TECHNICAL FIELD

The disclosure relates to the field of Quantum Computing, and more specifically to the simulation of quantum circuits on classical computers. In particular, the disclosure relates to a device for a quantum circuit simulator, and a quantum circuit simulator including at least one such device. Further, the disclosure relates to a method for quantum gate and qubit scheduling for a quantum circuit simulator, wherein the method may be performed by the device.

BACKGROUND

A universal quantum circuit simulator stores a mathematical representation of the whole state of a simulated quantum computer in a memory. The size of this state scales as 2 ⁿ , with n being the number of simulated qubits of the quantum computer. For 40 qubits, the size of this state is 16TiB. This requires usage of a multi-node computing system, in order to distribute the large state across multiple memories of the nodes. During simulation of the quantum circuit, access to the parts of the state from the remote nodes is required.

In order to simulate quantum computations on a classical computer, one can use a linear algebraic representation of the quantum computation (quantum circuit). In this representation, the state of an «-qubit quantum circuit is a vector in a Hilbert space with the orthonormal basis The dimension of the space is equal to 2 ⁿ . According

to quantum computation theory, the following relations hold:

From the above relations, the straightforward way to represent the state of the quantum computer in a memory is to store 2 ⁿ complex numbers {a _i } , which are called amplitudes of corresponding basis states. The value | determines the probability to observe the basis state i as an output of the quantum circuit/computer.

The quantum computation may be expressed as a linear unitary operator U acting on the vector yielding the resulting state

Since the basis in the Hilbert space is defined, the operator U is represented by a matrix of dimensions 2 ⁿ x 2 ⁿ .

In quantum computation, a quantum gate is defined as the basic unitary operator, which acts on one or a few qubits. Practical quantum gates are of sizes 1-, 2- and 3-qubits. Using these quantum gates, any quantum algorithm can be expressed. According to the above equation (5), any quantum algorithm can be represented by a unitary matrix and a relation between a sequence of quantum gates and an operator U:

In other words, the quantum algorithm can be expressed as tensor product of quantum gates, each quantum gate acting on a subset of qubits.

A typical set of quantum gates, which are used in most common quantum algorithms, is show in FIG. 8. Therein, CNOT and CZ are examples of a special kind of quantum gates, which are called controlled gates. Such quantum gates act on 2 or more qubits, wherein one or more qubits act as a control for some operation. The qubit, upon which an operation is performed, is called target, and other qubits are called control.

Using a graphical representation, it is possible to draw a quantum circuit for a quantum algorithm - as exemplarily shown in FIG. 9. Numbered horizontal lines represent qubits, and quantum gates acting on qubits are placed on corresponding lines. The quantum gates are applied in order from left to right. From the properties of the tensor product according to the above relation (3), one can conclude that quantum gates acting on disjoint sets of qubits are commute. A set of quantum gates sharing the same horizontal position is called a layer of a quantum circuit.

As already noted above, the universal quantum circuit simulator stores, in a computer memory, an array of 2 ⁿ complex numbers (coefficients a _i from relation (1)). Using e.g. IEEE754 double precision floating point representation, this requires 16 · 2 ⁿ bytes of memory. One can easily see that the memory requirements very quickly become intractable for a single computer, when the number of qubits grows (e.g. 40 qubits require 16TiB of memory). The simulator program in this case has to split the state vector into parts and store in memory of several computers (nodes, as already described above).

Let the quantum simulator operate on n = L + R qubits. Then, if a single computer can store just 2 ⁱ elements of a state vector, the number of required computer nodes is 2 ^R .

A natural way to select a basis in the above relation (1) is to assign to a basis state the state, in which qubits are |0) or |1) according to a binary representation of index i. For example: for three qubits there are 8 basis states In

the basis state all qubits are in the state |0), in the qubit 1 in the state 11)

and two others in state 0, and in qubits 1 and 2 are in state 11) and qubit 0 in

state |0).

According to a state vector distribution scheme, it is obvious that every node stores all amplitudes, which determine the probability of 10) and 11) for first L qubits, when states of other R qubits are fixed equal to the binary representation of a node’s rank. In this document, the first L qubits are called local qubits and the last R qubits are called global qubits.

When a quantum gate is applied to one or more local qubits, the matrix-vector multiplication is performed on each node locally, and does not require access to amplitudes stored on remote nodes, because other qubits are not affected by the gate.

When a quantum gate is applied to one or more global qubits, the matrix-vector multiplication cannot be performed, because a computing node cannot directly access the memory in a remote computer. In this situation, a mechanism of data exchange is required. A conventional approach proposed a method of qubit reordering when qubits are renumbered and corresponding amplitudes are transferred between nodes and stored in a corresponding node’s memory according to new qubit numbers and the node’s ranks. This process is called qubits swapping, because qubits and amplitudes exchange their positions, and is illustrated in FIG. 1 1. This method can be used to simulate a quantum gate, which originally is applied to global qubits. In this case one needs just exchange numbers between global qubits involved in an operation and some unused local qubits, then transfer corresponding amplitudes between nodes. After that, the quantum gate acting on local qubits can be simulated. It is common for distributed computing to use an MPI library to perform a data exchange between nodes, and so express data exchange patterns in the program in terms of MPI operations. The qubit swapping operation can be done using a single MPI_Alltoall operation. Any number of qubits less than or equal to R can be swapped at once. It is easy to show that the amount of transferred amplitudes is equal to where k is the number of swapped global qubits. From the above relation (4), it is obvious that swapping several qubits at once requires less data to transfer than swapping them sequentially one by one.

However, a typical quantum circuit can contain hundreds of thousands of gates. Without any optimization technique, each gate implies a matrix-vector multiplication and in a distributed case, amplitudes must be transferred between nodes a huge number of times. Thus, in the above-described approach, without a careful definition of a set of qubits to swap, there could be an extra overhead for the data exchange if some qubits in a set are not involved into a sufficient number of gates applications. The approach does not provide any suggestions on how to determine optimal set of qubits to reorder. Another approachFehler! Textmarke nicht definiert. describes an open source implementation of a distributed quantum circuit simulator - QuEST. In QuEST, the above-described method of qubit reordering is used, but the implementation is restricted to single qubit swaps only.

The most sophisticated approach to quantum circuit simulation uses a scheduling component (scheduler), which determines the order of gates to be applied and qubits sets to reorder. Gates are reordered into sequences called stages. A stage contains gates acting on local qubits. Inside the stage gates form subsequences called clusters. Gates from the same cluster are fused into a single multi-qubit gate, and this gate is simulated by a single matrix-vector multiplication. Between stages, a qubit reordering occurs.

FIG. 12 shows an illustration of such clusters of gates and stages. Assuming that qubits 0-2 are local currently and 3-4 are global, the first stage consists of 2 clusters of gates outlined by grey lines, and the second stage consists of cluster outlined by black lines. After applying gates for the first stage qubits, reordering occurs: 3, 4 are swapped with 1, 2, and then second stage can be applied.

The main problem in implementing this approach is the methods of construction of clusters and stages. The approach does not describe any algorithm, and does also not provide the source code of the scheduler.

In summary, although a main set of methods for quantum circuit simulation is available, including scheduling of gates, gates clusters construction, and qubits reordering, the problem of finding an optimal order of gates and qubits remains unsolved. All previous approaches do not describe any method to calculate qubits and gates permutation according to a well-defined optimality criteria.

SUMMARY

In view of the above-mentioned problems and disadvantages, embodiments of the present invention aim to improve the current approaches. An objective is to provide a sophisticated method for gates and qubits permutation calculation for a quantum circuit simulator. This should result in an optimal data exchange and an optimal quantum gate application schedule in a quantum circuit simulator, and should accordingly reduce the amount of data transferred between nodes. The calculated permutations should provide a minimum number of matrix-vector multiplications and a minimum amount of data transfer. To this end, a device and method should be provided, which can be used in distributed quantum circuit simulator for gate scheduling and qubits reordering scheduling.

The objective is achieved by the embodiments of the invention as described in the enclosed independent claims. Advantageous implementations of the present invention are further defined in the dependent claims.

In particular, embodiments of the invention propose a device and method, which calculate an optimal data exchange and quantum gate application schedule, and thus significantly reduce the amount of data transferred between nodes, as well as the amount of arithmetical operations to be performed. All of this leads to an increase of quantum circuit simulator performance, particularly up to several times.

The embodiments of the invention base on the understanding that associativity of a tensor product operation allows splitting the relation (3) into factors in different ways, thus constructing factors according to performance of computation or memory consumption considerations:

The above relation (5), and commute properties of quantum gates been applied, lay the core of embodiments of the invention optimizing a quantum circuit simulation by means of gate sequence permutation.

Based on an individual gate’s properties, and using a greedy algorithm, the device and method calculate specifically a permutation of gates and a permutation of qubits, which lead to a minimum number of clusters in a stage, and minimum number of stages during a quantum circuit simulation.

A first aspect of the invention provides a device for a quantum circuit simulator, the device being configured to: obtain a first sequence of quantum gates, generate a second sequence of quantum gates, which is a subsequence of the first sequence of quantum gates, by using a greedy algorithm, in particular with backtracking, calculate a local qubits set and a global qubits set based on the second sequence of quantum gates, generate a set of clusters of quantum gates, wherein each cluster includes a subset of the quantum gates of the second sequence of quantum gates merged together by using a greedy algorithm, generate a third sequence of quantum gates, which contains all quantum gates from the second sequence of quantum gates, according to an order of the clusters, provide the local qubits set and the global qubits set to the quantum circuit simulator, and output the third sequence of quantum gates to the quantum circuit simulator.

The calculated sets of local and global qubits are in particular“best” local qubits and global qubits sets.“Best” thereby means the best the algorithm can do. That is, the algorithm searches for many variants of these qubits sets, and may then select qubits sets which have the maximum number of gates in the second sequence. Local qubits sets can be deliberately predefined before running the algorithm by the device of the first aspect. This implies that the algorithm will include quantum gates, which act on these qubits.

The device of the first aspect can be used in a distributed quantum circuit simulator, and may provide gate scheduling and qubits reordering. In other words, the device can provide a sophisticated gates and qubits permutation calculation for the quantum circuit simulator. The calculated permutations allow an optimal data exchange and quantum gate application schedule in a quantum circuit simulator, thus significantly reducing the amount of data transferred between nodes of the simulator. In an implementation form of the first aspect, the device is further configured to, when generating the set of clusters of quantum gates: order a cluster including more quantum gates before a cluster including less quantum gates in the order of the clusters.

In an implementation form of the first aspect, the device is further configured to, when generating the set of clusters of quantum gates: generate the clusters based on a maximum possible number of qubits in a cluster.

The above implementation forms lead to an improved efficiency of the algorithm performed by the device of the first aspect.

In an implementation form of the first aspect, the device is further configured to, when generating the set of clusters of quantum gates: pick one-by-one all possible combinations of qubits associated with the second sequence of quantum gates based on the maximum possible number of qubits in a cluster, construct a cluster for each combination, and select the cluster with the greatest number of quantum gates in it.

In an implementation form of the first aspect, the device is further configured to, when generating the set of clusters of quantum gates: maintain a set of locked qubits, include a quantum gate into a cluster, if matrix representation of the quantum gate is diagonal, skip a quantum gate, if at least one of the qubits that quantum gate acts on does not belong to a picked combination of qubits, and/or skip a quantum gate, if at least one of the qubits that quantum gate acts on is in the set of locked qubits, add all qubits a quantum gate acts on to the set of locked qubits, if that quantum gate is skipped, and include a quantum gate into a cluster otherwise.

In an implementation form of the first aspect, the device is further configured to, when generating the set of clusters of quantum gates: determine a cluster including a maximum number of quantum gates, output the quantum gates of the determined cluster, in particular insert the output quantum gates into the third sequence of quantum gates, and remove the output quantum gates from the second sequence of quantum gates. In an implementation form of the first aspect, the device is further configured to, when calculating the local qubits set and the global qubits set: determine the local qubits set and/or the global qubits set based on a maximum number of local and/or global qubits, respectively.

In an implementation form of the first aspect, the device is further configured to, when generating the second sequence of quantum gates: fuse a quantum gate acting on a single qubit with an adjacent quantum gate in the first sequence of quantum gates acting on a subset of qubits including the same single qubit.

In an implementation form of the first aspect, the device is further configured to, when generating the second sequence of quantum gates: include, into the second sequence of quantum gates, quantum gates that operate on at most the maximum number of local qubits, and if the first sequence of quantum gates includes at least one quantum gate acting on a single qubit and another quantum gate acting on the same qubit and on at least one other qubit, include, into the second sequence of quantum gates, this singlequbit gate together with the other multi-qubit gate.

In an implementation form of the first aspect, the device is further configured to, when generating the second sequence of quantum gates: create a branch of the greedy algorithm with a quantum gate included into the second sequence of quantum gates, and or create a branch of the greedy algorithm with a quantum gate from the first sequence of quantum gates skipped, add all qubits a quantum gate acts on to the set of local qubits, if that quantum gate is included or, add all qubits a quantum gate acts on to the set of locked qubits, if that quantum gate is skipped.

In an implementation form of the first aspect, the device is further configured to, when generating the second sequence of quantum gates: create at most a maximum number of branches of the greedy algorithm.

In an implementation form of the first aspect, the device is further configured to, when applying a branch of the greedy algorithm: construct the second sequence of quantum gates with as much gates as possible, and test each gate from the first sequence of quantum gates and skip or include it into the second sequence of quantum gates based on the result of the test.

In an implementation form of the first aspect, the device is further configured to, when generating the second sequence of quantum gates: maintain a set of locked qubits, skip a quantum gate, if application of this quantum gate will require more qubits than a predetermined threshold to be local, and/or skip a quantum gate, if at least one of the qubits the quantum gate operates on is in a locked qubits set, and add all qubits a quantum gate acts on to the set of locked qubits, if that quantum gate is skipped.

In an implementation form of the first aspect, the device is further configured to, when generating the second sequence of quantum gates: include a quantum gate into the second sequence of quantum gates, if a matrix representation of that quantum gate is diagonal and do not add qubits a quantum gate acts on to the set of local qubits, and/or include a quantum gate into the second sequence of quantum gates, if all qubits that quantum gate operates on are already in the local qubits set.

In an implementation form of the first aspect, the device is further configured to, when calculating the local qubits set and the global qubits set: construct a set of all qubits, on which quantum gates from the first sequence of quantum gates act, include, in the local qubits set, all qubits on which quantum gates from the second sequence of quantum gates act, and include, in the global qubits set, all qubits which are in the set of all qubits and not in the local qubits set.

A second aspect of the invention provides a quantum circuit simulator comprising the device according to the first aspect or any of its implementation forms.

A third aspect of the invention provides a method for quantum gate and qubit scheduling for a quantum circuit simulator, the method comprising: obtaining a first sequence of quantum gates, generating a second sequence of quantum gates, which is a subsequence of the first sequence of quantum gates, by using a greedy algorithm, in particular with backtracking, calculating a local qubits set and a global qubits set based on the second sequence of quantum gates, generating a set of clusters of quantum gates, wherein each cluster includes a subset of the quantum gates of the second sequence of quantum gates merged together by using a greedy algorithm, generating a third sequence of quantum gates, which contains all quantum gates from the second sequence of quantum gates, according to an order of the clusters, providing the local qubits set and the global qubits sets to the quantum circuit simulator, and outputting the third sequence of quantum gates to the quantum circuit simulator.

A fourth aspect of the invention provides a computer program product comprising a program code for controlling the device according to the first aspect or any of its implementation forms, or for carrying out, when implemented on a processor, the method according to the third aspect or any of its implementation forms.

In an implementation form of the fourth aspect, the method further comprises, when generating the set of clusters of quantum gates: ordering a cluster including more quantum gates before a cluster including less quantum gates in the order of the clusters.

In an implementation form of the fourth aspect, the method further comprises, when generating the set of clusters of quantum gates: generating the clusters based on a maximum possible number of qubits in a cluster.

In an implementation form of the fourth aspect, the method further comprises, when generating the set of clusters of quantum gates: picking one-by-one all possible combinations of qubits associated with the second sequence of quantum gates based on the maximum possible number of qubits in a cluster, constructing a cluster for each combination, and selecting the cluster with the greatest number of quantum gates in it.

In an implementation form of the fourth aspect, the method further comprises, when generating the set of clusters of quantum gates: maintaining a set of locked qubits, include a quantum gate into a cluster, if matrix representation of the quantum gate is diagonal, skipping a quantum gate, if at least one of the qubits that quantum gate acts on does not belong to a picked combination of qubits, and/or skipping a quantum gate, if at least one of the qubits that quantum gate acts on is in the set of locked qubits, adding all qubits a quantum gate acts on to the set of locked qubits, if that quantum gate is skipped, and including a quantum gate into a cluster otherwise.

In an implementation form of the fourth aspect, the method further comprises, when generating the set of clusters of quantum gates: determining a cluster including a maximum number of quantum gates, outputting the quantum gates of the determined cluster, in particular inserting the output quantum gates into the third sequence of quantum gates, and removing the output quantum gates from the second sequence of quantum gates.

In an implementation form of the fourth aspect, the method further comprises, when calculating the local qubits set and the global qubits set: determining the local qubits set and/or the global qubits set based on a maximum number of local and/or global qubits, respectively.

In an implementation form of the fourth aspect, the method further comprises, when generating the second sequence of quantum gates: fusing a quantum gate acting on a single qubit with an adjacent quantum gate in the first sequence of quantum gates acting on a subset of qubits including the same single qubit.

In an implementation form of the fourth aspect, the method further comprises, when generating the second sequence of quantum gates: including, into the second sequence of quantum gates, quantum gates that operate on at most the maximum number of local qubits, and if the first sequence of quantum gates includes at least one quantum gate acting on a single qubit and another quantum gate acting on the same qubit and on at least one other qubit, including, into the second sequence of quantum gates, this singlequbit gate together with the other multi-qubit gate.

In an implementation form of the fourth aspect, the method further comprises, when generating the second sequence of quantum gates: creating a branch of the greedy algorithm with a quantum gate included into the second sequence of quantum gates, and/or creating a branch of the greedy algorithm with a quantum gate from the first sequence of quantum gates skipped, adding all qubits a quantum gate acts on to the set of local qubits, if that quantum gate is included or, adding all qubits a quantum gate acts on to the set of locked qubits, if that quantum gate is skipped.

In an implementation form of the fourth aspect, the method further comprises, when generating the second sequence of quantum gates: creating at most a maximum number of branches of the greedy algorithm.

In an implementation form of the fourth aspect, the method further comprises, when applying a branch of the greedy algorithm: constructing the second sequence of quantum gates with as much gates as possible, and testing each gate from the first sequence of quantum gates and skip or include it into the second sequence of quantum gates based on the result of the test.

In an implementation form of the fourth aspect, the method further comprises, when generating the second sequence of quantum gates: maintaining a set of locked qubits, skipping a quantum gate, if application of this quantum gate will require more qubits than a predetermined threshold to be local, and/or skipping a quantum gate, if at least one of the qubits the quantum gate operates on is in a locked qubits set, and adding all qubits a quantum gate acts on to the set of locked qubits, if that quantum gate is skipped.

In an implementation form of the fourth aspect, the method further comprises, when generating the second sequence of quantum gates: including a quantum gate into the second sequence of quantum gates, if a matrix representation of that quantum gate is diagonal and not adding qubits a quantum gate acts on to the set of local qubits, and/or include a quantum gate into the second sequence of quantum gates, if all qubits that quantum gate operates on are already in the local qubits set.

In an implementation form of the fourth aspect, the method further comprises, when calculating the local qubits set and the global qubits set: constructing a set of all qubits, on which quantum gates from the first sequence of quantum gates act, including, in the local qubits set, all qubits on which quantum gates from the second sequence of quantum gates act, and including, in the global qubits set, all qubits which are in the set of all qubits and not in the local qubits set. It has to be noted that all devices, elements, units and means described in the present application could be implemented in the software or hardware elements or any kind of combination thereof. All steps which are performed by the various entities described in the present application as well as the functionalities described to be performed by the various entities are intended to mean that the respective entity is adapted to or configured to perform the respective steps and functionalities. Even if, in the following description of specific embodiments, a specific functionality or step to be performed by external entities is not reflected in the description of a specific detailed element of that entity which performs that specific step or functionality, it should be clear for a skilled person that these methods and functionalities can be implemented in respective software or hardware elements, or any kind of combination thereof.

BRIEF DESCRIPTION OF THE DRAWINGS The above described aspects and implementation forms of the present invention will be explained in the following description of specific embodiments in relation to the enclosed drawings, in which

FIG. 1 shows a device for a quantum circuit simulator according to an embodiment of the invention.

FIG. 2 shows a pseudocode of a cluster scheduling method performed by a device for a quantum circuit simulator according to an embodiment of the invention.

FIG. 3 shows a block scheme of a cluster scheduling method performed by a device for a quantum circuit simulator according to an embodiment of the invention. FIG. 4 shows a pseudocode of a stage scheduling method performed by a device for a quantum circuit simulator according to an embodiment of the invention. FIG. 5 shows a block scheme of a stage scheduling method performed by a device for a quantum circuit simulator according to an embodiment of the invention. FIG. 6 shows, in (a), scheduler results on different supremacy circuits, and shows, in (b), results of a 30-layers supremacy circuit simulation by a quantum circuit simulator according to an embodiment of the invention compared to a QuEST simulator on 8-nodes cluster. FIG. 7 shows a method for quantum gate and qubit scheduling for a quantum circuit simulator according to an embodiment of the invention.

FIG. 8 shows typical quantum gates and their quantum circuit representation. FIG. 9 shows a graphical representation of a quantum circuit for a quantum algorithm.

FIG. 10 shows a scheme of state vector distribution. FIG. 11 illustrates qubit swapping.

FIG. 12 illustrates clusters of gates and stages.

DETAILED DESCRIPTION OF THE EMBODIMENTS

FIG. 1 shows a device 100 according to an embodiment of the invention. The device 100 is suitable for a quantum circuit simulator 110. The device 100 may be part of the quantum circuit simulator 110, or may be connected to the quantum circuit simulator 110. The device 100 is in particular configured to schedule quantum gates and qubits for the quantum circuit simulator 1 10, in order to improve the performance of the quantum circuit simulator. The quantum circuit simulator 1 10 may be one or more classical computers or computer nodes, which are together configured to simulate the execution of a quantum circuit on a quantum computer. The quantum circuit simulator 110 may include at least one device 100, or may work together with at least one device

100.

The device 100 is configured to obtain a first sequence 101 of quantum gates, e.g. according to a quantum circuit received as an input to the device 100. The quantum circuit may be a quantum circuit to be simulated on/by the quantum circuit simulator 110. The device 100 is further configured to generate a second sequence 102 of quantum gates, which is a subsequence of the first sequence 101 of quantum gates. The device 100 thereby uses a greedy algorithm, in particular with backtracking. That is, the second sequence of quantum gates 102 is generated based on the first sequence 101 of quantum gates using a greedy algorithm with backtracking.

Further, the device 100 is configured to calculate a local qubits set 103 a and a global qubits set 103b, respectively, based on the generated second sequence 102 of quantum gates. These qubits sets may be referred to as optimal or final qubits sets. In addition, the device 100 is also adapted to generate a set of clusters 104 of quantum gates, wherein each cluster 104 includes a subset of the quantum gates of the second sequence 102 of quantum gates, which are merged together by using a greedy algorithm. The greedy algorithm may be similar in nature to the greedy algorithm used for generating the second sequence 102. Then, the device 100 is configured to generate a third sequence 105 of quantum gates, which contains all quantum gates from the second sequence 102 of quantum gates, according to an order of the clusters 104 of quantum gates.

Finally, the device 100 is configured to provide the local qubits set 103a and the global qubits set 103b to the quantum circuit simulator 110, and to also output the third sequence 105 of quantum gates to the quantum circuit simulator. Based on these inputs, the quantum circuit simulator 110 can simulate the quantum circuit with less data required to be transferred between multiple nodes of the simulator 110, as well as with less arithmetical operations performed.

Notably, in the device 100 of FIG. 1 , the generating of the clusters 104 of quantum gates and the generation of the third sequence 105 of quantum gates may be referred to as cluster scheduling algorithm. This algorithm allows the device 100 to perform the quantum gate scheduling for the simulator 1 10. The calculation and outputting of the qubits sets 103a and 103b may be referred to as a stage scheduling algorithm. This algorithm allows the device 100 to perform qubit scheduling for the simulator 110.

FIG. 2 shows a pseudocode of a cluster scheduling algorithm that can be performed by the device 100 according to an embodiment of the invention, in particular by the device 100 of FIG. 1, in order to generate the sets of clusters 104 and output the third sequence 105 of quantum gates. FIG. 3 further shows a block scheme of the cluster scheduling algorithm.

The cluster scheduling algorithm has two parameters:“qubits”, i.e. the set of all qubits involved in an input sequence of quantum gates; and k, which is the maximum possible number of qubits in a cluster 104. The algorithm further takes a sequence of quantum gates as an input (i.e. in particular the second sequence 102 of quantum gates).

The algorithm further merges quantum gates into clusters 104 of quantum gates. It thereby tries to minimize a total number of clusters 104 generated. Further, the algorithm uses a greedy approach, which: a) finds a cluster 104 with a maximum number of quantum gates included; b) returns the cluster 104 as a result; and removes the cluster’s 104 quantum gates from the input sequence of quantum gates; and c) proceeds again with a).

At step 0, the algorithm may pick all possible combinations of k qubits one by one, may generate a sequence of quantum gates containing only qubits from this combination that could be merged in one cluster 104, and may pick the largest size list as next cluster 104.

The device 100 can further perform an immediate fusing of single-qubit quantum gates. A single-qubit quantum gate g acting on a qubit q does not change the total number of stages, if there exists at least one multi-qubit gate acting on qubit q. Thus, this quantum gate g can be immediately fused (merged) to/with any of its neighboring quantum gates containing the qubit q. This optimization is beneficial for significantly speeding up a stage scheduling algorithm, which can be performed by the device 100 and is described next. FIG. 4 shows a pseudocode of a stage scheduling algorithm that can be performed by the device 100 according to an embodiment of the invention, in particular by the device 100 of FIG. 1, in order to schedule and output qubits. FIG. 5 shows a block scheme of the stage scheduling algorithm.

The stage scheduling algorithm has two parameters: L _max , which is the maximum number of local qubits; and B _max , which is a maximum number of branches to create. The algorithm takes a list of quantum gates as input. The algorithm returns a set 103a of qubits, which have to be local during current stage. The algorithm thereby tries to minimize the total number of stages. The algorithm, in particular, uses a greedy approach, i.e. it constructs the stage, which contains as much quantum gates as possible.

The algorithm may also backtrack on a sequence of quantum gates and may maintain: a) locals, i.e. a set of qubits wanted to be local during the stage; b) locked, i.e. a set of locked qubits (qubits with some operation skipped); c) B, i.e. a maximum possible number of new branches in this branch of backtracking; and d) N, i.e. a number of taken quantum gates in this stage.

The process of the algorithm may be specifically according to the following case analysis:

• If at least one of gate qubits or gate control qubits is locked, a quantum gate has to be skipped.

• Else, if a gate matrix is diagonal, it could be applied to local and global qubits as well, without adding any requirements to the qubits.

• Else, if an application of this quantum gate will require too many qubits to be local, the gate is skipped.

• Else, if all gate qubits are already required to be local, a quantum gate could be applied as well without adding any requirements.

• Else, if applying/skipping a gate cannot be uniquely determined, the algorithm branches on two: one branch with this gate skipped; and another branch with this gate applied.

When the algorithm skips a gate, all its qubits may become locked. When the algorithm decides to apply a non-diagonal gate, all its qubits may be required to be local. If all qubits become locked during the backtracking, the algorithm may return to the previous level of recursion.

Some of the qubits could be kept local deliberately, e.g. by prepopulating locals set of qubits before starting the algorithm. This can allow other optimizations to be performed in the simulator 110, due to regulation of memory placement layout of amplitudes to be swapped.

FIG. 6 shows, in (a), results of the method performed by the device 100. The device 100 has been tested with 3 global qubits and a different numbers of total qubits. According to resulting permutation between stages, a swap of all global qubits with the same number of local qubits has been applied.

A quantum circuit simulator 110 according to an embodiment of the invention, i.e. including a device 100 as shown in FIG. 1, is compared with the QuEST simulator, in particular with a QuEST simulator on an 8-nodes cluster, in (b) of FIG. 6. The simulator 110 according to an embodiment of the invention demonstrates an order of magnitude better performance, due to a reduction of the number of matrix-vector multiplications. This is, because of the cluster stage algorithm/method performed by device 100, and the reduction of the amount of data transfer due to stage scheduling algorithm/method.

FIG. 7 shows a method 700 according to an embodiment of the invention. The method 700 is for quantum gate and qubit scheduling for a quantum circuit simulator 110. The method 700 may be performed by the device 100 of FIG. 1, or by a quantum circuit simulator 110 including such a device 100.

The method comprises: a step 701 of obtaining a first sequence 101 of quantum gates; a step 702 of generating a second sequence 102 of quantum gates, which is a subsequence of the first sequence 101 of quantum gates, by using a greedy algorithm, in particular with backtracking; a step 703 of calculating a local qubits set 103a and a global qubits set 103b based on the second sequence 102 of quantum gates; a step 704 of generating a set of clusters 104 of quantum gates, wherein each cluster 104 includes a subset of the quantum gates of the second sequence 102 of quantum gates merged together by using a greedy algorithm; a step 705 of generating a third sequence 105 of quantum gates, which contains all quantum gates from the second sequence 102 of quantum gates, according to an order of the clusters 104; a step 706 of providing the local qubits set 103a and the global qubits set 103b to the quantum circuit simulator 1 10; and a step 707 of outputting the third sequence 105 of quantum gates to the quantum circuit simulator 110.

The present invention has been described in conjunction with various embodiments as examples as well as implementations. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed invention, from the studies of the drawings, this disclosure and the independent claims. In the claims as well as in the description the word“comprising” does not exclude other elements or steps and the indefinite article“a” or“an” does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation.