METHOD FOR ERROR REDUCTION IN A QUANTUM COMPUTER

Abstract

It is already known that quantum computers can be used to simulate materials and molecules. However, quantum computers are error-prone and exhibit intrinsic noise, which has so far made the real technical application of quantum computers impossible. Approaches are already known from the prior art which, despite the error susceptibility, allow meaningful simulations of quantum mechanical systems to be created, but the errors still exist. Building on this, the invention now makes it possible to reduce the errors and to include the errors as part of the simulation. In addition, the invention makes it possible to inhibit the effect of intrinsic noise. This further improves the technical applicability of quantum computers for simulating materials and molecules.

Claims

1. A method for simulating a quantum mechanical system using a quantum computer which has a plurality of qubits (6, 7, 8), first a quantum mechanical model of the quantum mechanical system being mapped onto qubits (6, 7, 8) of the quantum computer and being simulated thereon and, within the context of evaluating the simulation (1), simulation results (10) being extracted by measurements of the quantum computer, wherein the simulation results (10) are influenced by a plurality of methods for error reduction which are used to complement one another and which reduce the effects of noise (2) acting on the quantum computer.

2. The method according to claim 1, wherein the simulation (1) of the quantum mechanical system involves mapping (3) logical states of the qubits (6, 7, 8) onto physical states of the qubits, this mapping (3) being optimized for error reduction.

3. The method according to claim 2, wherein the logical states of the qubits are each mapped onto the physical states of the qubits (6, 7, 8) for arbitrary rotation angles φ using a transformation operator $U\left(\varphi \right)=\exp \left(-i\varphi {\sigma }_y/2\right)=I\cdot \cos \left(\varphi /2\right)-i{\sigma }_y\sin \left(\varphi /2\right),$ where I is the identity matrix and σy is a Pauli matrix in a space spanned by the states $\left|0\right..Math.\equiv \left(1,0\right)\text{und}\left|1\right..Math.\equiv \left(0,1\right).$ .

4. The method according to claim 3, wherein the rotation angle φ for each qubit (6, 7, 8) is chosen such that the qubit (6, 7, 8), due to the inherent noise of the quantum computer, decays into a state which describes a meaningful physical system state of the simulated quantum mechanical system.

5. The method according to claim 2, wherein within the context of mapping (3) the quantum mechanical system onto the qubits (6, 7, 8) of the quantum computer, the mapping (3) is chosen such that each qubit (6, 7, 8) describes a meaningful physical single-particle state of the quantum mechanical system.

6. The method according to claim 5, wherein the mapping (3) of the quantum mechanical system onto the qubits (6, 7, 8) of the quantum computer is chosen such that each qubit (6, 7, 8) continues to describe a meaningful physical single-particle state of the quantum mechanical system after a decay.

7. The method according to claim 2, wherein the quantum mechanical system is divided into a cluster and a bath, the qubits (6, 7, 8) first being evaluated with regard to the system properties thereof and being categorized into high-performance qubits (6) and low-performance qubits (7, 8) and, within the context of a mapping process, an association of the high-performance qubits (6) for simulating the cluster and an association of the low-performance qubits (7) for simulating the bath being carried out.

8. The method according to claim 1, wherein the simulation (1) of the quantum mechanical system involves extrapolating the simulation results (10) into a low-noise, preferably noise-free, environment.

9. The method according to claim 8, wherein artificial noise (11) of different levels is iteratively generated in the quantum computer in order to extrapolate a noise-free state and decoherence times of the qubits (6, 7, 8) are measured on the basis of the artificial noise (11) in each case, a linear relationship between the artificial noise (11) and the decoherence times being determined and a transformation rule for transforming simulation results (10) into a low-noise, preferably noise-free, environment being derived therefrom and finally the simulation results (10) being transformed using the derived transformation rule.

10. The method according to claim 9, wherein an extrapolation (4) takes place by first a Trotter step being iteratively carried out, after which an excitation exchange is carried out between a bath qubit (7) and an auxiliary qubit (8) with a probability p << 1, the auxiliary qubit (8) is measured and, if the auxiliary qubit (8) was measured in its excited state, it is reset to its ground state and finally the Trotter step is started again, the decoherence times of the qubit (7, 8) being changed due to the measurements, and finally the simulation results (10) being transformed into a low-noise, preferably noise-free, state by extrapolating (4) the decoherence time and deriving a transformation rule, and applying this to the simulation results of the qubit (7, 8).

11. The method according to claim 1, wherein a temperature control (5) for producing a specific distribution function is carried out within the quantum computer by at least one auxiliary qubit (8) being put into an excited state so that thermal energy is absorbed.

Description

IN THE DRAWINGS

[0070] FIG. 1 is a schematic representation of the quantum simulation with all error correction methods according to the invention,

[0071] FIG. 2 is a schematic representation of an optimal mapping of logical qubits onto physical qubits at a suitable rotation angle, and

[0072] FIG. 3 is a representation of a linear noise extrapolation in a graph with (X) over Y and an auxiliary graph with Y over dt.

[0073] FIG. 1 is a schematic representation of a simulation 1 of a quantum mechanical system, for example a chemical structure, having three different error correction methods which are used to complement one another.

[0074] The central region in the middle visualizes the simulation 1 in the overall method within a logical space 13. The method works best for quantum simulation algorithms aiming for a steady state of the system. A noise source in a physical space injects noise 2 into the simulation 1 from the outside. An interface between physical qubits and logical qubits of the simulation space introduces a rotation angle φ between the two spaces and affects the noise seen by quantum simulation. An optimal angle φ minimizes the effect of noise. In the simulation, noise-induced heating can be reduced by adding Hamiltonians that introduce temperature control 5. Before the final low-noise simulation results 10 can be obtained, an extrapolation 4 is carried out, in which the simulation is performed multiple times, each time with different external noises and, if necessary, with additional artificial noises 11 in order to resolve contributions from different error sources more precisely.

[0075] FIG. 2 shows an example of optimal angles in a cluster-bath quantum simulation in the presence of an intrinsic decay. Qubit decay drives the physical qubits toward their ground states. By introducing an angle φ= Π between the right-hand physical and logical bath qubits 7, the corresponding electronic states are driven toward full filling. In the absence of cluster qubit decay, this mechanism drives the cluster-bath simulation to a solution that corresponds to the bath spectral densities

[00041]$S_{p\in cluster}^{-}\left(\omega \right)={\displaystyle \underset{i\in emptybath}{.Math.}{t}_i^2\frac{{\gamma }_i/2}{{\left({\gamma }_i/2\right)}^2+{\left(\omega -{\omega }_i\right)}^2}}$

[00042]$S_{p\in cluster}^{+}\left(\omega \right)={\displaystyle \underset{i\in filledbath}{.Math.}{t}_i^2\frac{{\gamma }_i/2}{{\left({\gamma }_i/2\right)}^2+{\left(\omega +{\omega }_i\right)}^2}}$

[0076] In the presence of cluster qubit decay, the cluster qubit angles leading to partial filling are advantageous.

[0077] Finally, FIG. 3 shows a linear noise extrapolation of the expected value .sup..Math.X.Math.. The noise-free result .Math.X.Math.(0) can be estimated by measuring the expected values under noise, (X)(Y > 0). The linear estimation comprises measurements under two noise levels, .sub.Y0 and .sub.Y1. Noise 2 can be increased, for example, by increasing the Trotter step time .sup.dτ or by increasing the probability of artificial decay p. The linear estimate can be improved with more measurements and non-linear extrapolation.

[0078] A method for simulating a quantum mechanical system is thus described above, which method uses the advantages of quantum mechanics for the simulation, but at the same time reduces the error susceptibility of these systems.

LIST OF REFERENCE SIGNS

[0079] 1 Simulation [0080] 2 Noise [0081] 3 Mapping [0082] 4 Extrapolation [0083] 5 Temperature control [0084] 6 Cluster qubits [0085] 7 Bath qubits [0086] 8 Auxiliary qubits [0087] 9 Environment [0088] 10 Simulation results [0089] 11 Artificial noise [0090] 12 Physical space [0091] 13 Logical space