Utilizing computational symmetries for error mitigation in quantum computations
Aspects of the present disclosure relate generally to systems and methods for use in the implementation and/or operation of quantum information processing (QIP) systems, and more particularly, to the use of computational symmetries for error mitigation in quantum computations in QIP systems. In some cases, an example method includes generating a quantum circuit by compiling a quantum program corresponding to a defined quantum computation, generating multiple execution variants of the quantum circuit by applying one or more computation-specific symmetries to the quantum circuit, with the one or more computation-specific symmetries corresponding to the defined quantum computation, causing quantum hardware to execute the multiple execution variants, receiving measurement datasets indicative of computation outputs, and determining a result of the computation by aggregating the measurement datasets.
1 . A computer-implemented method comprising,
generating a quantum circuit by compiling a quantum program corresponding to a defined quantum computation;
generating multiple execution variants of the quantum circuit by applying one or more computation-specific symmetries to the quantum circuit, with the one or more computation-specific symmetries corresponding to the defined quantum computation, each of the one or more computation-specific symmetries comprising a respective transformation of a realization of the quantum circuit that preserves the defined quantum computation;
causing quantum hardware to execute each one of the multiple execution variants;
receiving multiple measurement datasets indicative of computation outputs for respective ones of the multiple execution variants; and
determining a result of the defined quantum computation by aggregating the multiple measurement datasets.
2 . The computer-implemented method of claim 1 , further comprising causing a computing device to provide the result.
3 . The computer-implemented method of claim 1 , further comprising selecting the one or more computation-specific symmetries from a set of computation-specific symmetries corresponding to the defined quantum computation, with the selecting comprising sampling, via a symmetrization module, the set of computation-specific symmetries.
4 . The computer-implemented method of claim 3 , wherein the selecting comprises sampling a first symmetry and a second symmetry from the set of computation-specific symmetries, wherein the first symmetry and the second symmetry configured to reduce error correlation between respective resulting execution variants.
5 . The computer-implemented method of claim 3 , wherein the set of computation-specific symmetries comprises at least one of a qubit assignment, gate decomposition, a permutation of commuting gates, an addition of a gate that preserves a defined state, or a change of one or more gates and measurements compensated by one or more changes in postprocessing.
6 . The computer-implemented method of claim 1 , wherein the aggregating the multiple measurement datasets comprises,
selecting, based on an output probability distribution corresponding to the defined quantum computation, an aggregation process to combine the multiple measurement datasets; and
applying the aggregation process to the multiple measurement datasets.
7 . The computer-implemented method of claim 6 , wherein the aggregation process comprises componentwise averaging.
8 . The computer-implemented method of claim 7 , wherein the multiple measurement datasets define multiple sequences of bitstrings, and wherein applying the componentwise averaging comprises determining, over the multiple sequences of bitstrings, an average number of occurrences for each bitstring in the multiple sequence of bitstrings.
9 . The computer-implemented method of claim 6 , wherein the aggregation process comprises plurality voting.
10 . The computer-implemented method of claim 9 , wherein the multiple measurement datasets define multiple sequences of bitstrings, and wherein applying the plurality voting comprises determining, over the multiple sequences of bitstrings, a particular bitstring exhibiting a number of occurrences that exceeds a defined threshold number.
11 . A computing system comprising:
at least one processor;
at least one memory devices storing processor-executable instructions that, in response to being executed by the at least one processor, cause the computing system at least to:
generate a quantum circuit by compiling a quantum program corresponding to a defined quantum computation;
generate multiple execution variants of the quantum circuit by applying one or more computation-specific symmetries to the quantum circuit, with the one or more computation-specific symmetries corresponding to the defined quantum computation, each of the one or more computation-specific symmetries comprising a respective transformation of a realization of the quantum circuit that preserves the defined quantum computation;
cause quantum hardware to execute each one of the multiple execution variants;
receive multiple measurement datasets indicative of computation outputs for respective ones of the multiple execution variants; and
determine a result of the defined quantum computation by aggregating the multiple measurement datasets.
12 . The computing system of claim 11 , the at least one memory devices storing further processor-executable instructions that, in response to being executed, further cause the at least one processor to cause a computing device to provide the result.
13 . The computing system of claim 11 , the at least one memory devices storing further processor-executable instructions that, in response to being executed, further cause the at least one processor to select the one or more computation-specific symmetries from a set of computation-specific symmetries corresponding to the defined quantum computation, wherein selecting the one or more computation-specific symmetries comprises sampling the set of computation-specific symmetries.
14 . The computing system of claim 11 , wherein aggregating the multiple measurement datasets comprises,
selecting, based on an output probability distribution corresponding to the defined computation, an aggregation process to combine the multiple measurement datasets; and
applying the aggregation process to the multiple measurement datasets.
15 . The computing system of claim 14 , wherein the aggregation process comprises one of componentwise averaging or plurality voting.
16 . A quantum information processing (QIP) system comprising:
at least one processor; and
at least one memory device storing processor-executable instructions that, in response to being executed by the at least one processor, cause the QIP system at least to:
generate a quantum circuit by compiling a quantum program corresponding to a defined quantum computation;
generate multiple execution variants of the quantum circuit by applying one or more computation-specific symmetries to the quantum circuit, with the one or more computation-specific symmetries corresponding to the defined quantum computation, each of the one or more computation-specific symmetries comprising a respective transformation of a realization of the quantum circuit that preserves the defined quantum computation;
cause quantum hardware to execute each one of the multiple execution variants;
receive multiple measurement datasets indicative of computation outputs for respective ones of the multiple circuit variants; and
determine a result of the defined quantum computation by aggregating the multiple measurement datasets.
17 . The QIP system of claim 16 , the at least one memory devices storing further processor-executable instructions that, in response to being executed, further cause the at least one processor to cause a computing device to provide the result.
18 . The QIP system of claim 16 , wherein aggregating the multiple measurement datasets comprises,
selecting, based on an output probability distribution corresponding to the defined computation, an aggregation process to combine the multiple measurement datasets, the aggregation process one of a linear aggregation process or a non-linear aggregation process;
applying the aggregation process to the multiple measurement datasets.
19 . The QIP system of claim 18 , wherein the quantum hardware comprises multiple trapped-atom qubits individually addressable by a continuous-wave laser beam.
20 . The QIP system of claim 18 , wherein the quantum hardware comprises multiple superconducting qubits individually addressable by microwave electromagnetic radiation.