Patent Forecast

1. A method for identifying an excited energy state of a system of interacting electrons, comprising: (3) (6)

providing a first quantum circuit, the first quantum circuit defined by a generator function parameterised by a set of parameters, θ, wherein applying the first quantum circuit to a set of qubits in an initial state generates a state of the system represented by a wavefunction, Ψ;

providing n sets of values θ_n−1for the set of parameters, θ, wherein each set of values θ_n−1generates an nth valid energy state of the system represented by a wavefunction, Ψ_n−1, wherein n is one or more;

providing a second quantum circuit, the second quantum circuit defined by a discriminator function parameterised by a set of parameters, ϕ, wherein applying the second quantum circuit to the set of qubits in the state of the system represented by the wavefunction, provides an output representing an extent of overlap of the wavefunction with the wavefunction Ψ_n−1of each of the n known valid states of the system;

optimising the values of the set of parameters θ to substantially minimise the energy of the state generated by the first quantum circuit represented by the wavefunction Ψ, and to substantially minimise the extent of overlap of the state generated by the first quantum circuit represented by the wavefunction and each of the n known valid states of the system represented by respective wavefunction Ψ_n−1; and

cooperatively, training the discriminator function by optimising the value of the set of parameters ϕ to train the discriminator function to discriminate between the wavefunction Ψ of the state generated by the first quantum circuit and the wavefunction Ψ_n−1representing each of the n valid states of the system;

wherein the optimised values of the set of parameters θ correspond to a set of values θ_nparametrising the generator function defining the first quantum circuit for generating an n+1th valid energy state of the system represented by wavefunction, Ψ_n, which is an excited energy state of the system of interacting electrons.

2. The method of claim 1, wherein optimising the value of the set of parameters θ comprises: (4) (10)

generating a trial energy state of the system represented by a wavefunction Ψ_Tby applying, to the set of qubits in an initial state, the first quantum circuit defined by the generator function with the set of parameters θ having trial values θ_T;

determining an output β_Tto the second quantum circuit by applying, to the set of qubits in the state generated by the first quantum circuit defined by the generator function with the set of parameters having trial values θ_Tand to an ancilla qubit, the second quantum circuit, and then measuring the ancilla qubit, wherein the second quantum circuit is defined by the discriminator function with the set of parameters ϕ having a set of trial values ϕ_T;

calculating an energy E_Tof the trial energy state of the system represented by the wavefunction Ψ_T;

comparing the output β_Tof the second quantum circuit to a predefined distinctiveness threshold, T_d;

wherein if the output β_Tto the second quantum circuit is not within a predefined interval of values representing the distinctiveness threshold, T_d; and/or

if the energy E_Tof the trial energy state of the system represented by the wavefunction Ψ_Tis not substantially at a minima;

then varying the set of trial values θ_tand repeating the generating, determining, calculating and comparing steps;

or, if the output β_Tto the second quantum circuit is within the predefined interval of values representing the distinctiveness threshold, T_d;and

if the energy E_Tof the trial energy state of the system represented by the wavefunction Ψ_Tis substantially at a minima;

then identifying the set of values θ_Tas the set of values θ_nparametrising the generator function defining the first quantum circuit for generating the n+1th valid energy state of the system represented by wavefunction, Ψ_n, which is the identified excited energy state of the system of interacting electrons.

3. The method of claim 2, wherein the generating, determining and calculating steps take place at a quantum computer, and the comparing, varying and identifying steps take place at a classical computer. (0)

4. The method of claim 2, wherein calculating an energy E_Tof the trial energy state of the system represented by the wavefunction Ψ_Tcomprises: (0) (1)

5. The method of claim 2, wherein measuring the ancilla qubit to determine the output β_Tto the second quantum circuit comprises: (0) (1)

6. The method of claim 2, wherein the parameters θ_Tare varied based on the output of a cost function parameterised by the energy E_Tof the trial energy state of the system represented by the wavefunction Ψ_Tand the output β_Tto the second quantum circuit. (0)

7. The method of claim 1, wherein training the discriminator function by optimising the value of the set of parameters ϕ comprises: (3) (5)

generating an nth valid energy state of the system represented by the wavefunction, Ψ_n−1by applying, to a set of qubits in an initial state, the first quantum circuit defined by the generator function with the set of parameters having values θ_n−1;

determining an output β_Vto the second quantum circuit by applying, to the set of qubits in the state generated by the first quantum circuit defined by the generator function with the set of parameters having values θ_n−1and to an ancilla qubit, the second quantum circuit, and then measuring the ancilla qubit, wherein the second quantum circuit is defined by the discriminator function with the set of parameters ϕ having a set of trial values ϕ_T;

comparing the output β_Vof the second quantum circuit to a predefined similarity threshold, T_s;

wherein if the output β_Vof the second quantum circuit is not within a predefined interval of values representing the similarity threshold, T_s;

then varying the set of trial values ϕ_Tand repeating the generating, determining and comparing steps.

8. The method of claim 7, wherein the generating and determining steps take place at a quantum computer, and the comparing and varying steps take place at a classical computer. (0)

9. The method of claim 7, wherein measuring the ancilla qubit to determine the output β_Vto the second quantum circuit, comprises: (0) (1)

10. The method of claims 7, wherein the parameters ϕ_Tare varied based on the output of a cost function parameterised by the output to the second quantum circuit, β_V. (0)

11. The method of claim 1, wherein, prior to providing n sets of values θ_n−1for the set of parameters θ, the method further comprises applying a variational quantum eigensolver to identify the set of values, θ₀, parametrising the ground energy state of the system which is a first valid energy state of the system and represented by a wavefunction, Ψ₀. (0)

12. A computing apparatus for identifying an excited energy state of a system of interacting electrons, comprising: (3) (5)

a classical computer; and

a quantum computer comprising a set of qubits, the quantum computer configured to apply a first quantum circuit the first quantum circuit defined by a generator function parameterised by a set of parameters, θ, wherein applying the first quantum circuit to a set of qubits in an initial state generates a state of the system represented by a wavefunction, Ψ, and to apply a second quantum circuit defined by a discriminator function parameterised by a set of parameters, ϕ, wherein applying the second quantum circuit to the set of qubits in a state of the system represented by a wavefunction, Ψ provides an output representing an extent of overlap of the wavefunction Ψ with the wavefunction Ψ_n−1of each of the n known valid states of the system, wherein each of the n known valid states of the system are parametrised by a set of values θ_n−1for the set of parameters, θ;

wherein the computing apparatus is configured to optimise the values of the set of parameters θ to substantially minimise the energy of the state generated by the first quantum circuit represented by the wavefunction Ψ, and to substantially minimise the extent of overlap of the state generated by the first quantum circuit represented by the wavefunction Ψ and each of the n known valid states of the system represented by respective wavefunction Ψ_n−1; and

cooperatively, to train the discriminator function by optimising the value of the set of parameters ϕ to train the discriminator function to discriminate between the wavefunction of the state generated by the first quantum circuit and the wavefunction Ψ_n−1representing each of the n valid states of the system;

wherein the optimised values of the set of parameters θ correspond to a set of values θ_nparametrising the generator function defining the first quantum circuit for generating an n+1th valid energy state of the system represented by wavefunction, Ψ_n, which is an excited energy state of the system of interacting electrons.

13. The computing apparatus of claim 12, wherein the computing apparatus configured to optimise the values of the set of parameters θ to substantially minimise the energy of the state generated by the first quantum circuit represented by the wavefunction Ψ, and to substantially minimise the extent of overlap of the state generated by the first quantum circuit represented by the wavefunction Ψ and each of the n known valid states of the system represented by respective wavefunction Ψ_n−1comprises: (3) (12)

the quantum computer being configured to:

generate a trial energy state of the system represented by a wavefunction Ψ_Tby applying, to the set of qubits in an initial state, the first quantum circuit defined by the generator function with the set of parameters θ having trial values θ_T;

determine an output β_Tto the second quantum circuit by applying, to the set of qubits in the state generated by the first quantum circuit defined by the generator function with the set of parameters having trial values θ_Tand to an ancilla qubit, the second quantum circuit, and then measuring the ancilla qubit, wherein the second quantum circuit is defined by the discriminator function with the set of parameters ϕ having a set of trial values ϕ_T;

calculate an energy E_Tof the trial energy state of the system represented by the wavefunction Ψ_T; and

the classical computer being configured to:

compare the output β_Tof the second quantum circuit to a predefined distinctiveness threshold, T_d;

wherein if the output β_Tto the second quantum circuit is not within a predefined interval of values representing the distinctiveness threshold, T_d; and/or

if the energy E_Tof the trial energy state of the system represented by the wavefunction Ψ_Tis not substantially at a minima;

then vary the set of trial values θ_T;

or, if the output β_Tto the second quantum circuit is within the predefined interval of values representing the distinctiveness threshold, T_d; and

if the energy E_Tof the trial energy state of the system represented by the wavefunction Ψ_Tis substantially at a minima;

then identify the set of values θ_Tas the set of values θ_nparametrising the generator function defining the first quantum circuit for generating the n+1th valid energy state of the system represented by wavefunction, Ψ_n, which is the identified excited energy state of the system of interacting electrons.

14. The computing apparatus of claim 13, wherein the quantum computer being configured to calculate an energy E_Tof the trial energy state of the system represented by the wavefunction Ψ_Tcomprises the classical computer being configured to: (0) (1)

15. The computing apparatus of claim 13, wherein the quantum computer being configured to measure the ancilla qubit to determine the output β_Tto the second quantum circuit comprises the quantum computer configured to: (0) (1)

16. The computing apparatus of claim 13, wherein the classical computer being configured to vary the set of trial values θ_Tcomprises the classical computer configured to vary the parameters θ_Tbased on the output of a cost function parameterised by the energy E_Tof the trial energy state of the system represented by the wavefunction Ψ_Tand the output β_Tto the second quantum circuit. (0)

17. The computing apparatus of claim 12, wherein the computing apparatus configured to train the discriminator function by optimising the value of the set of parameters ϕ to train the discriminator function to discriminate between the wavefunction Ψ of the state generated by the first quantum circuit and the wavefunction Ψ_n−1representing each of the n valid states of the system, comprises: (1) (6)

the quantum computer configured to:

generate an nth valid energy state of the system represented by the wavefunction, Ψ_n−by applying, to a set of qubits in an initial state, the first quantum circuit defined by the generator function with the set of parameters having values θ_n−1;

determine an output β_Vto the second quantum circuit by applying, to the set of qubits in the state generated by the first quantum circuit defined by the generator function with the set of parameters having values θ_n−1and to an ancilla qubit, the second quantum circuit, and then measuring the ancilla qubit, wherein the second quantum circuit is defined by the discriminator function with the set of parameters ϕ having a set of trial values ϕ_T; and the classical computer configured to:

compare the output β_Vof the second quantum circuit to a predefined similarity threshold, T_s;

wherein if the output β_Vof the second quantum circuit is not within a predefined interval of values representing the similarity threshold, T_s;

then vary the set of trial values ϕ_Tand repeating the generating, determining and comparing steps.

19. The computing apparatus of claim 17, wherein the classical computer configured to vary the parameters ϕ_Tcomprises the classical computer configured to vary the parameters ϕ_Tbased on the output of a cost function parameterised by the output to the second quantum circuit, β_V. (0)

20. The computing apparatus of claims 12, wherein the classical computer is further configured to applying a variational quantum eigensolver to identify the set of values, θ₀, parametrising the ground energy state of the system which is a first valid energy state of the system and represented by a wavefunction, Ψ₀. (0)

18. (canceled) (0)

Application US20210241150

Method for Identifying a Valid Energy State

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