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

Abstract

As the hardware technology for quantum computing advances, its possible applications are actively searched and developed. However, such applications still suffer from the noise on quantum devices, in particular when using two-qubit gates whose fidelity is relatively low. One way to overcome this difficulty is to substitute such non-local operations by local ones. Such substitution can be performed by decomposing a non-local channel into a linear combination of local channels and simulating the original channel with a quasiprobability-based method. In this work, we first define a quantity that we call channel robustness of non-locality, which quantifies the cost for the decomposition. While this quantity is challenging to calculate for a general non-local channel, we give an upper bound for a general two-qubit unitary channel by providing an explicit decomposition. The decomposition is obtained by generalizing our previous work whose application has been restricted to a certain form of two-qubit unitary. This work develops a framework for a resource reduction suitable for first-generation quantum devices.

Circuit knitting with classical communication

“…Our main result (see Theorem 4.3 and Corollary 4.4) is that for a large class of two-qubit unitaries, all three quantities are equal. We show this result by first finding a lower bound to γ LOCC (U ) and compare that to a previously known upper bound [16] to γ LO (U ) and then showing that both bounds coincide for our considered class of two-qubit unitaries.…”

“…In fact, we prove a closed-form expression for the γ-factor as shown in Theorem 4.3 and Corollary 4.4. This is the first time that an exact characterization of the optimal sampling overhead is found, as previous works [3,16] only showed upper bounds. Table 1 gives an overview of gates for which we provide an analytical formula for the γ-factor under LO and LOCC.…”

“…Furthermore, previous work proposed explicit quasiprobability decompositions without any evidence for optimality. We show that the quasiprobability decomposition proposed in [16] are optimal for a certain class of two-qubit unitaries. Other existing circuit knitting approaches, such as [1,2], do not precisely specify the exponential scaling and state an overhead scaling as 2 O(n) , whereas our work makes a more precise statement.…”

“…Relation to existing circuit knitting techniques Circuit knitting through quasiprobability simulation of nonlocal gates has already been proposed previously [3,16]. However, previous works only focused on the LO setting and did not consider classical communication between the involved parties.…”

Quantum Simulation with Hybrid Tensor Networks

“…A future direction is to investigate the combination of these methods with quantum computing. Another independent approach of simulating large quantum systems with small quantum computers is to decompose multiqubit gates into a mixture of single-qubit gates [70][71][72][73][74], whose combination with our method may lead to an interesting future direction. After showing advantages over classical supercomputers in certain tasks [75,76], the next milestone is to solve practically meaningful and classically intractable tasks.…”