Simulating Large Quantum Circuits on a Small Quantum Computer

Abstract

Limited quantum memory is one of the most important constraints for near-term quantum devices. Understanding whether a small quantum computer can simulate a larger quantum system, or execute an algorithm requiring more qubits than available, is both of theoretical and practical importance. In this Letter, we introduce cluster parameters K and d of a quantum circuit. The tensor network of such a circuit can be decomposed into clusters of size at most d with at most K qubits of inter-cluster quantum communication. We propose a cluster simulation scheme that can simulate any ðK; dÞ-clustered quantum circuit on a d-qubit machine in time roughly 2 OðKÞ , with further speedups possible when taking more finegrained circuit structure into account. We show how our scheme can be used to simulate clustered quantum systems-such as large molecules-that can be partitioned into multiple significantly smaller clusters with weak interactions among them. By using a suitable clustered ansatz, we also experimentally demonstrate that a quantum variational eigensolver can still achieve the desired performance for estimating the energy of the BeH 2 molecule while running on a physical quantum device with half the number of required qubits.

Quantum Divide and Compute: Exploring the Effect of Different Noise Sources

“…An algorithm that allows circuit cutting was first described in [12]. In this section, we provide a self-contained derivation that allows to compute the probability distribution of a circuit that has been fragmented into several smaller disconnected pieces.…”

“…The formula for the multi-fragment case can be inferred from that of the two-fragment case: the procedure sketched for the two-fragment case can be recast in more generic terms, as described in [12]. This is done by considering the directed acyclic graph G = (V, E) corresponding to the quantum circuit at hand (see Fig.…”

“…Bravyi et al [11] showed that a quantum circuit on n + k qubits can be simulated by sparse circuits on n qubits and exponential classical processing that takes time 2 O(k) poly(n). A more general approach that allows fragmenting larger quantum circuits into smaller subcircuits was introduced in [12]. In this work, tensor-network techniques were used to show how to decompose a circuit with a large quantum volume [13] into smaller subcircuits with quantum volumes compatible with NISQ devices.…”

Overhead for simulating a non-local channel with local channels by quasiprobability sampling

“…To this end, a few approaches have been proposed. One is to decompose a large circuit into smaller ones by "cutting" circuits using a tomography-like method [10]. Also, in Ref.…”

“…In this context, we can view the decomposition performed in Ref. [10] as a quasiprobability decomposition of the identity channel into a measurement and state-preparation channel, and one in Ref. [11] as a quasiprobability decomposition of a non-local unitary channel into local ones.…”