Scalable tensor-network-based noise mitigation for near-term quantum computing

A computing system comprising a quantum processor and a classical computer, the computing system being configured to establish a model of a noisy physical execution of a quantum circuit by the quantum processor, the model being representative of a noisy physical execution of a unitary operation U by the quantum processor which results in a noisy final physical state of N qudits of the quantum processor, the model being represented by a quantum channel, wherein a density operator is at least an approximation of the noisy final physical state of the N qudits of the quantum processor;

• execute the noisy physical execution of the quantum circuit one or more times by the quantum processor by applying a sequence of G physical operations to the N qudits of the quantum processor to thereby obtain a set of measurement outcomes for each execution of the quantum circuit, wherein each measurement outcome comprises a physical quantum measurement applied to the noisy final physical state of the N qudits after each execution of the quantum circuit by the sequence of G physical operations;
• derive a quasi-state tensor network representation of a quasi-state comprising an approximation of the density operator of the noisy final state based on the set of measurement outcomes of the execution of the quantum circuit and a set of dual effects corresponding to the set of measurement outcomes;
• derive an observable tensor network representation of a Hermitian operator which is associated with an observable for a system of N qudits;
• derive a noise mitigation tensor network representation of a noise mitigation map, wherein the noise mitigation map is a concatenation of an inverse of the quantum channel followed by a unitary operation, wherein each of the tensor network representations comprises respectively a plurality of quasi-state tensors, observable tensors and noise mitigation tensors;
• provide the quasi-state tensor network representation, the observable tensor network representation and the noise mitigation tensor network representation to a classical computer;
• and
• execute, by the classical computer, a tensor network contraction algorithm to thereby calculate a value of the observable associated with the Hermitian operator for a final quantum state of the N qudits of the quantum circuit, the tensor network contraction algorithm including instructions for contracting a tensor network representation of in terms of the quasi-state tensors, the observable tensors and the noise mitigation tensors according to a predetermined contracting rule of physical and virtual indices of the tensors to thereby obtain a noise mitigated value of an expectation value of the observable associated with the Hermitian operator for the final quantum state of the quantum circuit.

A non-transitory computer program product including instructions which, when the program is carried out by a computer system comprising a classical computer and a quantum processor, cause the computer system to:

• establish a model of a noisy physical execution of a quantum circuit by the quantum processor, the model being representative of a noisy physical execution of a unitary operation by the quantum processor which results in a noisy physical final state of N qudits of the quantum processor, the model being represented by a quantum channel, wherein a density operator is at least an approximation of the noisy final physical state of the N qudits of the quantum processor;
• execute the noisy physical execution of the quantum circuit one or more times by the quantum processor by applying a sequence of G physical operations to the N qudits of the quantum processor to thereby obtain a set of measurement outcomes for each execution of the quantum circuit, wherein each measurement outcome comprises a physical quantum measurement applied to the noisy final physical state of the N qudits after each execution of the quantum circuit by the sequence of G physical operations;
• derive a quasi-state tensor network representation of a quasi-state comprising an approximation of the density operator of the noisy final state based on the set of measurement outcomes of the execution of the quantum circuit and a set of dual effects corresponding to the set of measurement outcomes;
• derive an observable tensor network representation of a Hermitian operator which is associated with an observable for a system of N qudits;
• derive a noise mitigation tensor network representation of a noise mitigation map, wherein the noise mitigation map is a concatenation of an inverse of the quantum channel ε followed by a unitary operation, wherein each of the tensor network representations comprises respectively a plurality of quasi-state tensors, observable tensors and noise mitigation tensors;
• provide the quasi-state tensor network representation, the observable tensor network representation and the noise mitigation tensor network representation to a classical computer;
• and
• execute, by the classical computer, a tensor network contraction algorithm to thereby calculate a value of the observable associated with the Hermitian operator for a final quantum state of the N qudits of the quantum circuit, the tensor network contraction algorithm including instructions for contracting a tensor network representation in terms of the quasi-state tensors, the observable tensors and the noise mitigation tensors according to a predetermined contracting rule of physical and virtual indices of the tensors to thereby obtain a noise mitigated value of an expectation value of the observable associated with the Hermitian operator for the final quantum state of the quantum circuit.