A method for reducing computation time while simulating quantum computation on a classical computer by performing an algorithm used to determine the most efficient input contraction, the method including receiving, by a processor, a tensor network representing a quantum circuit, computing, by the processor, an ordering for the tensor network by an ordering algorithm, contracting, by the processor, the tensor network by eliminating indices according to the ordering resulting in a contracted tensor network, and returning, by the processor, the contracted tensor network.

An alternative approach to flux pumping in superconducting devices is described for fast and extremely precise tuning of the current during persistent mode operation. Rather than bringing in new flux from outside the circuit, the alternative approach stores a small flux in a tunable inductor (also referred to herein as a “flux bank”) at the initial point of powering. Flux can be transferred back and forth from this bank to the main coil by simply changing the inductance of the bank. This allows for fine and fast adjustments of the persistent current without the use of thermal switches found in other approaches (which limit the adjustment speed and accuracy).

An alternative approach to flux pumping in superconducting devices is described for fast and extremely precise tuning of the current during persistent mode operation. Rather than bringing in new flux from outside the circuit, the alternative approach stores a small flux in a tunable inductor (also referred to herein as a “flux bank”) at the initial point of powering. Flux can be transferred back and forth from this bank to the main coil by simply changing the inductance of the bank. This allows for fine and fast adjustments of the persistent current without the use of thermal switches found in other approaches (which limit the adjustment speed and accuracy).

Data compression includes: inputting data comprising a vector that requires a first amount of memory; compressing the vector into a compressed representation while preserving information content of the vector, including: encoding, using one or more non-quantum processors, at least a portion of the vector to implement a quantum gate matrix; and modulating a reference vector using the quantum gate matrix to generate the compressed representation, wherein the compressed representation requires a second amount of memory that is less than the first amount of memory; and outputting the compressed representation to be displayed, stored, and/or further processed.

The driver Hamiltonian is modified in such a way that the quantum approximate optimization algorithm (QAOA) running on a circuit-model quantum computing facility (e.g., actual quantum computing device or simulator), may better solve combinatorial optimization problems than with the baseline/default choice of driver Hamiltonian. For example, the driver Hamiltonian may be chosen so that the overall Hamiltonian is non-stoquastic.

The driver Hamiltonian is modified in such a way that the quantum approximate optimization algorithm (QAOA) running on a circuit-model quantum computing facility (e.g., actual quantum computing device or simulator), may better solve combinatorial optimization problems than with the baseline/default choice of driver Hamiltonian. For example, the driver Hamiltonian may be chosen so that the overall Hamiltonian is non-stoquastic.

Methods, systems, and devices for quantum key distribution (QKD) in passive optical networks (PONs) are described. A PON may be a point-to-multipoint system and may include a central node in communication with multiple remote nodes. In some cases, each remote node may include a QKD transmitter configured to generate a quantum pulse indicating a quantum key, a synchronization pulse generator configured to generate a timing indication of the quantum pulse, and filter configured to output the quantum pulse and the timing indication to the central node via an optical component (e.g., an optical splitter, a cyclic arrayed waveguide grating (AWG) router). The central node may receive the timing indications and quantum pulses from multiple remote nodes. Thus, the central node and remote nodes may be configured to communicate data encrypted using quantum keys.

Methods, systems, and devices for quantum key distribution (QKD) in passive optical networks (PONs) are described. A PON may be a point-to-multipoint system and may include a central node in communication with multiple remote nodes. In some cases, each remote node may include a QKD transmitter configured to generate a quantum pulse indicating a quantum key, a synchronization pulse generator configured to generate a timing indication of the quantum pulse, and filter configured to output the quantum pulse and the timing indication to the central node via an optical component (e.g., an optical splitter, a cyclic arrayed waveguide grating (AWG) router). The central node may receive the timing indications and quantum pulses from multiple remote nodes. Thus, the central node and remote nodes may be configured to communicate data encrypted using quantum keys.

Systems and methods for estimating a property of an error in a circuit implemented on an n-qubit quantum system are provided, where the circuit comprises a gate set that comprises a first subset () and a second subset () of elementary gates. The first subset comprises a third subset () of elementary gates each of which consists of an n-fold tensor product of a plurality of single qubit gates. A first procedure is executed that comprises preparing the system in a state ψ and then applying D.sub.1=T.sub.1 to the system. The procedure further comprises, for each respective clock cycle t in clock cycles t∈{2, . . . , m+1}, (a) applying H to the system, where H is an elementary gate in the second subset, and then (b) applying a gate D.sub.t=T.sub.tGHT.sub.t−1.sup.†H.sup.† to the system, where D.sub.t is an element of the first subset. The procedure further comprises performing a measurement readout R. The procedure is repeated for one or more values of {right arrow over (T)} or one or more states ψ or one or more measurement readout procedures R, where m is a positive integer greater than 1, G is an element of the first subset of elementary gates, {right arrow over (T)}=(T.sub.1, . . . , T.sub.m, T.sub.m+1=I), and T.sub.1, . . . , T.sub.m are elements of , with the proviso that n>2.

Systems and methods for estimating a property of an error in a circuit implemented on an n-qubit quantum system are provided, where the circuit comprises a gate set that comprises a first subset () and a second subset () of elementary gates. The first subset comprises a third subset () of elementary gates each of which consists of an n-fold tensor product of a plurality of single qubit gates. A first procedure is executed that comprises preparing the system in a state ψ and then applying D.sub.1=T.sub.1 to the system. The procedure further comprises, for each respective clock cycle t in clock cycles t∈{2, . . . , m+1}, (a) applying H to the system, where H is an elementary gate in the second subset, and then (b) applying a gate D.sub.t=T.sub.tGHT.sub.t−1.sup.†H.sup.† to the system, where D.sub.t is an element of the first subset. The procedure further comprises performing a measurement readout R. The procedure is repeated for one or more values of {right arrow over (T)} or one or more states ψ or one or more measurement readout procedures R, where m is a positive integer greater than 1, G is an element of the first subset of elementary gates, {right arrow over (T)}=(T.sub.1, . . . , T.sub.m, T.sub.m+1=I), and T.sub.1, . . . , T.sub.m are elements of , with the proviso that n>2.