US-12619897-B2 - Method for simulating and evaluating an electronic system

Abstract

Quantum mechanical systems, such as for instance electronic states in molecules or solid bodies, can be simulated using quantum computers. However, at present quantum computers only provide a limited quantity of qubits for the calculation. This deficiency is attributable to unsolved problems in connection with inherent noise and scalability, with the result that quantum computers currently only enable simulations of small quantum systems. A method simulates and evaluates an electronic system with a continuous spectral density on the basis of the interruption of the quantum simulation by measurements. The quantum simulation is interrupted to read the qubits, the qubit measurements are stored in a classical parity register and restored to the qubits, and the simulation is continued after the restore.

Inventors

• Juha Leppäkangas

Assignees

• HQS Quantum Simulations GmbH

Dates

Publication Date

20260505

Application Date

20201214

Priority Date

20200313

Claims (6)

1. 1 . A method for simulating and evaluating an electronic system having a continuous spectral density, the method comprising: generating a continuous spectral function in a quantum simulation of an electronic cluster-bath model using a quantum computer having a plurality of qubits, wherein features of the electronic system are simulated on individual qubits and read from the qubits; wherein the quantum simulation is interrupted to read the qubits, the qubit measurements are stored in a classical parity register and restored to the qubits, and the simulation is continued after the restore; wherein the simulation of the electronic system comprises an accurate simulation of a cluster, as well as a simulation of a bath and an electron hopping interaction according to a mean-field approach for describing electron-electron correlations in the modeled electronic system; and wherein the reading of the qubits occurs in a Trotter step which iteratively carries out the steps of: applying a time evolution operation U QC (dt,R) taking into account parities stored in the parity register R; exchanging excitation states between a respective bath qubit and an auxiliary gubit assigned to said bath qubit; measuring a state of the auxiliary gubit; changing an associated parity R→R+1 (mod2) if an initial state of the auxiliary qubit and the measured state of the auxiliary qubit do not match; and setting an initial state of the auxiliary gubit to 0 with a probability ρ − and to 1 with a probability ρ + , and returning to the first step.
2. 2 . The method according to claim 1 , wherein sharp, spectral peaks of states of the qubits of the quantum computer associated with the bath are broadened to Lorentzian functions, thereby controlling a broadening of the peaks.
3. 3 . The method according to claim 1 , wherein the auxiliary qubit is initialized to state 1.
4. 4 . The method according to claim 1 , wherein the parity R is changed only if the auxiliary qubit is measured in state 0.
5. 5 . The method according to claim 1 , wherein auxiliary qubits are uniquely assigned to a plurality of bath qubits and a plurality of auxiliary qubits are read in parallel.
6. 6 . The method according to claim 1 , wherein the antisymmetry of the fermionic wave function is taken into account by coding using the Jordan-Wigner decomposition.

Description

CROSS REFERENCE TO RELATED APPLICATIONS This application is the National Stage of PCT/DE2020/101060 filed on Dec. 14, 2020, which claims priority under 35 U.S.C. § 119 of German Application No. 10 2020 106 959.6 filed on Mar. 13, 2020, the disclosure of which is incorporated by reference. The international application under PCT article 21 (2) was not published in English. The present invention relates to a method for simulating and evaluating an electronic system, in particular a solid body or a molecule with a continuous spectral density using a quantum computer having a plurality of qubits, wherein features of the electronic system are simulated on individual qubits and read from the qubits. Such a method is already known from DE 10 2019 135 807 A1. This solves the problem of inherent noise and scalability deficiencies for the calculation and simulation of quantum mechanical systems, such as electronic systems, by means of a simulator for large, continuous quantum systems by using the noise as a resource to produce a continuous bath. A quantum computer is a technically well-controlled quantum system of which the calculation is based on the use of the laws of quantum mechanics. The basic unit of the quantum computer is the quantum bit, the so-called qubit. Like the well-known classical bit, the qubit can assume the values 0 and 1. The main difference from the classical states is that the quantum memory can be in any superposition of the possible bit strings. It follows that a quantum register of N qubits encodes the information of 2N variables. A sufficiently large and well-functioning quantum computer can be used to solve certain mathematical problems that cannot be solved by classical computers. Such problems also include simulations of other quantum mechanical systems. However, there are many technical difficulties in building a large quantum computer. These difficulties can be roughly broken down into two major challenges, namely isolating the qubits from a noisy environment and controlling a large number of qubits simultaneously. These two sets of problems are not independent of one another, and improving the quantum computer with regard to one of the two problems usually adversely affects the quantum computer with regard to the other. It is currently possible to build quantum computers with around 20 to 50 qubits that work comparatively well. It is expected that more than 100 physical qubits will be available for commercial use in the near future. A very promising application of small quantum computers is the simulation of other quantum mechanical systems. In fact, it can be shown that quantum simulation algorithms can be faster than any classical computer, even for a small number of qubits. Against this background, the present invention is based on the object of providing an alternative to the previously known method for simulating and evaluating an electronic system by artificially generating a continuous electronic spectrum that makes it possible to simulate large electronic quantum systems with a small number of qubits. This is achieved by a method for simulating and evaluating an electronic system according to the features of independent claim 1. Further meaningful configurations of such a system can be found in the subsequent dependent claims. According to the invention, gate-based quantum simulation is considered in the present case. Here, the evolution of system time is reproduced by fast control pulses applied to physical qubits, which in turn describe the quantum state of the modeled system in some way. More specifically, the quantum simulation generated by the quantum computer is controlled by the Hamiltonian HQc(t), which works with qubits of the quantum computer. The simulated system is described by the Hamiltonian H, which controls the time evolution of the electrons. These systems are ideally equivalent, meaning that there is an accurate mapping between the physical quantum state and the simulated quantum state. The quantum simulation time evolution operator UQc is designed to reproduce the system time evolution operator U in the following sufficient approximation: U=exp [-iHt]≈UQ⁢C=T⁢exp [-i⁢∫0tdt′⁢HQ⁢C(t′)] Units are used in which h=1 is applicable. A gate-based quantum evolution is created by successive applications of identical Trotter steps, each representing a small time evolution over the simulation time dt. Ideally, each sequence performs the operation UQC(dt)=∏setsexp⁡(-iHset⁢dt) Here, all terms oscillate within Hset. All sets together cover all terms of the simulated Hamiltonian. The multiplication takes place in a selected, optimal order. The total time evolution over time t=ndt is then UQC(t)=[UQC(d⁢t)]n. A widely studied model of various electronic systems that the present quantum computer system can simulate is the cluster-bath model defined by a Hamiltonian of the type H=HC+HB+HIHC=∑pq∈clustertpq⁢cp†⁢cq+12⁢∑pqrs∈clusterhpqrs⁢cp†⁢cq†⁢cr⁢csHB=∑i∈bathωi⁢ci†⁢ciHI=∑p∈cluster,