Quantum Coprocessor Research Articles

A QSimulator Quantum Programming System

In this paper the authors propose their own QSimulator quantum programming system, which is a software tool for deve­loping and debugging quantum algorithms in a high-level C++ language. The basic structure of the presented system is de­scribed, including quantum algorithms and quantum operations, available to the programmer. The components of the system and their fundamental basis are briefly outlined. This system emulates the behaviour of a quantum coprocessor in a standard computational basis and thus can be used for debugging and programming quantum algorithms in the language of quantum circuits. The system proposed by the authors also implements the Grover search algorithm and the Durr-Hoyer minimization algorithm based on it. Many tasks can be formulated in terms of the search task. In particular, the SAT problem. In this article, we also propose a variant of constructing an oracle in the form of a quantum circuit for the SAT problem, which can be integrated into the Grover algorithm implemented in the presented system. Automatic oracle generation for the SAT task will help save time in developing quantum algorithms related to this task when working with our system.

A superconducting adiabatic neuron in a quantum regime.

We explore the dynamics of an adiabatic neural cell of a perceptron artificial neural network in a quantum regime. This mode of cell operation is assumed for a hybrid system of a classical neural network whose configuration is dynamically adjusted by a quantum co-processor. Analytical and numerical studies take into account non-adiabatic processes as well as dissipation, which leads to smoothing of quantum coherent oscillations. The obtained results indicate the conditions under which the neuron possesses the required sigmoid activation function.

RESEARCH OF DIGITAL QUBITES FOR HETEROGENEOUS DIGITAL QUANTUM COPROCESSORS

Recently, interest is growing towards real quantum computers, which are analog and probabilistic devices by nature. Theinterest is also growing to their digital version, both software and hardware. One approach to the construction of real quantum computers is to use quantum chips. The hardware implementation of digital quantum computers involves the use offield programmable gate arrays.A digital quantum coprocessor has already been createdwhich has over a thousand digital qubitsand can perform such complex algorithms as a quantum Fourier transformation. The created and working digital quantum coprocessorcan already be used to work out various quantum algorithms, algorithms for the interaction of a classic computer and its quantum coprocessor, as well as for research various options for building digital qubits.The purpose of this work is to study the effect of the accuracy of the presentation of the state of digital qubit on the probability of obtaining the correct results of the digitalquantum coprocessor.For the study, a heterogeneous digital quantum coprocessor with thirty two digital qubits is selected, which will perform the Fourier quantum transformation. The article describes the basics of building digital quantum coprocessors.Schemes that illustrate the interaction of a classic computer and a quantum coprocessor, the architecture of the coprocessor and the possible structures of its digital qubitsare given. Two variants of the coprocessor, homogeneous one with one pseudo-random codes generator and one comparator, and heterogeneous one, with a generator and a comparator in each digital quantum cell, from which digital qubits consist, are shown.Two options for comparators are also shown -with a direct functional converter and with reverse one.In this work, the influence of the length of the qubit state codes of heterogeneous digital quantum coprocessors on the probability of the correct results formation is investigated.It was shown that the probability of obtaining the correct results at the output of the digital heterogeneous coprocessor is sharply (up to fifty percent) improved with a decrease of the qubit state code length, that is, with a decrease in the coprocessor hardware cost.With a length of a code equal to twobits, the quality of the operation of the heterogeneous coprocessor becomes commensurate with the quality of the homogeneous one. The need for additional research in this direction, including with homogeneous coprocessors, is shown.

CAPACITIVE COMPLEXITY OF DETERMINING GCD IN THE SHOR S ALGORITHM

The article analyzes the results of finding the period r of the function y = axmodM (a is a random number) which is used in the Shor's factorization algorithm for quantum computers. The module M is the product of two primes p and q. The article analyzes the solutions r obtained for various a, for which the capacitive complexity H of finding the greatest common divisor GCD(ar/2 + 1, M) is the least. A digital quantum computer is a classic processor and its digital quantum coprocessor. A digital quantum coprocessor with hundreds and thousands of digital qubits can be implemented in one programmable logic integrated circuit FPGA. In the Shor’s algorithm, the factorization problem of the number M reduces to the problem of determining the period r of the function y. It is known that GCD(ar/2 + 1, M) can be a divisor of the number M The task of the quantum coprocessor in implementing the Shor’s algorithm is to find the period r. After that it is necessary to find the GCD. Since for random a the problem of finding the period r has many solutions, these solutions can be compared by the value of one of the arguments when finding the GCD - the number ar / 2 . In this case, H = (rlog2a)/2 is taken for analysis. It approximately represents the bit depth of binary codes that a classic computer will have to process when determining the GCD. H can vary over a wide range from tens to thousands of bits even for small values of M. In this research the period r, which ensures the least complexity of the subsequent task of finding the GCD, is most often a solution for a = 3 and a = 2, but it can also occur often with other values of a. To clarify the revealed patterns, especially for large M, it is necessary to conduct additional research.

Demonstration of Adiabatic Variational Quantum Computing with a Superconducting Quantum Coprocessor.

Adiabatic quantum computing enables the preparation of many-body ground states. Realization poses major experimental challenges: Direct analog implementation requires complex Hamiltonian engineering, while the digitized version needs deep quantum gate circuits. To bypass these obstacles, we suggest an adiabatic variational hybrid algorithm, which employs short quantum circuits and provides a systematic quantum adiabatic optimization of the circuit parameters. The quantum adiabatic theorem promises not only the ground state but also that the excited eigenstates can be found. We report the first experimental demonstration that many-body eigenstates can be efficiently prepared by an adiabatic variational algorithm assisted with a multiqubit superconducting coprocessor. We track the real-time evolution of the ground and excited states of transverse-field Ising spins with a fidelity that can reach about 99%.

Enhancing a Near-Term Quantum Accelerator's Instruction Set Architecture for Materials Science Applications

Quantum computers with tens to hundreds of noisy qubits are being developed today. To be useful for real-world applications, we believe that these near-term systems cannot simply be scaled-down non-error-corrected versions of future fault-tolerant large-scale quantum computers. These near-term systems require specific architecture and design attributes to realize their full potential. To efficiently execute an algorithm, the quantum coprocessor must be designed to scale with respect to qubit number and to maximize useful computation within the qubits' decoherence bounds. In this work, we employ an application-system-qubit co-design methodology to architect a near-term quantum coprocessor. To support algorithms from the real-world application area of simulating the quantum dynamics of a material system, we design a (parameterized) arbitrary single-qubit rotation instruction and a two-qubit entangling controlled-Z instruction. We introduce dynamic gate set and paging mechanisms to implement the instructions. To evaluate the functionality and performance of these two instructions, we implement a two-qubit version of an algorithm to study a disorder-induced metal-insulator transition and run 60 random instances of it, each of which realizes one disorder configuration and contains 40 two-qubit instructions (or gates) and 104 single-qubit instructions. We observe the expected quantum dynamics of the time-evolution of this system.

Self-verifying variational quantum simulation of lattice models.

Hybrid classical-quantum algorithms aim to variationally solve optimization problems using a feedback loop between a classical computer and a quantum co-processor, while benefiting from quantum resources.Here we present experiments that demonstrate self-verifying, hybrid, variational quantum simulation of lattice models in condensed matter and high-energy physics. In contrast to analogue quantum simulation, this approach forgoes the requirement of realizing the targeted Hamiltonian directly in the laboratory, thus enabling the study of a wide variety of previously intractable target models. We focus on the lattice Schwinger model, a gauge theory of one-dimensional quantum electrodynamics. Our quantum co-processor is a programmable, trapped-ion analogue quantum simulator with up to 20 qubits, capable of generating families of entangled trial states respecting the symmetries of the target Hamiltonian. We determine ground states, energy gaps and additionally, by measuring variances of the Schwinger Hamiltonian, we provide algorithmic errors for the energies, thus taking a step towards verifying quantum simulation.

QPCF: Higher-Order Languages and Quantum Circuits

qPCF is a paradigmatic quantum programming language that extends PCF with quantum circuits and a quantum co-processor. Quantum circuits are treated as classical data that can be duplicated and manipulated in flexible ways by means of a dependent type system. The co-processor is essentially a standard QRAM device, albeit we avoid to store permanently quantum states in between two co-processor’s calls. Despite its quantum features, qPCF retains the classic programming approach of PCF. We introduce qPCF syntax, typing rules, and its operational semantics. We prove fundamental syntactic properties of the system. Moreover, we provide some higher-order examples of circuit encoding.

FPGA-based Digital Quantum Coprocessor

FPGA-based Digital Quantum Coprocessor

Coprocessors for quantum devices

Quantum devices, from simple fixed-function tools to the ultimate goal of a universal quantum computer, will require high quality, frequent repetition of a small set of core operations, such as the preparation of entangled states. These tasks are perfectly suited to realisation by a co-processor or supplementary instruction set, as is common practice in modern CPUs. In this paper, we present two quintessentially quantum co-processor functions: production of a GHZ state, and implementation of optimal universal (asymmetric) quantum cloning. Both are based on the evolution of a fixed Hamiltonian. We introduce a new technique for deriving the parameters of these Hamiltonians based on the numerical integration of Toda-like flows.

Efficient Variational Quantum Simulator Incorporating Active Error Minimization

One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc, in order to accelerate the process of discovery. It is important to ask: Can this be achieved using near future quantum processors, of modest size and under imperfect control, or must it await the more distant era of large-scale fault-tolerant quantum computing? Here we propose a variational method involving closely integrated classical and quantum coprocessors. We presume that all operations in the quantum coprocessor are prone to error. The impact of such errors is minimised by boosting them artificially and then extrapolating to the zero-error case. In comparison to a more conventional optimised Trotterisation technique, we find that our protocol is efficient and appears to be fundamentally more robust against error accumulation.