Systems and methods for optimizing quantum computers

1. A computer system for constructing a model of noise afflicting a quantum computer comprising a plurality of qubits, the computer system comprising:

one or more processors; and

a memory storing instructions that, when executed by the one or more processors, cause the one or more processors to:

obtain a graph G that describes a conditional independence structure of the noise, wherein the graph G includes a node for each qubit in the plurality of qubits and wherein the noise afflicting the quantum computer is logically reduced to Pauli noise;

break the graph G into a plurality of sets, wherein each set Cj in the plurality of sets (i) corresponds a qubit j in the plurality of qubits and (ii) comprises a representation of the qubit j and parent qubits ∂+j in the graph G;

for each set Cj in the plurality of sets, characterize a corresponding local conditional probability distribution Pr(e j |e ∂+j ), wherein e j ϵ j is a Pauli error on the j th qubit, and e ∂+j is a Pauli error on the parent qubits of the j th qubit, by estimating a local Pauli fidelity for the set Cj thereby learning the model of the noise afflicting the quantum computer; and

estimate a performance of at least one fixed quantum error-correcting code on the quantum computer using the model of the noise afflicting the quantum computer.

2. The computer system of claim 1 , wherein the instructions further cause the one or more processors to logically reduce the noise afflicting the quantum computer to Pauli noise by an application of Pauli twirling.

3. The computer system of claim 1 , wherein:

the corresponding local conditional probability distribution comprises all possible Pauli errors on Cj or a subset thereof,

the graph G corresponds to a factor graph, and

each node in a plurality of nodes of the graph G has a constant number of parent qubits.

4. The computer system of claim 3 , wherein the factor graph is a Bayesian network or a Markov network.

5. The computer system of claim 1 , wherein the graph G corresponds to a Bayesian network or a Markov network, and

wherein each node in a plurality of nodes of the graph G independently has a number of parent qubits that is O(log(n)) or less, wherein n is the number of qubits in the quantum computer.

6. The computer system of claim 1 , wherein the estimating the local Pauli fidelity for the set Cj comprises:

(i) selecting a stabilizer group S in a plurality of stabilizer groups and preparing an approximation of an eigenstate |ψ>=S k |ψ> for all stabilizers S k ϵ , wherein |ψ> is the eigenstate and S k is the stabilizer,

(ii) applying a Pauli-twirled noise map ε that is to be characterized m times, wherein m is a positive integer,

(iii) measuring a corresponding stabilizer basis, wherein each individual probability is a mixture of multiple exponentials, one for each possible eigenvalue in a plurality of eigenvalues,

(iv) applying a Walsh-Hadamard transformation on the measurement of the measuring (iii) thereby transforming the measurement into a fidelity decay curve using a randomized benchmarking fidelity decay argument,

(v) reconstructing a fidelity decay curve from the applying (iv) using regression, and

(vi) repeating the selecting (i), the applying (ii), the measuring (iii), the applying (iv), and the reconstructing (v) for each stabilizer group in the plurality of stabilizer groups thereby obtaining each possible Pauli error for Cj, and thereby obtaining an estimate of Pr(eCj), wherein Pr(eCj) is a marginal probability distribution of Pauli errors on Cj.

7. The computer system of claim 6 , wherein the instructions further cause the one or more processors to obtain Pr(e j |e ∂+1 ) using a conditional probability relation Pr(e j |e ∂+1 )=Pr(e C j )/Pr(e ∂+1 ) thereby learning the model of the noise afflicting the quantum computer.

8. The computer system of claim 1 , wherein estimating the performance of the at least one fixed quantum error-correcting code comprises mapping the at least one fixed quantum error-correcting code to an associated Ising model.

9. The computer system of claim 8 , wherein estimating the performance of the at least one fixed quantum error-correcting code further comprises identifying a partition function that provides an optimal threshold for the at least one fixed quantum error-correcting code.

10. The computer system of claim 1 , wherein the instructions further cause the one or more processors to:

decode the at least one fixed quantum error-correcting code, using the graph G, after the at least one fixed quantum error-correcting code has been applied to the quantum computer, wherein the decoding comprises contracting a set of tensor networks for the at least one fixed quantum error-correcting code.

11. The computer system of claim 1 , wherein the instructions further cause the one or more processors to:

decode the at least one fixed quantum error-correcting code, using the graph G, after the at least one fixed quantum error-correcting code has been applied to the quantum computer, wherein the decoding comprises application of a Monte Carlo method for the at least one fixed quantum error-correcting code.

12. The computer system of claim 1 , wherein the at least one fixed quantum error-correcting code in-comprises a plurality of fixed quantum error-correcting codes, and

wherein the instructions further cause the one or more processors to:

estimate a performance of each fixed quantum error-correcting code of the plurality of fixed quantum error-correcting codes on the quantum computer using the model of the noise afflicting the quantum computer, and

decode each fixed error-correcting code, using the graph G, after the fixed quantum error-correcting code has been applied to the quantum computer, thereby identifying an optimal fixed quantum error-correcting code in the plurality of fixed quantum error-correcting codes.

13. The computer system of claim 12 , wherein decoding the at least one fixed quantum error-correcting code, using the graph G, after the at least one fixed quantum error-correcting code has been applied to the quantum computer, comprises contracting a set of tensor networks for the at least one fixed quantum error-correcting code.

14. The computer system of claim 12 , wherein decoding the at least one fixed quantum error-correcting code, using the graph G, after the at least one fixed quantum error-correcting code has been applied to the quantum computer comprises application of a Monte Carlo method for the at least one fixed quantum error-correcting code.

15. A method for constructing a model of noise afflicting a quantum computer comprising a plurality of qubits at a computer system comprising one or more data processors and a memory, the memory comprising non-transitory instructions executable by the one or more data processors, the method comprising:

obtaining a graph G that describes a conditional independence structure of the noise afflicting the quantum computer, wherein the graph G includes a node for each qubit in the plurality of qubits and wherein the noise afflicting the quantum computer is logically reduced to Pauli noise;

breaking the graph G into a plurality of sets, wherein each set Cj in the plurality of sets (i) corresponds a qubit j in the plurality of qubits and (ii) comprises a representation of the qubit j and parent qubits ∂+j in the graph G; and

for each set Cj in the plurality of sets, characterizing a corresponding local conditional probability distribution Pr(e j |e ∂+j ), wherein e j ϵ j is a Pauli error on the j th qubit and e ∂+j is a Pauli error on the parent qubits of the j th qubit, by estimating a local Pauli fidelity for the set Cj, thereby learning the model of the noise afflicting the quantum computer; and

estimating a performance of a fixed quantum error-correcting code on the quantum computer using the model of the noise afflicting the quantum computer.

16. The method of claim 15 , further comprising:

mapping the fixed quantum error-correcting code to an associated Ising model, wherein estimating the performance of the fixed quantum error-correcting code comprises identifying a partition function that provides an optimal threshold for the fixed quantum error-correcting code.

17. The method of claim 15 , further comprising:

decoding the fixed quantum error-correcting code, using the graph G, after the fixed quantum error-correcting code has been applied to the quantum computer, wherein the decoding comprises contracting a set of tensor networks for the fixed quantum error-correcting code.

18. The method of claim 15 , further comprising:

decoding the fixed quantum error-correcting code, using the graph G, after the fixed quantum error-correcting code has been applied to the quantum computer, wherein the decoding comprises application of a Monte Carlo method for the fixed quantum error-correcting code.

19. The method of claim 15 , further comprising:

logically reducing a source of noise afflicting the quantum computer to Pauli noise by an application of Pauli twirling.

20. A non-transitory computer readable storage medium storing one or more programs, the one or more programs comprising instructions, which when executed by a computer system with one or more processors, cause the computer system to:

obtain a graph G that describes a conditional independence structure of a noise afflicting a quantum computer comprising a plurality of qubits, wherein the graph G includes a node for each qubit in the plurality of qubits and wherein the noise afflicting the quantum computer is logically reduced to Pauli noise;

break the graph G into a plurality of sets, wherein each set Cj in the plurality of sets (i) corresponds a qubit j in the plurality of qubits and (ii) comprises a representation of the qubit j and parent qubits ∂+j in the graph G; and

for each set Cj in the plurality of sets, characterize a corresponding local conditional probability distribution Pr(e j |e ∂+j ), wherein e j ϵ j is a Pauli error on the j th qubit and e ∂+j is a Pauli error on the parent qubits of j th qubit, by estimating a local Pauli fidelity for the set Cj, thereby learning a model of the noise afflicting the quantum computer; and

estimate a performance of a fixed quantum error-correcting code on the quantum computer using the model of the noise afflicting the quantum computer.