Sampling from a set spins with clamping

A computational system comprising:

• at least one analog processor comprising:
• a plurality of qubits;
• a plurality of coupling devices, wherein each coupling device provides controllable communicative coupling between a respective pair of the plurality of qubits;
• at least one processor-based device communicatively coupled to the at least one analog processor;
• and
• at least one non-transitory computer-readable storage medium that stores processor-executable instructions, which when executed causes at least one processor-based device to:
• receive a function;
• receive a temperature ladder that specifies at least a first temperature;
• request a plurality of samples from an analog processor implementing the function;
• initialize a plurality of Markov chains each including one or more entries with a null value;
• associate each Markov chain in the plurality of Markov chains to a respective temperature from the temperature ladder, a first Markov chain associated with the first temperature, and a set of Markov chains in the plurality of Markov chains not associated with the first temperature;
• for each respective entry in each Markov chain of the plurality of Markov chains:
• if the respective entry is in the first Markov chain, and if a hardware sample is available in the plurality of samples requested from the analog processor implementing the function, update the respective entry in the first Markov chain with the hardware sample, and
• otherwise, generate a value for the respective entry, and update the respective entry with the value under a probabilistic acceptance rule;
• and
• return at least one of the Markov chains from the plurality of Markov chains.

A method of operation in a sampling device that comprises both an analog processor and at least one processor-based device communicatively coupled to one another, the analog processor comprising a plurality of qubits, and a plurality of coupling devices, wherein each coupling device provides controllable communicative coupling between two of the plurality of qubits, the method comprising:

• receiving a function;
• receiving a temperature ladder specifying at least a first temperature;
• requesting, asynchronously, a plurality of samples from the analog processor implementing the function;
• initializing a plurality of Markov chains each including one or more entries with a null value;
• associating with each Markov chain in the plurality of Markov chains to a respective temperature from the temperature ladder wherein a first Markov chain is associated with the first temperature, and a set of Markov chains in the plurality of Markov chains is not associated with the first temperature;
• for a respective entry in each Markov chain of the plurality of Markov chains:
• if the respective entry is in the first Markov chain associated with the first temperature, and if a hardware sample is available in the plurality of samples requested from the analog processor implementing the function, update the respective entry in first chain associated with the first temperature with the hardware sample, and
• otherwise, generate a value for the respective entry and accept the value under a probabilistic update rule;
• and
• returning a Markov chain from the plurality of Markov chains.

A system for use in quantum processing, comprising:

• at least one nontransitory processor-readable medium that stores at least one of processor executable instructions or data;
• and
• at least one processor communicatively coupled to the least one nontransitory processor-readable medium, and which, in response to execution of the at least one of processor executable instructions or data:
• request a set of samples from an analog processor implementing a function;
• seed a Markov chain with a sample drawn from the set of samples;
• update the Markov chain in accordance with an update rule;
• and
• return the Markov chain, the Markov chain comprising one or more entries.

A method of operating a sampling device, the method comprising:

• requesting a set of samples from an analog processor wherein the analog processor implements a function;
• seeding a Markov chain with a sample drawn from the set of samples;
• updating the Markov chain in accordance with an update rule;
• and
• returning the Markov chain, the Markov chain comprising one or more entries.