check the trade-off between the necessary entanglement resource and the achievable fidelity.
We investigate in detail the effects of a QND vibrational number measurement made on single ions in a recently proposed measurement scheme for the vibrational state of a register of ions in a linear rf trap [C. D'Helon and G.J. Milburn, Phys. Rev. A 54, 5141 (1996)]. The performance of a measurement shows some interesting patterns which are closely related to searching.
Preparation of a quantum register is an important step in quantum computation and quantum information processing. It is straightforward to build a simple quantum state such as $|i_1 i_2 ... i_n\ket$ with $i_j$ being either 0 or 1, but is a non-trivial task to construct an {\it arbitrary} superposed quantum state. In this Paper, we present a scheme that can most generally initialize a quantum register with an arbitrary superposition of basis states. Implementation of this scheme requires $O(Nn^2)$ standard 1- and 2-bit gate operations, {\it without introducing additional quantum bits}. Applicat…
It is proposed to use four atomic optical energy levels as a two qubit quantum register. A single Pr3+ atom in a monocrystal LaF3 subjected to resonant laser irradiation is used as an example to illustrate the implementation of the universal set of quantum gates. The equilibrium state of this physical system is a desirable input state for quantum computation and therefore there is no need for its special preparation procedure.
We quantify and analyze the controller's power in controlled remote state preparation schemes. Our analysis provides a lower bound on the control power required for controlled remote preparation of arbitrary D-dimensional states. We evaluate several existing controlled remote state preparation protocols and show that some proposed non-maximally entangled channels are not suitable for perfect controlled remote preparation of arbitrary quantum states from the con- troller's point of view. We find that for remotely preparing D-dimensional states, the entropy of each controller should be no less t…
Quantum control of large spin registers is crucial for many applications ranging from spectroscopy to quantum information. A key factor that determines the efficiency of a register for implementing a given information processing task is its network topology. One particular type, called star-topology, involves a central qubit uniformly interacting with a set of ancillary qubits. A particular advantage of the star-topology quantum registers is in the efficient preparation of large entangled states, called NOON states, and their generalized variants. Thanks to the robust generation of such correl…
We propose a deterministic remote state preparation scheme for photon polarization qubit states, where entanglement, local operations and classical communication are used. By consuming one maximally entangled state and two classical bits, an arbitrary (either pure or mixed) qubit state can be prepared deterministically at a remote location. We experimentally demonstrate the scheme by remotely preparing 12 pure states and 6 mixed states. The fidelities between the desired and achieved states are all higher than 0.99 and have an average of 0.9947.
We propose and experimentally verify a novel method for the remote preparation of entangled bits (ebits) made of a single-photon coherently delocalized in two well-separated temporal modes. The proposed scheme represents a remotely tunable source for tailoring arbitrary ebits, whether maximally or non-maximally entangled, which is highly desirable for applications in quantum information technology. The remotely prepared ebit is studied by performing homodyne tomography with an ultra-fast balanced homodyne detection scheme recently developed in our laboratory.
Quantum computing algorithms require that the quantum register be initially present in a superposition state. To achieve this, we consider the practical problem of creating a coherent superposition state of several qubits. Owing to considerations of quantum statistics, this requires that the entropy of the system go down. This, in turn, has two practical implications: (i) the initial state cannot be controlled; (ii) the temperature of the system must be reduced. These factors, in addition to decoherence and sensitivity to errors, must be considered in the implementation of quantum computers.
It is shown that (i) all entangled states can be mapped by single-copy measurements into probability distributions containing secret correlations, and (ii) if a probability distribution obtained from a quantum state contains secret correlations, then this state has to be entangled. These results prove the existence of a two-way connection between secret and quantum correlations in the process of preparation. They also imply that either it is possible to map any bound entangled state into a distillable probability distribution or bipartite bound information exists.
In classical Arthur-Merlin games, the class of languages whose membership proofs can be verified by Arthur using logarithmic space (AM(log-space)) coincides with the class P \cite{Co89}. In this note, we show that if Arthur has a fixed-size quantum register (the size of the register does not depend on the length of the input) instead of another source of random bits, membership in any language in NP can be verified with any desired error bound.
We describe and analyze an efficient register-based hybrid quantum computation scheme. Our scheme is based on probabilistic, heralded optical connection among local five-qubit quantum registers. We assume high fidelity local unitary operations within each register, but the error probability for initialization, measurement, and entanglement generation can be very high (~5%). We demonstrate that with a reasonable time overhead our scheme can achieve deterministic non-local coupling gates between arbitrary two registers with very high fidelity, limited only by the imperfections from the local uni…
In this paper, I take a step toward answering the following question: for m different small circuits that compute m orthogonal n qubit states, is there a small circuit that will map m computational basis states to these m states without any input leaving any auxiliary bits changed. While this may seem simple, the constraint that auxiliary bits always be returned to 0 on any input (even ones besides the m we care about) led me to use sophisticated techniques. I give an approximation of such a unitary in the m = 2 case that has size polynomial in the approximation error, and the number of qubits…
We propose a general scheme for dissipatively preparing arbitrary pure quantum states on a multipartite qubit register in a finite number of basic control blocks. Our "splitting-subspace" approach relies on control resources that are available in a number of scalable quantum technologies (complete unitary control on the target system, an ancillary resettable qubit and controlled-not gates between the target and the ancilla), and can be seen as a "quantum-controller" implementation of a sequence of classical feedback loops. We show how a large degree of flexibility exists in engineering the req…
We report preparation in the ground state of collective modes of motion of two trapped 9Be+ ions. This is a crucial step towards realizing quantum logic gates which can entangle the ions' internal electronic states. We find that heating of the modes of relative ion motion is substantially suppressed relative to that of the center-of-mass modes, suggesting the importance of these modes in future experiments.
The amount of information transferred during standard quantum teleportation or remote state preparation is equal to the preparation information of the transmitted state, rather than the classical communication required by respective protocol. This is shown by noting that the information required to specify the operation that verifies the transmitted state is identical to the preparation information, at the given level of precision m (in bits). Depending on the resolution of the projective Hilbert space, the preparation information can be made arbitrarily precise and hence indefinitely larger t…
Due to inhomogeneous broadening, the absorption lines of rare-earth-ion dopands in crystals are many order of magnitudes wider than the homogeneous linewidths. Several ways have been proposed to use ions with different inhomogeneous shifts as qubit registers, and to perform gate operations between such registers by means of the static dipole coupling between the ions. In this paper we show that in order to implement high-fidelity quantum gate operations by means of the static dipole interaction, we require the participating ions to be strongly coupled, and that the density of such strongly cou…
The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical interest using modest numbers of quantum bits. Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm. The recursive algorithm reduces the number of quantum bits required for the readout register from about 20 to 4. Mappings of the molecul…
We propose a deterministic remote state preparation (RSP) scheme for preparing an arbitrary (including pure and mixed) qubit, where a partially entangled state and finite classical communication are used. To our knowledge, our scheme is the first RSP scheme that fits into this category. One other RSP scheme proposed by Berry shares close features, but can only be used to prepare an arbitrary pure qubit. Even so, our scheme saves classical communication by approximate 1 bit per prepared qubit under equal conditions. When using a maximally entangled state, the classical communication for our sch…
Shannon in celebrated works had shown that n bits of shared key is necessary and sufficient to transmit n-bit classical information in an information-theoretically secure way. Ambainis, Mosca, Tapp and de Wolf in quant-ph/0003101 considered a more general setting, referred to as Private quantum channels, in which instead of classical information, quantum states are required to be transmitted and only one-way communication is allowed. They show that in this case 2n bits of shared key is necessary and sufficient to transmit an n-qubit state. We consider the most general setting in which we allow…
We propose a scheme to measure the parity of two distant qubits, while ensuring that losses on the quantum channel between them does not destroy coherences within the parity subspaces. This capability enables deterministic preparation of highly entangled qubit states whose fidelity is not limited by the transmission loss. The key observation is that for a probe electromagnetic field in a particular quantum state, namely a superposition of two coherent states of opposite phases, the transmission loss stochastically applies a near-unitary back-action on the probe state. This leads to a parity me…
Quantum computers will be able solve important problems with significant polynomial and exponential speedups over their classical counterparts, for instance in option pricing in finance, and in real-space molecular chemistry simulations. However, key applications can only achieve their potential speedup if their inputs are prepared efficiently. We effectively solve the important problem of efficiently preparing quantum states following arbitrary continuous (as well as more general) functions with complexity logarithmic in the desired resolution, and with rigorous error bounds. This is enabled …
Distinct Feedback-Strength Requirements for Quantum-State Ensemble Preparation under Channel-Equivalent Monitoring
School of Computer Science and Engineering, Macau University of Science and Technology（澳门科技大学计算机科学与工程学院）；Zhuhai MUST Science and Technology Research Institute（珠海澳门科技大学研究院）；School of Information and Software Engineering, University of Electronic Science and Technology of China（电子科技大学信息与软件工程学院）
Initializing classical data in a quantum device is an essential step in many quantum algorithms. As a consequence of measurement and noisy operations, some algorithms need to reinitialize the prepared state several times during its execution. In this work, we propose a quantum state preparation algorithm called CVO-QRAM with computational cost O(kM), where M is the number of nonzero probability amplitudes and $k$ is the maximum number of bits with value 1 in the patterns to be stored. The proposed algorithm can be an alternative to create sparse states in future NISQ devices.
Remote state preparation (RSP) is the act of preparing a quantum state at a remote location without actually transmitting the state itself. Using at most two classical bits and a single shared maximally entangled state, one can in theory remotely prepare any qubit state with certainty and with perfect fidelity. However, in any experimental implementation the average fidelity between the target and output states cannot be perfect. In order for an RSP experiment to demonstrate genuine quantum advantages, it must surpass the optimal threshold of a comparable classical protocol. Here we study the …
Loading classical data into quantum registers is one of the most important primitives of quantum computing. While the complexity of preparing a generic quantum state is exponential in the number of qubits, in many practical tasks the state to prepare has a certain structure that allows for faster preparation. In this paper, we consider quantum states that can be efficiently represented by (reduced) decision diagrams, a versatile data structure for the representation and analysis of Boolean functions. We design an algorithm that utilises the structure of decision diagrams to prepare their assoc…
State preparation and measurement (SPAM) errors limit the performance of near-term quantum computers and their potential for practical application. SPAM errors are partly correctable after a calibration step that requires, for a complete implementation on a register of $n$ qubits, $2^n$ additional measurements. Here we introduce an approximate but efficient method for multiqubit SPAM error characterization and mitigation requiring the classical processing of $2^n \! \times 2^n$ matrices, but only $O(4^k n^2)$ measurements, where $k=O(1)$ is the number of qubits in a correlation volume. We demo…
The quantum uncertainty principle famously predicts that there exist measurements that are inherently incompatible, in the sense that their outcomes cannot be predicted simultaneously. In contrast, no such uncertainty exists in the classical domain, where all uncertainty results from ignorance about the exact state of the physical system. Here, we critically examine the concept of preparation uncertainty and ask whether similarly in the quantum regime, some of the uncertainty that we observe can actually also be understood as a lack of information (LOI), albeit a lack of quantum information. W…
A `register' in quantum information processing -- is composition of k quantum systems, `qudits'. The dimensions of Hilbert spaces for one qudit and whole quantum register are d and d^k respectively, but we should have possibility to prepare arbitrary entangled state of these k systems. Preparation and arbitrary transformations of states are possible with universal set of quantum gates and for any d may be suggested such gates acting only on single systems and neighbouring pairs. Here are revisited methods of construction of Hamiltonians for such universal set of gates and as a concrete new exa…
Quantum teleportation uses prior shared entanglement and classical communication to send an unknown quantum state from one party to another. Remote state preparation (RSP) is a similar distributed task in which the sender knows the entire classical description of the state to be sent. (This may also be viewed as the task of non-oblivious compression of a single sample from an ensemble of quantum states.) We study the communication complexity of approximate remote state preparation, in which the goal is to prepare an approximation of the desired quantum state. Jain [Quant. Inf. & Comp., 2006] s…
Verifiable blind quantum computing allows a client with poor quantum devices to delegate universal quantum computing to a remote quantum server in such a way that the client's privacy is protected and the honesty of the server is verified. In existing protocols, the client has to send single-qubit states to the server. These states might be decohered by the channel noise. Furthermore, the client hides some "trap" qubits in the server's register so that the client can detect the server's deviation. In reality, however, these trap qubits are disturbed by imperfect operations by the server, which…
Solid-state nuclear spins surrounding individual, optically addressable qubits provide a crucial resource for quantum networks, computation and simulation. While hosts with sparse nuclear spin baths are typically chosen to mitigate qubit decoherence, developing coherent quantum systems in nuclear spin-rich hosts enables exploration of a much broader range of materials for quantum information applications. The collective modes of these dense nuclear spin ensembles provide a natural basis for quantum storage, however, utilizing them as a resource for single spin qubits has thus far remained elus…
We study the amount of classical communication needed for distributed quantum information processing. In particular, we introduce the concept of "remote preparation" of a quantum state. Given an ensemble of states, Alice's task is to help Bob in a distant laboratory to prepare a state of her choice. We find several examples of an ensemble with an entropy S where the remote preparation can be done with a communication cost lower than the amount (2S) required by standard teleportation. We conjecture that, for an arbitrary N-dimensional pure state, its remote preparation requires 2log_2 N bits of…
